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A car is being driven, in a straight line and at a uniform speed, towards the base of a vertical tower. The top of the tower is observed from the car and, in the process, it takes 10 minutes for the angle of elevation to change from 45° to 60°. After how much more time will this car reach the base of the tower? options: (A)5(√3 + 1), (B)6(√3 + √2), (C)7(√3 – 1), (D)8(√3 – 2), (E)None of these | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation:
Let the height of the building be h. Initially, he was at an angle of 450. tan 45 = h/distance between car and tower. h = distance between car and tower (since tan 45 = 1).
Now, after 10 minutes, it travelled a certain distance, and angle changed to 600.
tan 60 = h/x x = h/√3
So, in 10 minutes, it has travelled a distance of h – x = h - h/√3.
10 minutes = h *( 1 – 1√3)
h can be travelled in 10 / (1 – 1√3).
To travel a distance of x, which is h/√3, it takes :
h = 10 / (1 – 1/√3)
h / √3 = 10/ √3 * (1 – 1/√3). Multiply numerator and denominator by 1 + √3 ( conjugate of 1 - √3). We get, x = h/√3 = 10 (1 + √3) / 2 = 5* (1 + √3)
So, it takes 5(1 + √3) minutes to reach the base of the tower.
Answer : A |
The original price of an item is discounted 22%. A customer buys the item at this discounted price using a $20-off coupon. There is no tax on the item, and this was the only item the customer bought. If the customer paid $1.90 more than half the original price of the item, what was the original price of the item? options: (A)$61, (B)$65, (C)$67.40, (D)$70, (E)$78.20 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | E, Explanation: Let x be the original price of the item
Discounted price = 0.78x
Payment made by the customer after using the $20 coupon = 0.78x - 20
0.78x - 20 = x/2 + 1.9
x = 78.20
Answer: E |
Find out which of the following values is the multiple of X, if it is divisible by 9 and 12? options: (A)36, (B)15, (C)17, (D)5, (E)7 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: 9=3*3
12=3*4
The number should definitely have these factors 3*3*4
36 is the number that has these factors
So, 36 is the multiple of X
Answer is A |
If the probability that Stock A will increase in value during the next month is 0.56, and the probability that Stock B will increase in value during the next month is 0.74. What is the greatest value for the probability that neither of these two events will occur? options: (A)0.22, (B)0.26, (C)0.37, (D)0.46, (E)0.63 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | B, Explanation: The probability that stock A does not increase is 0.44, and the probability that stock B does not increase is 0.26. Now, how can the probability that both do not increase be more than individual probability of not increasing for each? So the probability that both do not increase can not be more than 0.26. Basically the probability that both do not increase is between 0 and 0.26. |
A trader sold an article at a profit of 20% for Rs.360. What is the cost price of the article? options: (A)270, (B)300, (C)280, (D)320, (E)315 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | B, Explanation: Cost Price = Selling Price / (100+Profit%) × 100 => 360 / (100+20) × 100 => 360 / 120 × 100 = Rs.300
Option B |
20 marbles were pulled out of a bag of only white marbles, painted black, and then put back in. Then, another 20 marbles were pulled out, of which 1 was black, after which they were all returned to the bag. If the percentage of black marbles pulled out the second time represents their percentage in the bag, how many marbles in total Q does the bag currently hold? options: (A)40, (B)200, (C)380, (D)400, (E)3200 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | D, Explanation: We know that there are 20 black marbles in the bag and this number represent 1/20 th of the number of all marbles in the bag, thus there are total Q of 20*20=400 marbles.
Answer: D. |
Find the total no. of distinct bike no.'s that can beformed using 2 letters followed by 2 no.'s. How many letters need to be distinct? options: (A)74453, (B)64543, (C)74325, (D)65000, (E)97656 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | D, Explanation: Out of 26 alphabets two distinct letters can be chosen in 26P2 ways. Coming to the numbers part, there are 10 ways to choose the first digit and similarly, there are another 10 ways to choose the second digit. Hence, there are in total 10X10 = 100 ways.
Combined with letters there are 6P2 X 100 ways = 65000 ways to choose vehicle numbers.
D |
A train running at a speed of 100 miles/hour, takes 10 hours to reach its destination. After covering quarter of the distance, it starts raining and the train has to be slowed to speed of 75 miles/hour. What is the total journey duration? options: (A)10, (B)11.5, (C)12.5, (D)13.5, (E)15 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | C, Explanation: Distance to destination = 100 X 10 = 1000 miles.
Distance remaining when it starts to rain = 1000 - 250 = 750 miles.
Speed for remaining distance = 75 miles / hour.
Time taken to cover remaining distance = 750 / 75 = 10 hours.
Total duration of the journey = 2.5 + 10 = 12.5 hours.
The correct option is C. |
Of the 200 students in a school, at least 45% attended the prom night and at least 35% took part in the debating session. What is the maximum number of students who could have neither attended the prom night nor the debating session? options: (A)27, (B)81, (C)90, (D)99, (E)110 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | E, Explanation: To maximize the number of students who did neither, we should minimize the number of students who debated or attended the prom.
Let's assume that all 35% of students who debated also attended the prom.
Then 35% did both, 10% only attended prom, and 55% did neither.
0.55*200 = 110
The answer is E. |
A sales person gets a 10% commission on each sale he makes. How many sales of $250 each must he make in order to reach a salary of at least $1000? options: (A)15, (B)24, (C)25, (D)40, (E)52 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | D, Explanation: 10% of 250 = 25.
Total salary required = 1000
Earning from single sale = 25
# of sales = 1000/25 =40
So 40 sales
D is the correct choice |
A company produces 420 units of a particular computer component every month, at a production cost to the company of $110 per component, and sells all of the components by the end of each month. What is the minimum selling price per component that will guarantee that the yearly profit (revenue from sales minus production costs) will be at least $626,400 ? options: (A)226, (B)230, (C)240, (D)260, (E)280 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | B, Explanation: 450*12(x-110)=626400
where x is a selling cost of one item
x-110, is a profit from one item
450 - number of items produced and sold per month
12 - is a number of month in a year
Simplifying the equation will lead to x-110=116, then x = 230
B |
At a certain factory, 10 percent of the staplers produced on Monday were defective and 2 percent of the non-defective staplers were rejected by mistake. If 72 of the non-defective staplers were rejected, what was the number of staplers produced that day? options: (A)4,000, (B)4,200, (C)4,500, (D)4,800, (E)5,000 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: We're told that 10% of staplers in a factory are defective.
X = Total staplers
0.1X = defective staplers
0.9X = normal staplers
Next, we're told that 2% of the normal staplers were rejected by mistake and that this = 72 staplers.
0.9X(0.02) = 72
0.018X = 72
18X = 72,000
X = 4,000
Final Answer:
A |
Machine A puts out a yo-yo every 6 minutes. Machine B puts out a yo-yo every 9 minutes. After how many minutes will they have produced 10 yo-yos? options: (A)24 minutes, (B)32 minutes, (C)36 minutes, (D)64 minutes, (E)72 minutes | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | C, Explanation: A's speed = 3 yo-yos every 18 minutes
B's speed = 2 yo-yos every 18 minutes
A + B's speed = 3 + 2 = 5 yo-yos every 18 minutes
both together will finish 10 yo-yos in 36 minutes
correct option is C |
Add: +45 and -30 options: (A)-30, (B)+30, (C)0, (D)15, (E)-15 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | D, Explanation: 45 - 30 = 15
ANSWER : D |
In how many ways can the letters of the word "PROBLEC" be rearranged to make 7 letter words such that none of the letters repeat? options: (A)2!, (B)3!, (C)7!, (D)8!, (E)9! | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | C, Explanation: There are seven positions to be filled.
The first position can be filled using any of the 7 letters contained in PROBLEM.
The second position can be filled by the remaining 6 letters as the letters should not repeat.
The third position can be filled by the remaining 5 letters only and so on.
758
Therefore, the total number of ways of rearranging the 7 letter word = 7*6*5*4*3*2*1 = 7! Ways.
C |
Let A and B be independent events with P (A) = 0.2 and P(B) = 0.8. Find P(A/B)? options: (A)0.2, (B)0.4, (C)0.6, (D)1.2, (E)1.5 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: P(A/B) = P (A n B)/P(B)
Here, P (A n B) = 0.16
P(A/B) = 0.16/0.8 = 0.2
A |
Consider there is an staircase elevator and you are coming down. If you walk 20 steps and stop, then you reach bottom in 10 minutes. If you walk 10 steps and stop, you reach to the ground in 20 minutes. What is the speed of the elevator? options: (A)1 step/minute, (B)2 step/minute, (C)3 step/minute, (D)4 step/minute, (E)None of the above | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: Let total number of steps in the elevator be n and let the speed be e
Elevator covered n-20 steps in 10 mins
(n-20)/e=10.................1
Elevator covered n-10 steps in 20 mins
(n-10)/e=20......................2
From (1) and (2)
n=30
e=1 step/min
Hence (A) is correct answer. |
Last year, a Home Appliance Store sold an average(arithmetic mean) of 42 microwave ovens per month. In the first 10 months of this year,the store has sold an average(arithmetic mean) of only 20 microwave ovens per month. What was the average number of microwave ovens sold per month during the entire 22 months period ? options: (A)21, (B)30, (C)31, (D)32, (E)None of the above | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | D, Explanation: 42×12+20×10 /12+10=504+200/22=704/22=32
Answer D |
An exam is given in a certain class. The average (arithmetic mean) of the highest score and the lowest score is equal to x. If the average score for the entire class is equal to y and there are z students in the class, where z > 5, then in terms of x, y, and z, what is the average score for the class excluding the highest and lowest scorers? options: (A)(zy – 2x)/z, (B)(zy – 2)/z, (C)(zx – y)/(z – 2), (D)(zy – 2x)/(z -2), (E)(zy – x)/(z + 2) | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | D, Explanation: Highest: H
Lowest: L
Number of students in the class: Z
Number of students in the class excluding the highest and lowest : Z-2
Average of Highest and Lowest: (H + L)/2=X => H+L=2X
Average of Entire Class : (H+L+Others)/Z=Y => Others= ZY-2X
Average of the others in the class: (ZY-2X)/(Z-2)
Answer: D |
[5 + ? × 19 - 15 - 7]/[13 × 13 - 156] = 6 options: (A)4, (B)4.5, (C)5, (D)5.5, (E)6.5 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | C, Explanation: (? × 19 - 17)/(169 - 156) = 6
=> ? × 19 - 17 = 13 × 6 = 76
=> ? × 19 = 78 + 17 = 95
? = 95/19 = 5
Answer: Option C |
A grocer makes a 25% profit on the selling price for each bag of flour it sells. If he sells each bag for $100 and makes $3,000 in profit, how many bags did he sell? options: (A)12, (B)16, (C)24, (D)30, (E)40 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | C, Explanation: Profit on one bag: 100*1.25= 125
Number of bags sold = 3000/125 = 24
Answer is C. |
Alex and Jacob works at a toy shop that make toys. Alex takes 7 hours to make a toy, and Jacob takes 9 hours to make a toy. During a month, both of them makes 35 toys in total. If both of them have worked for almost similar number of hours how many toys have been prepared by Jacob? options: (A)15, (B)16, (C)17, (D)18, (E)19 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: Lets say Alex has worked for x hrs., and Jacob has worked for y hrs. So, number of toys prepared by Alex is x/7, and Jacob is y/9. Since total number of toys prepared by both of them is 35.
=> x/7 + y/9 = 35.
=> 9x + 7y = (35)(63)
=> 7y = (35)(63) - 9x
=> y = (5)(63) - (9/7)x
=> y = 315 - (9/7)x
=> x is to be a multiple of 7. Also, we need to minimize the difference between x & y. Here are some possible values,
x = 126, y = 315 - (9/7)126 = 153
x = 133, y = 315 - (9/7)133 = 144
x = 140, y = 315 - (9/7)140 = 135
x = 147, y = 315 - (9/7)147 = 126
As we can see minimum difference between x and y is when x is 140 hrs. and y is 135 hrs. Thus total toys created by Jacob = y/9 = 135/9 = 15.
Answer: A |
John likes to have lightly flavored tea every evening. In a 50% strong milk tea, he replaces 15% of it with milk twice. Then, he replaces 10 percent of the resultant solution with more milk.
What is the final concentration of tea John drinks? options: (A)15.38%, (B)42%, (C)39.86%, (D)22.35%, (E)32.51% | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | E, Explanation: Imagine starting out with 100 ml of 50% milk tea.
In step 1, 15% of the tea is replaced with milk. Thus, 85% of the original tea remains. Since this is done twice, we have a concentration of 50x0.85x0.85% (=36.125%) of tea solution.
Finally, 10% of this solution is replaced with milk again. So, the final concentration of tea is 36.125*0.9%
This equals 32.51% of tea solution.
Answer: E |
In a class 1/16 of the students study math, 1/10 of the students study bio, 1/8 of the students study english. The total number of students is a 4 digit number. Find the diffrence between maximum number of students and minimum number of students. options: (A)8880, (B)8870, (C)8890, (D)7890, (E)6780 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: LCM of 16,10,8 = 80
the largest 4 digit number divisible by 80 = 9920
The smallest 4 digit number divisible by 80 = 1040
So, required difference = 9920-1040= 8880
ANSWER:A |
On a normal day Bill usually averages about 15 mph when riding his bicycle. On a windy day, his speed is reduced by 4 mph. How far can Bill travel on a windy day in 21 minutes? Round to the nearest hundredth. options: (A)2 miles, (B)2.25 miles, (C)3.25 miles, (D)3.85 miles, (E)2.85 miles | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | D, Explanation: 15 mph - 4 mph= 11 mph
11 mph x (21/60)= 3.85 miles
Answer D |
A retailer sold an appliance for 40 percent above cost, which represented a gross profit of $20.00. For what price did the retailer sell the appliance? options: (A)$27.30, (B)$51.00, (C)$63.00, (D)$70.00, (E)$91.00 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | D, Explanation: Let the cost be A. Then the selling price is A+0.4*A.
So the profit is 0.4 * A.
0.4*A=20 ---> A=50.
So the selling price is 50+20=70.
The answer is (D). |
At 6% per annum simple interest, Rahul borrowed Rs. 500. What amount will he pay to clear the debt after 4 years options: (A)750, (B)700, (C)620, (D)600, (E)None of these | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | C, Explanation: We need to calculate the total amount to be paid by him after 4 years, so it will be Principal + simple interest.
So,
=>500+500∗6∗4 /100=>Rs.620
Option C |
A computer routine was developed to generate two numbers (x,y) the first being a random number between 0 and 100 inclusive, and the second being less than or equal to the square root of the first. Each of the following pair satisfies the routine except options: (A)(99,10), (B)(85,9), (C)(50,7), (D)(1,1), (E)(1,0) | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: 99 is generated
We don't know what the square root of 99 is because we would need a calculator, but we know the square root of 100 is 10, so the square root of 99 has to be less than 10.
ANSWER:A |
A jeep travels a certain distance taking 6 hours in the forward journey. During the return journey, it increased its speed by 12km/hr and took 4 hours. What is the distance travelled by the jeep? options: (A)126km, (B)144km, (C)127km, (D)228km, (E)128km | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | B, Explanation: Let 'x' be the distance and 'y' be the speed of the forward journey. Then, we have 6v=d and 4(v+12)=d
=> v=d/6 and v=d/4 - 12
=> d/6 = d/4 - 12
=> d/12 = 12
=> d=144
Answer: B |
When I was 2 years old, my brother was half my age. Now I am 60 years old, how old is my brother? options: (A)A)59, (B)B)69, (C)C)79, (D)D)89, (E)E)99 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: Half of 2 is 1. =>2+58=60-> 1+58=59
Answer A |
The original retail price of an appliance was 60 percent more than its wholesale cost. If the appliance was actually sold for 20 percent less than the original retail price, then it was sold for what percent more than its wholesale cost? options: (A)20%, (B)28%, (C)36%, (D)40%, (E)42% | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | B, Explanation: wholesale cost = 100;
original price = 100*1.6 = 160;
actual price = 160*0.8 = 128.
Answer: B. |
On a map, the length of the road from Town F to Town G is measured to be 20 inches. On this map, 1/4 inch represents an actual distance of 10 miles. What is the actual distance, in miles, from Town F to Town G along this road? options: (A)800, (B)720, (C)960, (D)1140, (E)1160 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: Here we are given a ratio: 1/4 inch on the map = 10 miles, so 1 inch on the map = 40 miles. If the map-distance between the towns is 20 inches, then the actual distance must be 20 x 40 = 800
Answer: A. |
When folded into two equal halves a rectangular sheet had a perimeter of 48cm for each part folded along one set of sides and the same is 66cm when folded along the other set of sides. Find the area of the sheet. options: (A)1584, (B)1120, (C)792, (D)1320, (E)1200 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | B, Explanation: Let the sheet be folded along its breadth and its perimeter = 48cm
Therefore, (l/2 + b) = 48 ... (i)
Now, let the sheet be folded along its length, and the perimeter = 66cm
(l + b/2)= 66 …... (ii)
Solving (i) and (ii), we get,
l = 56cm, b = 20cm
Area = l*b
Area = 1120 cm2
ANSWER IS B |
Suppose you can travel from a place M to a place N by 3 buses, from place N to place O by 4 buses, from place O to place P by 1 buses and from place P to place Q by 3 buses. In how many ways can you travel from M to Q ? options: (A)24, (B)36, (C)72, (D)84, (E)None | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | B, Explanation: The bus from M to N can be selected in 3 ways. The bus from N to O can be selected in 4 ways. The bus from O to P can be selected in 1 way. The bus from P to Q can be selected in 3 ways. So, by the General Counting Principle, one can travel from M to Q in 3*4*1*3= 36 ways
Answer B |
A rectangular solid, 3 x 4 x 15, is inscribed in a sphere, so that all eight of its vertices are on the sphere. What is the diameter of the sphere? options: (A) 13.3542, (B) 15.8113, (C) 18.3451, (D) 19.5667, (E) 20.8888 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | B, Explanation: In an inscribed rectangle in a sphere, we will have a line joining the opposite vertices as the diameter.
According to the Pythagoras theorem, sides 3, 4 give diagonal as 5 ==> with 5 and 15, we get 5sqrt(10).
5sqrt(10) or 15.8113 is the diameter of the sphere.
answer = B |
A starts travel towards south 3km, then travel 5 km towards east, and again travels 3 km to north, and finally travels 2km towards west. In the end how far from is A from home? options: (A)3km, (B)2km, (C)4km, (D)5km, (E)6km | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: 3s,5e,3n,2w
5-2=3e
3-3=0
3km
ANSWER:A |
While selling a watch, a shopkeeper gives a discount of 5%. If he gives a discount of 7%, he earns Rs. 15 less as profit. The marked price of the watch is: options: (A)Rs. 697.50, (B)Rs. 712.50, (C)Rs. 787.50, (D)Rs. 750, (E)Rs. 780 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | D, Explanation: If he increases the discount by 2%, then his profit is 15 less. Let the marked price be X.
.02x = 15
x = 750 marked price
ANSWER:D |
A student instead of finding the value of 7/8 of a number, found the value of 7/18 of the number. If his answer differed from the actual one by 770, find the that number. options: (A)1584, (B)2520, (C)1728, (D)1656, (E)None | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: According to the question,
=> [7/8 - 7/18 ]x = 770
=> 7*10*x /18*8 = 770
=> x = 11*18*8
=> 1584.
Answer : A |
The monthly salary S of a shop assistant is the sum of a fixed salary of $500 plus 5% of all monthly sales. What should the monthly sales be so that her monthly salary reaches $1500? options: (A)$50000, (B)$40000, (C)$30000, (D)$20000, (E)None of these | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | D, Explanation: Let S be the total monthly salary and x be the monthly sales, hence
S = 500 + 5% * x
Find sales x so that S = 1500, hence
1500 = 500 + 5% * x = 500 + 0.05 x
Solve for x
x = (1500 - 500) / 0.05 = $20000
Answer D |
An aeroplane flies along the four sides of a square at the speeds of 200, 400, 600 and 800km/hr. Find the average speed of the plane around the field? options: (A)384, (B)562, (C)458, (D)156, (E)452 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: Let the each side of the square is x km
average speed of plane is y km/hr
(x/200)+(x/400)+(x/600)+(x/800) = 4x/y
25x/2400 = 4x/y
y= 384 km/hr
Answer is A |
Jack buys 18 sharpeners (white and brown) for rs. 100. If he pays 1 rupee more for each white than brown sharpeners. How many of white and how many brown sharpeners did he buy? options: (A)10,8, (B)9,8, (C)7,8, (D)5,6, (E)11,12 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: Total cost=100
number of sharp=18
cost of white=cost of brown+1
100/18=5.5...-(1)
also 100%18=10...-(2)
as cost of white is 1 more than that of brown
from 1 int. value will be 5
now remainder is 10 so 10 sharp. will be of cost (5+1)
=> 10*(5+1)+8*5
=>10*6+8*5
=60+40
100
white=10
brown=8
ANSWER:A |
Hoses A and B spout water at different constant rates, and hose A can fill a certain pool in 8 hours. Hose A filled the pool alone for the first 2 hours and the two hoses, working together, then finished filling the pool in another 3 hours. How many hours would it have taken hose B, working alone, to fill the entire pool? options: (A)8, (B)15, (C)12, (D)6, (E)3 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: Since hose A can fill the pool in 8 hours, then in 2 + 3 = 5 hours it will fill 5/8th of the pool. Thus the remaining 3/8th is filled by hose B in 3 hours. This means that hose B,working alone, to fill the entire pool will need 3*8/3 = 8 hours.
Answer: A. |
If 120 is reduced to 96, what is the reduction percent? options: (A)30%, (B)40%, (C)20%, (D)10%, (E)5% | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | C, Explanation: reduction = 120 – 96 = 24
∴ Reduction percent = (24/120)×100% =20%
Answer:C |
I know a 5 digit number having a property that with a 1 after it, it is three times as large as it would be with a 1 before it.
What is that number? options: (A)42857, (B)32456, (C)76523, (D)24567, (E)43566 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: Let the number be x
10x +1 = 3(100,000 + x)
=> x = 42857. |
At Daifu university, 24% of all students are members of both a chess club and a swim team. If 20% of members of the swim team are not members of the chess club, what percentage of all Daifu students are members of the swim team? options: (A)20%, (B)30%, (C)40%, (D)50%, (E)60% | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | B, Explanation: Assume there are total of 100 students. 24 students are members of both clubs. We are told that:20% of members of the swim team are not members of the chess club, thus if S is a # of members of the swim team then 0.2S is # of members of only the swim teem:
24+0.2S=S --> S=30.
Answer: B. |
If the population of a city increases by 5 % annually, what will be the population of the city in 2 years time if its current population is 78000? options: (A)81900, (B)85995, (C)85800, (D)90000, (E)None of these | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | B, Explanation: The % change in population of city in two years time is 1.05*1.05 = 1.1025 = 10.25%
Therefore, after 2 years the population of the city will be 1.1025 * 78000 = 85995
ANSWER B |
Two cars start at the same time from opposite ends of a highway that is 50 miles long. One car is riding at 12 mph and the second car is riding at 13 mph. How long after they begin will they meet? options: (A) 1, (B) 1.25, (C) 1.50, (D) 1.75, (E) 2 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | E, Explanation: Time they will meet = total distance/ relative speed= 50/12+13 = 50/25 = 2
Answer is E |
A shopkeeper employed a servant at a monthly salary of 1500. In addition to it, he agreed to pay him a commission of 15% on the monthly sale. How much sale in Rupees should the servant do if he wants his monthly income as 6000? options: (A)30000, (B)415000, (C)31500, (D)50000, (E)None of these | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: Servant’s commission amount
= 6000 – 1500 = 4500
i.e.,15% = 4500
or,100% = 4500⁄15 × 100 = 30000
Answer A |
A man borrows Rs.360 If he pays it back in 12 monthly installments of Rs.31.50, what is his interest rate? options: (A)1.5%, (B)4.5%, (C)10%, (D)5%, (E)12% | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | D, Explanation: Instead of paying monthly 360/12 = 30Rs, the man pays 31.50Rs. Therefore, the interest rate is 1.5/30 = 0.5/10 = 5/100 = 5%.
Answer D |
The price of a product is reduced by 30% . By what percentage should it be increased to make it 100% options: (A)41.86%, (B)42.86%, (C)43.86%, (D)44.86%, (E)45.86% | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | B, Explanation: If initial price is Rs 100 and reduced price is Rs 70.
Then, to make it 100 again, price should increase by 100*30/70= 300/7 % or 42.86% approx
ANSWER:B |
I have a money pouch containing Rs. 700. There are equal number of 25 paise coins, 50 paise coins and one rupee coins.
How many of each are there? options: (A)453, (B)651, (C)400, (D)487, (E)286 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | C, Explanation: 25 paise + 50 paise + 100 paise = 175 paise and Rs. 700 = 70,000 paise
70,000/175 = 400 |
A man spends Rs. 3500 per month and saves 12 1/2% of his income. His monthly income is ? options: (A)Rs. 4400, (B)Rs. 4270, (C)Rs. 4000, (D)Rs. 3937.50, (E)None of these | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | C, Explanation: 87 1/2% of P = 3500
⇒ {(175/2) x P} / 100 = 3500
∵ P = (3500 x 2 x 100) / 175 = 4000
Correct Option: C |
Five dozen toys are packed in a box and 98 boxes are kept in a tempo. How many tempos can lift 29400 toys in one round ? options: (A)4, (B)5, (C)7, (D)6, (E)8 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | B, Explanation: Five dozen = 5 x 12 = 60
⇒ No of toys can be kept in 1 box = 60
∴ No of toys can be kept in 98 boxes = 60 x 98 = 5880
∴ 29400 toys can be lifted by = 29400 / 5880 = 5 tempos
Option: B |
There are 10 oranges in a basket. Find the no. of ways in which 2 oranges are chosen from the basket? options: (A)45, (B)90, (C)120, (D)150, (E)180 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: Required number of ways = 10C2 = 10*9/2 = 45
Answer is A |
A company contracts to paint 3 houses. Mr.Brown can paint a house in 6 days while Mr.Black would take 8 days and Mr.Blue 12 days. After 8 days Mr.Brown goes on vacation and Mr. Black begins to work for a period of 6 days. How many days will it take Mr.Blue to complete the contract? options: (A)7, (B)8, (C)10, (D)11, (E)12 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | D, Explanation: let x is amount of work to be done to paint one house.
So Brown's one day work is x/6, black's can do x/8 work in
one day and blue is x/12.
Total houses is 3, so tatal work to be done is 3x.
3x= 8*(x/6) + 6*(x/8) + y*(x/12)
finally y = 11.
blue will complete the remaining work in 11 days.
ANSWER:D |
Train A leaves a station every 16 minutes and Train B leaves every 17 minutes. If both trains just left the station simultaneously, how long until they do so again? options: (A)272 minutes, (B)304 minutes, (C)190 minutes, (D)70 minutes, (E)35 minutes | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: We have to find the LCM:
17 is a prime number which means the LCM of 16 and 17 has to be 16*17=272
Correct answer is A. |
A hollow cube of size 5cm is taken, with the thickness of 1cm. It is made of smaller cubes of size 1cm .If the outer surface of the cube is painted how many faces of the smaller cubes remain unpainted? options: (A)438, (B)550, (C)500, (D)450, (E)498 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: Volume of Big Cube considering it is not hollow = L3 = 5*5*5 = 125 cm3
Size of hollow cube (considering 1 cm thickness on two faces of large cube = 5 - 2 = 3cm
Volume of hollow cube = 3*3*3 = 27 cm3
So Total Volume filled up by smaller cubes = Volume of Larger Cube - Volume of hollow cube
= 125 - 27
= 98 cm3
Volume of 1 small cube = 1*1*1 = 1 cm3
Total number of small cubes in the larger cube = 98 / 1 = 98
and Number of faces of 98 small cubes (6 faces each cube has) = 98*6 = 588 faces
Total Surface area of 6 faces of larger cube painted = 6*L2 = 6*5*5 = 150cm2
Surface area of one face of small cube = 1*1 = 1cm2
Number of faces of small cube painted = 150/1 = 150 faces
Hence number of faces of the smaller cubes remain unpainted= 588-150
= 438
answer.A |
In a chocolate store, all chocolates are either vanilla or cocoa flavored only. 10% of the chocolates are cocoa flavored, 90% of the rest are squashed. What percentage of the chocolates are both vanilla flavored and not squashed? options: (A)1%, (B)2%, (C)5%, (D)9%, (E)10% | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | D, Explanation: If 10% of chocolates are cocoa flavored, then 90% are vanilla flavored.
90% of 90% are squashed, i.e. 81% are squashed.
Vanilla flavored and non squashed= 90-81= 9%
D is the answer |
There is well of depth 30m and frog is at bottom of the well. He jumps 3m up one day and falls back 2m down the same day. How many days will it take for the frog to come out of the well? options: (A)25 days, (B)26 days, (C)27 days, (D)28 days, (E)29 days | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | D, Explanation: frog jumps 3 m up day & falls back 2 m down at night
so,frog will be 3-2=1 m up in a day.
Thus, in 27 days it will be 27 m up
on 28 th day it will be at top i.e 27+3 = 30 m & will not fall down.
ANSWER:D |
The sum of the 5 consecutive two digit odd numbers when divided by 10 becomes a perfect square, which of the following can be one of these 5 numbers? options: (A)47, (B)91, (C)41, (D)67, (E)44 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | C, Explanation: perfect square:- 1,4,9,16,25,36
sum=square*10=10,40,90,160,250,360
sum of 4 odd consecutive numbers is multiple of 4
so the only number left are 40,160,360
sum/4=40/4=10 is not possible
sum/4=360/4=90 is not possible
sum/4=160/4=40 is the only option available i.e 41
ANSWER:C |
In a class, 8% of total students are interested in Football. 4/5 of total students are interested in Cricket. 10% of total students are interested in Basketball and remaining 20 students are not interested in any games. How many students are there in the class? options: (A)850, (B)800, (C)900, (D)950, (E)1000 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | E, Explanation: Let x is total no. of students
8x/100+4x/5+10x/100+20=x
By solving this
x=1000
ANSWER:E |
Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years. What is definitely the difference between R and Q's age? options: (A)22, (B)27, (C)29, (D)Cannot be determined, (E)None of the above | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | D, Explanation: R - Q = R - T
Q = T.
Also R + T = 50; R + Q = 50
So, (R - Q) cannot be determined.
Answer:D |
Calculate the maximum distance you can travel with $8.50 on a cab which charges $3.50 for the first quarter-mile and 10 cents for each additional quarter mile. options: (A)11.75 miles, (B)12.75 miles, (C)17.75 miles, (D)14.75 miles, (E)10.75 miles | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | B, Explanation: Subtract the fee for te first quarter mile $8.50 - $3.50 = $5
Calculate how many extra additional quarter miles---$5/10 cents => 50 quarter miles => 12.5 miles
Total distance is 12.5 miles + 1/4 (first quarter mile)
12.75 miles
Answer: B |
In IPL season, Sachin current batting average is 51. In the finals, he scores 78 runs, then is batting average will be 54. Find out the total number of matches played by Sachin in this season. options: (A)6, (B)8, (C)9, (D)10, (E)11 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | C, Explanation: Let total number of matches = x
then, total runs 54*x
total runs before final = 51*(x-1)
runs in the final match
54*x - 51*(x-1) = 78
x= 9
ANSWER:C |
Amy is organizing her bookshelves and finds that she has 10 different types of books. She then codes each book with either a single letter or a pair of two different letters. If each type of book is uniquely represented by either a single letter or pair of letters, what is the smallest number of letters Amy will need to create the codes for all 10 types of books? (Assume the order of letters in a pair does not matter.) options: (A)3, (B)4, (C)5, (D)10, (E)20 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | D, Explanation: The question asks for the smallest value of n, such that (n + nC2) = 10 (n represents the number of letters. In this equation, n by itself is for single-letter codes and nC2 is for two-letter codes).
At this point, you'd need to pick numbers, since there's really no easy way to solve nC2 = (10 – n) without a calculator.
Looking at the answer choices, you can eliminate 10 and 20, so you can quickly narrow down the values you need to test. (i.e. (10 – n) suggests n can not be less than 10.)
As a general rule, whenever you're asked for the smallest value that satisfies a condition, start by testing the smallest number in the answers. Conversely, if you're asked for the largest value, start with the greatest answer.
Plug-in n=4 to (n + nC2) = (4 + 4C2) = 4 + (4x3 /2) = (4 + 6) = 10 ANS:D |
A rectangular piece of 150 sq m has a length which is 1m more than the 4 times the breadth. What is the perimeter of the piece? options: (A)60 m, (B)61 m, (C)62 m, (D)63 m, (E)64 m | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | C, Explanation: Let its breadth be = x m.
So length will be = (4x+1) m.
Now,
x * (4x+1) = 150
or, 4x^2+x-150 = 0
or, (4x+25)(x-6) = 0
Either 4x = -25 or x = 6
As breadth can not take negetive value so x = 6
So its length is 4*6+1 = 25
So perimeter will be 2*(25+6)=62 mLet its breadth be = x m.
So length will be = (4x+1) m.
Now,
x * (4x+1) = 150
or, 4x^2+x-150 = 0
or, (4x+25)(x-6) = 0
Either 4x = -25 or x = 6
As breadth can not take negetive value so x = 6
So its length is 4*6+1 = 25
So perimeter will be 2*(25+6)=62 m
ANSWER:C |
One gram of a certain health food contains 9 percent of the minimum daily requirement of vitamin E and 8 percent of the minimum daily requirement of vitamin A. If vitamins E and A are to be obtained from no other source, how many grams of the health food must be eaten daily to provide at least the minimum daily requirement of both vitamins? options: (A)8.5, (B)10.5, (C)12.5, (D)14.5, (E)16.5 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | C, Explanation: 100% / 8% = 12.5
12.5 grams of the health food provides 12.5(8%) = 100% of the vitamin A requirement and more than 100% of the vitamin E requirement.
The answer is C. |
Assistants are needed to prepare for preparation. Each helper can make either 2 large cakes or 35 small cakes/hr. The kitchen is available for 3 hours and 20 large cakes & 700 small cakes are needed. How many helpers are required? options: (A)8, (B)10, (C)12, (D)15, (E)19 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | B, Explanation: 20 large cakes will require the equivalent of 10 helpers working for one hour. 700 small cakes will require the equivalent of 20 helpers working for one hour. This means if only one hour were available we would need 30 helpers. But since three hours are available we can use 10 helpers.
B |
R, S, T, and U are points on a line, and U is the midpoint of line segment ST. If the lengths of line segments RS, RT, and ST are 5, 17, and 22, respectively. What is the length of line segment RU? options: (A)6, (B)7, (C)8, (D)9, (E)10 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: Since SR + RT = 22 = ST, then R is somewhere between S and T.
Since ST is 22, then SU is 11 because U is the midpoint of ST.
Since SR < SU, then R is somewhere between S and U.
Then SR + RU = SU.
5 + RU = 11
RU = 6
The answer is A. |
Six pita breads contain the same amount of falafel as do two rolls. Three rolls contain the same amount of falafel as five baguettes do. Two baguettes contain the same amount of falafel as how many pita breads? options: (A)12/25, (B)3/2, (C)3, (D)2, (E)25/3 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | C, Explanation: 6P = 2R
3R = 5B
2B = ?P
Thus, P : R : B = 18 : 6 : 12
P : B = 18 : 12
= 3 : 2
Thus P = 3
Answer : C |
A shopkeeper in order to promote his new shop put a discount of 20% on all the items for one day. Now he must sell the items at original price the other day. By what percentage must he increase the price to original? options: (A)21%, (B)20%, (C)25%, (D)33%, (E)18% | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | C, Explanation: Suppose every item is priced at $100. On 20% discount, the price will become $80. Now he must add $20 to each item for original price which is 25% of $80. |
The bus fare for two persons for travelling between Agra and Aligarh id four-thirds the train fare between the same places for one person. The total fare paid by 6 persons travelling by bus and 8 persons travelling by train between the two places is Rs.1512. Find the train fare between the two places for one person? options: (A)126, (B)77, (C)88, (D)66, (E)54 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: Let the train fare between the two places for one person be Rs.t
Bus fare between the two places for two persons Rs.4/3 t
=> 6/2 (4/3 t) + 8(t) = 1512
=> 12t = 1512 => t = 126.
Answer:A |
A rectangle has a length of 8 centimeters and a width of 3 centimeters. Find the perimeter. options: (A)18cm, (B)22cm, (C)20cm, (D)30cm, (E)28cm | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | B, Explanation: Perimeter = 2(8 cm) + 2(3 cm) = 16 cm + 6 cm = 22 cm
answer:B. |
Suppose you want to arrange your English, Hindi, Mathematics, History, Geography and Science books on a shelf. In how many ways can you do it ? options: (A)520, (B)720, (C)920, (D)None, (E)Cannot be determined | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | B, Explanation: We have to arrange 6 books. The number of permutations is 6*5*4*3*2*1= 720
Answer : B |
A straight picket fence is composed of x pickets each of which is 1/2 inch wide. If there are 6 inches of space between each pair of pickets, which of the following represents the length of fence in feet? options: (A)13x/2, (B)13x/2 - 6, (C)13x/24, (D)(13x+1)/24, (E)(13x-12)/24 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | E, Explanation: Number of pickets = x
Size of pickets = 1/2
length of pickets = 1/2x
If there are x pickets, it implies that there are x -1 spaces between the picket
Length of space = 6
total number of length = 1/2 x + 6(x-1) in inches
total length in feet =( 1/2 x + 6(x-1))/12
Simplify to get (13X-12)/24
ANSWER:E |
A ship went on a voyage. After it had traveled 180 miles a plane started with 10 times the speed of the ship. Find the distance when they meet from starting point. options: (A)238, (B)289, (C)200, (D)287, (E)187 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | C, Explanation: Let the speed of the ship = m miles/hr. and plane took 't' hours to meet the ship
Then, m×t is the distance ship traveled after plane started
So we have, mt + 180 = 10mt
⇒ 9mt = 180
⇒ mt = 20
Hence distance = 180 + 20 = 200 miles
Answer:C |
In a large forest, 300 deer were caught, tagged, and returned during 2001. During 2002, 500 deer were caught at random, of which only 20 had tags from the previous year. If the percent of deer in the forest that had tags during the second year and were caught in the 500 deer sample is representative of the percent of the total deer population in the forest with tags, what is the total deer population in the forest (assuming no change in population between 2001 and 2002)? options: (A)300, (B)500, (C)5000, (D)6000, (E)7500 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | E, Explanation: Let N = the total number of deer in the forest.
During the first year, the percent of deer in the entire population with tags was: 300/N
20/500 is the percent of deer caught during the second year that had tags. Since this sample percent matches the percent for the entire population (i.e., the total number of tagged deer divided by the total number of deer), the two ratios are equal.
Equating these two percents:
Sample = Population
(20/500)=(300/N)
N = (300/1)*(500/20)
N=7500
Answer E |
In a railway station, there are two trains going. One in the harbor line and one in the main line, each having a frequency of 10 minutes. The main line service starts at 5 o'clock and the harbor line starts at 5.02 A.M. A man goes to the station every day to catch the first train that comes. What is the probability of the man catching the first train? options: (A)0.9, (B)0.8, (C)0.6, (D)0.65, (E)1.5 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | B, Explanation: For each 10 min interval, if man comes in first 2 min, he'll catch the 1st train, if he comes in next 8 min, he'll catch the 2nd train.
Hence, for harbor line = (2/10) = 0.2 and for main line 0.8.
Answer:B |
The average (arithmetic mean) of the weight of 10 vehicles is 12.2 tons. The average weight of the group of vehicles increased by 2.6 tons after a new heavy duty truck was added to the group? What is the weight in tons of the heavy duty truck? options: (A)40.8, (B)41.6, (C)42.2, (D)43.5, (E)44.8 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: The new average is 14.8 tons.
On average, the ten trucks are 2.6 tons below the average for a total weighting of 26 tons.
Therefore, the added truck must be 14.8 + 26 = 40.8 tons
The answer is A. |
Boomtown urban planners expect the city’s population to increase by 10% per year over the next two years. If that projection were to come true, the population two years from now would be exactly double the population of one year ago. Which of the following is closest to the percent population increase in Boomtown over the last year? options: (A)20%, (B)40%, (C)50%, (D)65%, (E)75% | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | D, Explanation: Population now - 100;
Population one year from now - 110;
Population two years from now - 121;
Since the population two years from now (121) is exactly double the population one year ago then the population one year ago was 121/2=60.5.
Now, the question asks about the population increase over the last year, so from 60.5 (last year) to 100 (now): percent increase=difference/original*100=(100-60.5)/60.5*100=39.5/60.5*100=~2/3*100=~65%.
Answer: D. |
Arjun and Sajal are friends, each has some money. If Arun gives $30 to Sajal, the Sajal will have twice the money left with Arjun. But, if Sajal gives $10 to Arjun, Arjun will have thrice as much as is left with Sajal. How much money does each have? options: (A)62, 35, (B)62, 34, (C)34, 62, (D)42, 62, (E)62, 42 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | B, Explanation: Suppose Arun has $X and Sajal has $Y. then,
2(x-30)= y+30 => 2x-y =90 …(i)
and x +10 =3(y-10) => x-3y = - 40 …(ii)
Solving (i) and (ii), we get x =62 and y =34.
Arun has $62 and Sajal has $34.
Answer B. |
Julie’s yard is rectangular. One side of the yard is 100 feet wide. The total area of the yard is 3,000 square feet. What is the length of the other side of the yard? options: (A)30 feet, (B)20 feet, (C)10 feet, (D)50 feet, (E)60 feet | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: Area = length x width. Divide area by width to find the missing side.
3000 ÷100 = 30
The other side is 30 feet.
Correct answer A |
The greatest common factor of two positive integers is 11. The least common multiple of these two integers is 7700. If one of the integers is 350, what is the other? options: (A)242, (B)308, (C)352, (D)412, (E)456 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: GCF*LCM = product of 2 numbers
11*7700 = product of 2 numbers
other number = 11*7700/350 = 242
Answer is A |
A square piece of cloth is trimmed by 4 feet on one edge to form a rectangular piece, which is then cut diagonally in half to create two triangles. If the area of each of triangle is 70 square feet, what was the perimeter (in feet) of the original piece of square cloth? options: (A)56, (B)58, (C)60, (D)62, (E)64 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: Let x be the length of one side of the original square.
The area of the rectangle is x(x-4)=140.
x=14.
The perimeter of the square was 4*14=56 feet.
The answer is A. |
The length of the ribbon was originally 30 cm. It was reduced in the ratio 5 : 3. What is its length now? options: (A)18, (B)30, (C)6, (D)15, (E)12 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: Length of ribbon originally = 30 cm
Let the original length be 5x and reduced length be 3x.
But 5x = 30 cm
x = 30/5 cm = 6 cm
Therefore, reduced length = 3 cm
= 3 × 6 cm = 18 cm
Answer:A |
M = abc is a three digit number and N = cba, if M > N and M - N + 396c = 990. Then how many values of M are more than 300. options: (A)20, (B)30, (C)40, (D)200, (E)None | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: From the given data,
abc – cba + 396c = 990
100a + 10b + c – (100c + 10b + a) + 396c = 990
99a – 99c + 396c = 990
Observe that each term is divisible by 99. So on dividing the above expression by 99, we get
a – c + 4c = 10
a + 3c = 10
For c = 1, a = 7
c = 2, a = 4
c = 3, a = 1
'b' can take any value from 0 to 9
We have to find the value of M more than 300. So minimum value of 'a' should be 4.
So total possibilities are 402, 412, ...., 492 = 10 values
701, 711, ....., 791 = 10 values
So total values = 20.
Correct option: A |
there are more than 501 students in a school such that 20% of them exactly took physics and 28% of them exactly took math. What could be the least possible no of students in the school? options: (A)550, (B)570, (C)600, (D)700, (E)none of these | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | E, Explanation: 20% means 1/5 and 28% means 7/25,taking the lcm of the denominators 5 and 25 we get 25,the least multiple of 25 which is greater than 501 is 525. So, answer is none
ANSWER:E |
If Raj was one-third as old as Rahim 5 years back and Raj is 17 years old now, How old is Rahim now? options: (A)37, (B)41, (C)40, (D)42, (E)43 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | B, Explanation: Raj’s age today = 17 decades,
Hence, 5 decades back, he must be 12 years old.
Rahim must be 36 years old, Because (3×12).
5 years back Rahim must be 41 years old today. Because (36+5). |
A cow is tethered in the middle of a field with a 14 feet long rope. If the cow grazes 10 sq.ft. per day, then approximately what time will be taken by the cow to graze the whole field? options: (A)51 days, (B)61 days, (C)71 days, (D)81 days, (E)91 days | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | B, Explanation: Area of the field grazed = [22/7*14*14]sq.ft. = 616 sq.ft.
Number of days taken to graze the field = 616/10 days
=> 61 days
ANSWER:B |
A book was sold for Rs 27.50 with a profit of 10%. If it were sold for Rs. 25.75, then would have been percentage of profit and loss ? options: (A)2% Profit, (B)3% Profit, (C)2% Loss, (D)3% Loss, (E)4% Loss | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | B, Explanation: S.P.=(100+gain%100∗C.P)
So, C.P. = (100/110∗25.75)
When S.P. = 25.75 then
Profit=25.75−25=Re.0.75
Profit%=0.75/25∗100=3%
Answer is B |
In how many ways can a teacher in a kindergarten school arrange a group of 3 children (Susan, Tim and Zen) on 3 identical chairs in a straight line so that Susan is on the left of Tim? options: (A)7, (B)3, (C)2, (D)1, (E)6 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | B, Explanation: Total ways in which 3 children can be arranged on 3 chairs = 3*2*1 = 6
But in half cases Susan will be left of Tim and in other half of cases Tim will be on left of Susan
i.e. Desired cases in which Susan is on the left of Tim = (1/2)*6 = 3
B |
The telephone bill of a certain establishment is party fixed and partly varies as the number of calls consumed. When in a certain month 540 calls made the bill is Rs.1800. In another month 620 calls are consumed then the bill becomes Rs.2040. In another month 500 units are consumed due to more
holidays. The bill for that month would be : options: (A)Rs.1560, (B)Rs.1680, (C)Rs.1840, (D)Rs.1950, (E)Rs.1690 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | B, Explanation: Let the fixed amount be Rs. X and the cost of each unit be Rs. Y.
Then, 540y + x = 1800 …. And 620y + x = 2040
On subtracting (i) from (ii), we get 80y = 240 -> y = 3
Putting y = 3 in (i) we get :
540 * 3 + x = 1800 x = (1800-1620) = 180
. : Fixed charges = Rs.180, Charge per unit = Rs.3.
Total charges for consuming 500 units = 180 +(500*3) = Rs.1680
Answer:B |
Two balls A and B rotate along a circular track. Ball A makes 2 full rotations in 26 minutes. Ball B makes 5 full rotation in 35 minutes. If they start rotating now from the same point, when will they be at the same starting point again? options: (A)1 hour and 31 minutes, (B)2 hour and 31 minutes, (C)3 hour and 31 minutes, (D)4 hour and 31 minutes, (E)5 hour and 31 minutes | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: If ball A makes 2 rotations in 26 minutes, it makes 1 rotation in 13 minutes. If ball B makes 5 rotations in 35 minutes, it makes 1 rotation in 7 minutes.
The two balls start rotating now and makes several rotations before they are at the SAME starting points. Ball A would have done a WHOLE number X of rotations and ball B would have done a WHOLE number Y of rotations. Also they would have rotated during the same period of time T. Hence
T = 13 X = 7 Y
Hence 13 X = 7 Y
Solve the above for X
X = 7 Y / 13
We want the time when they are FIRST at the same starting point. Therefore X and Y are the smallest whole numbers of the equation X = 7 Y / 13. The smallest value of Y that gives X as a whole number is 13. Hence
X = 7 (13) / 13 = 7
Time T is given by
T = 13 X = 13 * 7 = 91 minutes = 1 hour and 31 minutes
correct answer A |
A bookshelf contains 45 books, 30 of which are hardcover and 20 of which are fiction. What is the maximum number of books that are both hardcover and fiction? options: (A)10, (B)15, (C)18, (D)20, (E)30 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | D, Explanation: Total Books = 45
Hard Cover = 30
Non hardcover = 15
Fiction = 20
Non-Fiction = 25
Maximum number of Hardcover fiction will be 20( Assuming All the Fiction Books are Hard Cover )
Hence, the correct answer will be (D) |
A newspaper costs $4 on Sunday and $1 the rest of the days of the week. If a hotel orders twice as many papers on Sunday as it does the rest of the days of the week and pays $210 per week for newspapers, how many newspapers does it buy on Monday? options: (A)15, (B)30, (C)45, (D)60, (E)75 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: Number of paper bought on monday = x
# of paper bought on sunday = 2x
Total cost = 210 = 6*x(rest of the day cost)+8*x (sunday cost)
14x = 210
x = 15
Ans A |
A number of friends decided to go on a picnic and planned to spend Rs. 96 on eatables. Four of them, however, did not turn up. As a consequence, the remaining ones had to contribute Rs. 4 extra, each. The number of those who attended the picnic was options: (A)8, (B)12, (C)16, (D)24, (E)25 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | A, Explanation: Let the number of persons be x. Then,
96/x-4-96/x=4 => x=12
So, required number =x-4=8.
Answer is A |
A wire in the shape of rectangle of length 27 cm and breadth 17 cm is rebent to form a square. What will be the measure of each side? options: (A)9, (B)11, (C)22, (D)25, (E)31 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | C, Explanation: Perimeter of rectangle = 2 (27 + 17) cm
= 88cm
Perimeter of square of side x cm = 4x
Therefore, perimeter of rectangle = Perimeter of Square
88 cm = 4x
x = 22
Therefore, each side of square = 22 cm
ANSWER : OPTION C |
A man divides Rs 8600 among 5 sons, 4 daughters and 2 nephews. If each daughter receives four times as much as each nephew, and each son receives five as much as each nephew. How much does each daughter receive ? options: (A)Rs 400, (B)Rs 500, (C)Rs 600, (D)Rs 700, (E)Rs 800 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | E, Explanation: If each nephew got Rs x, then
2x+16x+25x = 8600
x= 200
Each daughter got 4*200 = Rs 800
ANSWER:E |
Silu and Meenu were walking on the road.
Silu said, "I weigh 51 Kgs. How much do you weigh?"
Meenu replied that she wouldn't reveal her weight directly as she is overweight.
But she said, "I weigh 29 Kgs plus half of my weight. "How much does Meenu weigh? options: (A)12, (B)28, (C)27, (D)58, (E)91 | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | D, Explanation: It is given that Meenu weighs 29 Kgs plus half of her own weight.
It means that 29 Kgs is the other half. So she weighs 58 Kgs.
Solving mathematically, let's assume that her weight is A Kgs.
A = 29 + A/2
2 × A = 58 + A
A = 58 Kgs.
Answer:D |
Roy was suffering from severe headaches. He went to see his doctor and the doctor gave him 5 tablets asking him to take one tablet every 15 minutes.
How much time will it take Roy to consume all the 5 tablets? options: (A)45 Min, (B)75 Min, (C)90 Min, (D)120 Min, (E)60 Min | Please read the question and options carefully, then select the most appropriate answer and provide the corresponding explanation. | E, Explanation: Tablet 1 will be taken in 0 min.
Tablet 2 will be taken in 15 min.
Tablet 3 will be taken in 30 min.
Tablet 4 will be taken in 45 min.
Tablet 5 will be taken in 60 min. |