mathewhe/aqua_rat huggingface dataset:
Question: Doug, who runs track for his high school,
was challenged to a race by his younger
brother, Matt. Matt started running first,
and Doug didn’t start running until Matt
had finished a quarter-mile lap on the
school track. Doug passed Matt as they
both finished their sixth lap. If both boys
ran at a constant speed, with Doug running
2 miles an hour faster than Matt, what was
Matt’s speed?
(A) 10.5 miles per hour
(B) 10 miles per hour
(C) 9 miles per hour
(D) 8 miles per hour
(E) 7.5 miles per hour
Rationale: Doug runs 2 miles an hour faster than Matt, so let Matt’s speed equal x miles per hour.
Then Doug’s speed equals x + 2 miles per hour. Each lap is one-quarter of a mile, so Doug
runs 1.5 miles in the time it takes Matt to run 1.25 miles. Place this information in a chart:
DOUGH RATE:x-2 TIME:1.5/1 DISTANCE:1.5
MATT RATE:X TIME:1.25/X DISTANCE:1.25
The two boys took the same amount of time from the time Doug started, so make an
equation by setting the two times in the chart equal to each other, and then solve for x:
1.5/X+2=1.25/X
1.5X=1.25(X+2)
1.5X=1.25X+2.5
0.25X=2.5
X=10
So Matt ran at 10 miles per hour.
correct answer B)10 miles per hour
Answer: (B) 10 miles per hour
Question: A person plans to start a business with x% of a list of 10,000 products in his inventory. Next year after a business loss, the person wants to reduce the list by (x − 4)%. In terms of x, how many products will be in the inventory?
(A) x*x – 4x
(B) (x)(104 – x)
(C) (100)(104 – x)
(D) (100)(96 – x)
(E) (x-4)/100
Rationale: Based on the answer choices and the question, this question begs the use of x=4 as a sample number.
Initial = 4%*10000 = 400
Reduction = 4-4=0%, so no math required here to calculate the reduction; just make sure that you can calculate 400 in your answer.
A. x*x – 4x = 0; No
B. (x)(104 – x) = 400; Winner!
C. (100)(104 – x) > 400; No
D. (100)(96 – x) > 400; No
E. (x-4)/100 = 0; No
B
Answer: (B) (x)(104 – x)
Question: A grocer has 400 pounds of coffee in stock, 20 percent of which is decaffeinated. If the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated, what percent, by weight, of the grocer’s stock of coffee is decaffeinated?
(A) 28%
(B) 30%
(C) 32%
(D) 34%
(E) 40%
Rationale: 1. 20% of 400=80 pounds of decaffeinated coffee
2. 60% of 100=60 pounds of decaffeinated coffee
3. Wt have 140 pounds of decaffeinated out of 500 pounds, that means 140/500*100%=28%.
The correct answer is A.
Answer: (A) 28%
Question: A father was as old as his son's present at the time of your birth. If the father's age is 38 years now, the son's age 5years back was?
(A) 10 years
(B) 12 years
(C) 14 years
(D) 15 years
(E) 16 years
Rationale: Let the son's present age be x years. Then, (38 - x) = x
2x = 38.
x = 19.
Son's age 5 years back (19 - 5) = 14 years.
C
Answer: (C) 14 years
Question: If n is an integer and n^4 is divisible by 32, which of the following could be the remainder when n is divided by 32?
(A) 2
(B) 4
(C) 5
(D) 6
(E) 10
Rationale: Given:
n^4/32 = int
n^4/2^5 = int
1/2(n/2)^4 = int
try n= int = 2,4,6,8... because n/2 must be an integer
n=2 wont work because 1/2(n/2)^4 needs to be an integer.
n=4, result = 1/2 (2)^4 = 8, so the remainder of n/32 = remainder of 8/32 = 8 (not an option)
n=8, result = 1/2(8/2)^4 = 1/2(4)^4 = 1/2x16x16= 16x8, so the remainder of n/32 = remainder of 16x8/32 = 4 (option B)
Answer: (B) 4
Question: The average monthly salary of 20 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary?
(A) 2000
(B) 3000
(C) 3600
(D) 4800
(E) 4000
Rationale: Manager's monthly salary
= Rs. (1600 * 21 - 1500 * 20) = Rs. 3600
ANSWER C
Answer: (C) 3600
Question: n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4 ?
(A) 2
(B) 4
(C) 7
(D) 9
(E) 11
Rationale: Let n = 4q + 3. Then 2n = 8q + 6 = 4(2q + 1 ) + 2.
Thus, when 2n is divided by 4, the remainder is 2.
Option A
Answer: (A) 2
Question: Find the value for m?
19(m + n) + 17 = 19(-m + n) - 59
(A) 0
(B) -1
(C) 1
(D) 2
(E) -2
Rationale: 19m + 19n + 17 = -19m + 19n - 59
38m= -76 => m = -2
E
Answer: (E) -2
Question: In what time will a train 300 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.5 sec
(B) 9.7 sec
(C) 3.5 sec
(D) 2.9 sec
(E) 7.5 sec
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 300/40
= 7.5 sec.
Answer: E
Answer: (E) 7.5 sec
Question: 24 = 3a + 5b
3 > |–a|
If ‘a’ and ‘b’ are both integers, then what is the highest possible values of ‘b’ that can be used to solve the above equation.
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Let us understand the meaning of 5 > |-a|
1) when we write |-x| this means the same as |x|.
2) Mod is very easy concept if you solve mod question by considering as a distance. when a mod is written as |x-(a)| = b, this means the distance from point 'a' (both side left and right of 'a' on number line) is b. |x-(a)| < b means the distance is between the two extreme distance(left and right side of 'a' on number line, considering the max distance is 'b' from 'a' - as per this scenario.....hence the value of 'a' must be between these two extremes. |x-(a)| > b means the distance is greater than the distance of 'b'..i.e the value of a could be anywhere more than 'b'.
Now come to the question. First its given|-a| < 3 ==> |a| < 3 ===> |a-0| < 3 ==> the distance from zero is less than 3. So the point ‘a’ will be -2,-1,0,1,2 as distance from 0 to these values is less than 3.
Now, lets move to equation 3a + 5b = 24 ==> b = (24 – (3 * a))/5. According to question, b is an integer, hence to make ‘b’ integer (24 – (3*a)) must be divisible by 5. Now remove the value which can’t make (24-(3*a)) divisible by 5 from the possible values of a. It will remain is -2. With only one value of ‘a’ we can have only one value of ‘b’ and that is b = (24 – 3 *(-2))/5 ==> b = (24 + 6)/5 ==> b = 6. Hence the highest value that b can take is 6 and the answer is E (value 6).
Answer: (E) 6
Question: Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 15 minutes. The waste pipe can empty the full cistern in?
(A) 10 min
(B) 7 min
(C) 5 min
(D) 9 min
(E) 4 min
Rationale: 1/10 + 1/15 - 1/x
= 1/10
x = 10
Answer: A
Answer: (A) 10 min
Question: A trader purchased two colour televisions for a total of Rs. 35000. He sold one colour television at 30% profit and the other 40% profit. Find the difference in the cost prices of the two televisions if he made an overall profit of 32%?
(A) Rs.21000
(B) Rs.21028
(C) Rs.21098
(D) Rs.21021
(E) Rs.21007
Rationale: Let the cost prices of the colour television sold at 30% profit and 40% profit be Rs. x and Rs. (35000 - x) respectively.
Total selling price of televisions = x + 30/100 x + (35000 - x) + 40/100 (35000 - x)
=> 130/100 x + 140/100 (35000 - x) = 35000 + 32/100 (35000)
x = 28000
35000 - x = 7000
Difference in the cost prices of televisions = Rs.21000
Answer:A
Answer: (A) Rs.21000
Question: In August,a cricket team that played 120 matches won 28% of the games it played.After a continuous winning streak,this team raised its average to 52%.How many matches did the team win to attain this average?
(A) 40
(B) 52
(C) 60
(D) 80
(E) 98
Rationale: let the no of matches played more=x
so,
(120+x)*52/100=33.6+x
by solving we get x=60
ANSWER:C
Answer: (C) 60
Question: If 13 lions can kill 13 deers in 13 minutes how long will it take 100 lions to kill 100 deers?
(A) 1 minutes
(B) 13 minute
(C) 100 minutes
(D) 10000 minutes
(E) 1000 minutes
Rationale: we can try the logic of time and work,our work is to kill the deers so 13(lions)*13(min)/13(deers)=100(lions)*x(min)/100(deers)hence answer is x=13
ANSWER:B
Answer: (B) 13 minute
Question: In a class, the average age of 30 boys is 13 years and the average of 20 girls is 12 years. what is the average age of the whole class?
(A) 12 Years
(B) 12.3 Years
(C) 12.6 Years
(D) 13 Years
(E) 15 Years
Rationale: Total age of 50 students
(30X 13+20 X 12) = 630
Average = 630/50 = 12.6 Years
C
Answer: (C) 12.6 Years
Question: How many positive three-digit integers are divisible by both 3 and 5?
(A) 50
(B) 60
(C) 65
(D) 70
(E) 80
Rationale: A number to be divisible by both 3 and 5 should be divisible by the least common multiple of 3 and 5 so by 15.
Multiples of 15 between 100 and 999, inclusive is
(last-first)/multiple+1=(990-105)/15+1=59+1=60
Answer: B.
Answer: (B) 60
Question: Abel can complete a work in 10 days, Ben in 12 days and Carla in 15 days. All of them began the work together, but Abel had to leave after 3 days and Ben 4 days before the completion of the work. How long did the work last?
(A) 6 8/9
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Abel in the 3 days that he worked completed 3/10 of the job = 7/10 remains
Then if Ben had to leave 4 days before the completion, this means that Carla had to work alone for these 4 days in which she completed 4/15 of the job.
Now together, Ben and Carla completed the job in (1/12 + 1/15)(t) = 13/30
3/20 (t) = 13/30 ---> t = 26/9=2 8/9
Therefore, these 2 8/9 days worked plus the 4 days that Carla had to work by herself add to 6 8/9 days
Answer: A
Answer: (A) 6 8/9
Question: How many times are the hands of a clock at right angle in a day?
(A) 22
(B) 24
(C) 44
(D) 34
(E) 38
Rationale: In 12 hours, they are at right angles 22 times.
In 24 hours, they are at right angles 44 times.
Answer: Option C
Answer: (C) 44
Question: Townville has 100 residents, and 20 of them are females. If half of Townville’s male residents are smokers, and 1/2 of the female residents are smokers, which of the following represents the total number of Townville’s residents who are NOT smokers?
(A) 40
(B) 45
(C) 50
(D) 55
(E) 60
Rationale: Number of people =100
Females = 20
men = 100-20=80
Half of the men are smoker80/2=40, that means the remaining men 80-40=40 are non smokers.
1/2 females are smoker. i.e 1/2*20 = 10
20-10=10 females are non smokers
So, total number of non smokers in the town are 40+10 =50
Answer : C
Answer: (C) 50
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 12 sec
(B) 24 sec
(C) 48 sec
(D) 60 sec
(E) 62 sec
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 6/125 = 48 sec.
ANSWER:C
Answer: (C) 48 sec
Question: A jeep takes 3 hours to cover a distance of 440 Km. how much should the speed in Kmph be maintained to cover the same direction in 1/2th of the previous time?
(A) 48 Kmph
(B) 252 Kmph
(C) 293 Kmph
(D) 263 Kmph
(E) 265 Kmph
Rationale: Time = 3
Distance = 340
1/2 of 3 hours = 6 * 1/2 = 1.5 Hours
Required speed = 440/1.5 = 293 Kmph
C)
Answer: (C) 293 Kmph
Question: There are 3 people A,B & C. Rs.700 is divided among A,B & C so that A receives 1/2 as much as B and B 1/2 as much as C. What is the C's share is?
(A) Rs.100
(B) Rs.200
(C) Rs.400
(D) Rs.500
(E) Rs.550
Rationale: Let C's share = Rs.x. Then
B's share = Rs.x2
And, A's share = Rs.x4
A:B:C = x4:x2:x=1:2:4
Hence, C's share = Rs.(700×47) = Rs.400
C
Answer: (C) Rs.400
Question: Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 17% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?
(A) 5%
(B) 13%
(C) 21%
(D) 11%
(E) 30%
Rationale: 60-(x+17+z) + 50-(x+17+y) + 35-(z+17+y) + x + y + z +17 = 100
where x = people who bought MilkChicken
y = people who bought chickenApples
z= people who bought Milk and Apples
x+y+z= the number of people who bought just exactly two products.
Hence solving the above equation we get,
111 -(x+y+z) = 100
Thus, x+y+z= 11
Answer: D
Answer: (D) 11%
Question: A cricket bat is sold for $900, making a profit of $225. The profit percentage would be
(A) 24%
(B) 25.5%
(C) 33.33%
(D) 36.3%
(E) 40%
Rationale: 225/(900 - 225) = 33.33%.
Answer: C
Answer: (C) 33.33%
Question: BILAL spends 30% of his salary on house rent and 55% of the remaining money on food and clothes. He saves the remaining amount. If he saves ?59724 yearly, how much amount does he spend on food and clothes per month ?
(A) 5316
(B) 4792
(C) 5817
(D) 6080
(E) 6083
Rationale: Let his monthly salary be y.
House rent expenditure = 30/100 y = 3y/10
âˆ´ Remaining = 7y/10
Expense of food = 7y/10 x 55/100 = 77y/200
âˆ´ Remaining = 7y/10 - 77y/200
= 140y - 77y/200 = 63y/200
Monthly saving = 59724/12 = 4977
âˆ´ 63y/200 = 4977 = y= 4977 x 200/63 = 15800
Expenditure on food and clothes = 77y/200
= 6083
Answer: (E) 6083
Question: The angle of elevation of the sun, when the length of the shadow of a tree is √3 times the height of the tree is
(A) 30°
(B) 45°
(C) 60°
(D) 90°
(E) None
Rationale: Solution
Let AB be the tree and AC be its shadow.
Then, < ABC	= θ.
Then, AC/AB	= √3
cotθ= √3
θ=30°
Answer A
Answer: (A) 30°
Question: If the two-digit integers K and N are positive and have the same digits, but in reverse order, which of the following CANNOT be the sum of K and N?
(A) 181
(B) 165
(C) 121
(D) 99
(E) 44
Rationale: Since the question asks for the answer that CANNOT be the sum of K and N, and the answers are numbers, we can use a combination of TESTing VALUES and TESTing THE ANSWERS to eliminate the possible values and find the answer to the question.
We're told that K and N are two-digit positive integers and have the SAME DIGITS but in REVERSE ORDER. We're asked which of the 5 answers CANNOT be the SUM of K and N.
Let's start with the 'easiest' answer first:
44. Can we get to 44 in the manner described?
Yes, if the numbers are 13 and 31.....13+31 = 44. Eliminate Answer E
Now let's work through the rest of the list....
Can we get to 99 in the manner described?
Yes, there are several ways to do it. For example, if the numbers are 18 and 81.....18+81 = 99. Eliminate Answer D
Can we get to 121 in the manner described?
Yes, there are several ways to do it. For example, if the numbers are 38 and 83.....38+83 = 121. Eliminate Answer C
Can we get to 165 in the manner described?
Yes, there are a couple of ways to do it. For example, if the numbers are 78 and 87.....78+87 = 165. Eliminate Answer B
There's only one answer left....
A
Answer: (A) 181
Question: For any real number x, the operatoris defined as:
(x) = x(3 − x)
If p + 1 =(p + 1), then p =
(A) −3
(B) 0
(C) 1
(D) 2
(E) 3
Rationale: (x) = x(1 − x)
(p + 1) = (p + 1)(3 - p - 1) =(2 -p)(p+1)
We are given that p + 1 =(p + 1)
Therefore (2-p)(p+1) = (p + 1)
Or (p + 1) + (p-2)(p+1) = 0
(p + 1)(p-2) = 0
p = -1,p=2
Option D
Answer: (D) 2
Question: In how many different number of ways 5 boys and 2 girls can sit on a shopa which can accommodate persons?
(A) 180
(B) 190
(C) 200
(D) 210
(E) None
Rationale: Option 'D'
7p3 = 7 × 6 × 5 = 210
Answer: (D) 210
Question: A train traveled the first d miles of its journey it an average speed of 60 miles per hour, the next d miles of its journey at an average speed of y miles per hour, and the final d miles of its journey at an average speed of 160 miles per hour. If the train’s average speed over the total distance was 98 miles per hour, what is the value of y?
(A)  68
(B)  84
(C)  90
(D)  120
(E)  125
Rationale: Average speed=Total distance traveled /Total time taken
3d/d/60+d/y+d/160=98
Solving for d and y,
15y=11y+480
4y=500
y=125
Answer E
Answer: (E)  125
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 9 minutes, then the area of the park (in sq. m) is:
(A) 153601
(B) 153600
(C) 153602
(D) 153603
(E) 194400
Rationale: Perimeter = Distance covered in 9 min. =(12000/60) x 9m = 1800 m.
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1800 or x = 180.
Length = 540 m and Breadth = 360 m.
Area = (540 x 360) m2 = 194400 m2.
Answer: E
Answer: (E) 194400
Question: Of the 8 members of teacher in school, 5 can teach Physics, 7 can teach Math, and 4 can teach both subject. If one member is chosen at random, what is the probability that the member chosen will be someone who can not teach either subject?
(A) a) 5/18
(B) b) 7/18
(C) c) 1/2
(D) d) 0
(E) e) 13/18
Rationale: You know how to solve for Total number of people who can teach at least one subject:
Total = n(A) + n(B) - n(A and B)
Total people who can teach at least one subject = 5 + 7- 4 = 8
So 8 people know how to teach at least one subject. Hence, if you pick anyone, the probability is 0 that he/she wouldn't know how to teach any subject.
Answer (D)
Answer: (D) d) 0
Question: In a certain Parallelogram the degree measure of one angle exceeds that of the other by 70 what is the degree measure of the smaller angle?
(A) 55
(B) 80
(C) 85
(D) 90
(E) 95
Rationale: In a parallelogram opposite angles are equal and the angles at each side are supplementary to each other (supplementary angles are two angles that add up to 180°).
Given: x+(x+70)=180 --> x=55.
Answer: A.
Answer: (A) 55
Question: A man sells 45 lemons for Rs 40 and loses 20%. At how much price should he sell 24 lemons to the next customer to make a 20% profit?
(A) 37
(B) 299
(C) 72
(D) Rs 32
(E) 01
Rationale: Explanation:
Let cost price of lemons be x.
Selling price of lemons becomes CP - loss.
=>SP= x-(20/100)x
=>40=x(80/100)
=>50
So 45 lemons cost Rs 50
Cost of 1 lemon = 50/45 Rs
Cost of 24 lemons = (50/45)*24 =80/3 Rs
Selling Price of 24 lemons =(80/3)+(20/100)(80/3)=Rs 32
ANSWER:D
Answer: (D) Rs 32
Question: If M = 775 × 778 × 781, what is the remainder when M is divided by 14?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: M 775/14 leaves a remainder 5
778/14 leaves a remainder 8
781/14 leaves a remainder 11
5*8*11 =440
So the remainder will be the remainder of 440/14 which is 6
Ans A
Answer: (A) 6
Question: A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is:
(A) 15 hrs
(B) 20 hrs
(C) 25 hrs
(D) 30 hrs
(E) 10 hrs
Rationale: first pipe = x
ssecond and third (x-5)and (x-9)
1/x+1/(x-5)=1/(x-9)=>X=15
ANSWER A
Answer: (A) 15 hrs
Question: 6 women can do 75 units of work in 8 days by working 5hrs/day. In how many days can 4 women do 30 units of work by working 8hrs/day ?
(A) 3days
(B) 4days
(C) 5days
(D) 6days
(E) 7days
Rationale: 6x8x5/75=4x8xA/30
solve this for A then we get A=3days
ANSWER:A
Answer: (A) 3days
Question: If a - b = 3 and a^2 + b^2 = 29, find the value of ab.
(A) 12
(B) 15
(C) 10
(D) 18
(E) 13
Rationale: 2ab = (a^2 + b^2) - (a - b)^2
= 29 - 9 = 20
ab = 10.
Answer is C.
Answer: (C) 10
Question: 1,257
1,275
1,527
........
........
+7,521
The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1,2,5 and 7 exactly once in each integer. What is the sum W of the 24 integers ?
(A)  26,996
(B)  44,406
(C)  60,444
(D)  66,660
(E)  99,990
Rationale: This is the way i solved it :
Total no. of different combos = 24, total digits 4 therefore each digit must repeat 24/4 = 6 times in each row .. So the right most row would add up to 1x6 + 2x6 + 5x6 + 7x6 = 6+12+30+42 = 90 .. Each row would add up to 90, so 90 in the first means we have 9 that carries over and we get 0 , the second time its 90+9 and 9 stays and one 9 goes to the row to the left, so the last two digits of the SUM W should be 90 (E) .. We could go on and solve the exact number but since only one answer choice has the last digits as 90 we needn't go any further..
Answer: (E)  99,990
Question: In an exam, C scored 35 percent, D scored 65 percent and E 50 percent. The maximum score awarded in the exam is 2000. Find the average mark scored by all the three candidates?
(A) 100
(B) 500
(C) 1000
(D) 1500
(E) 2000
Rationale: Average mark scored by all the three boys
= [35/100 (2000) + 65/100 (2000) + 50/100 (2000)] / 3
= 1000
Answer: C
Answer: (C) 1000
Question: On multiplying a number by 7, the product is a number each of whose digits is 3. The smallest such number is:
(A) 47619
(B) 49619
(C) 47719
(D) 57619
(E) 47611
Rationale: Last digit should be 9.
when multiplying 7 with 9 , we get 63.
place 3 at unit place , we get 6 as carry.
Next digit of number should be such that we get product with 7 as a number whose last digit is 13-6=7.
such number is 1.
when 7 is multiplied with 1 , we get 7.
add carry 6 to it and we get 13.
so 3 will get at tens place and 1 carry for next place.
so next digit should give last digit as 2 (3-1=2).
such digit is 6.
...
..
so continuing like this , we get desired number as 47619
ANSWER:A
Answer: (A) 47619
Question: What is the sum of the odd integers from 55 to 65, inclusive?
(A) 495
(B) 360
(C) 555
(D) 600
(E) 605
Rationale: The mean is 60.
Sum=Mean(# of elements)
There are 6 odd numbers between 55-65 inclusive. 6*60=360
B
Answer: (B) 360
Question: If x = -5 and y = 8, what is the value of 2(x-y)^2 - xy ?
(A) 358
(B) 348
(C) 368
(D) 388
(E) 378
Rationale: x = -5 and y = 8
x-y = -5 - 8 = -13
x*y = -5 * 8 = -40
Now we apply it in the equation 2(x-y)^2 - xy =2(-13)^2-(-40)
==>2*169 +40 = 338+40 =378
Answer : E
Answer: (E) 378
Question: A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 11 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
(A) 6.24
(B) 7.4
(C) 7.92
(D) 6.28
(E) 7.24
Rationale: Net part filled in 1 hour = (1/4 - 1/11) = 7/44
The cistern will be filled in 44/7 hrs i.e., 6.28 hrs.Answer: D
Answer: (D) 6.28
Question: If Mason is now twice as old as Gunther was 10 years ago, and G is Gunther's current age in years, which of the following represents the sum of Mason and Gunther's ages 10 years from now?
(A) 4G-8
(B) 3G
(C) 2G-8
(D) AG-8
(E) 5F-2
Rationale: G is Gunther's current age.
Let Mason's current age be M.
given M = 2(G-10).
four years from now Mason's age will be = 2(G-10) + 10 = 2G-10
four years from now Gunther's age will be = G+10
Sum of ages of Mason and Gunther's after 4 years = 2G-10+G+10 = 3G
Ans : B
Answer: (B) 3G
Question: A room is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width. Find the least number of square tiles of equal size required to cover the entire floor of the room?
(A) 110
(B) 124
(C) 96
(D) 117
(E) 127
Rationale: Length = 6 m 24 cm = 624 cm
Width = 4 m 32 cm = 432 cm
HCF of 624 and 432 = 48
Number of square tiles required = (624 * 432)/(48 * 48) = 13 * 9 = 117
ANSWER:D
Answer: (D) 117
Question: If the cp of 12 rubbers is equal to the sp of 8 rubbers, the gain %is ?
(A) 25%
(B) 30%
(C) 50%
(D) 70%
(E) 80%
Rationale: (Explanation:Friends, we know we will need gain amount to get gain percent, right.
So lets get gain first.
Let the cost price of 1 pen is Re 1 Cost of 8 pens = Rs 8 Selling price of 8 pens = 12
Gain = 12 - 8 = 4 Gain%=(GainCost*100)%=(48*100)%=50%
C
Answer: (C) 50%
Question: If a: b :: 3 : 7, then what is (5a+6b): (a-3b)?
(A) -57:2
(B) -57:11
(C) 11 : 10
(D) -11 : 10
(E) -1 : 10
Rationale: a/b= 3/7
Dividing numerator & denominator of ' (5a+6b)/(a-2b) 'by b,
[5(a/b)+6]/[(a/b)-3]= [5*(3/7)+6]/[(3/7)-3]= -57/2
ANSWER:A
Answer: (A) -57:2
Question: The speed of a train is 90 kmph. What is the distance covered by it in 10 minutes?
(A) 15 kmph
(B) 8 kmph
(C) 9 kmph
(D) 1 kmph
(E) 2 kmph
Rationale: Explanation:
Distance=Speed*Time
90 * 10/60 = 15 kmph
ANSWER:A
Answer: (A) 15 kmph
Question: There are 690 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?
(A) 75
(B) 100
(C) 115
(D) 175
(E) 225
Rationale: female = x
Male = 690-x
x/2 + 690-x/4 = 1/3* (690)= 230
x= 230
x/2 = 115 is supposed to be the answer
M is missing something
Correct Option C
Answer: (C) 115