divelab/Sys2Bench huggingface dataset:
Question: What is the are of an equilateral triangle of side 20 cm?
Options:
A)64√5
B)64√9
C)64√4
D)64√3
E)100√3
Rationale: Area of an equilateral triangle = √3/4 S2
If S = 20, Area of triangle = √3/4 * 20 * 20 = 100√3 cm2;
Answer: E
Answer: E
Question: The difference between simple interest and compound interest on Rs. 1200 for one year at 10% per annum reckoned half yearly is
Options:
A)2
B)7
C)3
D)0
E)8
Rationale: Explanation:
S.I
= Rs.(1200x10x1/100)
= Rs.120.
C.I
= Rs[(1200x1+5/100)² -1200]
= Rs.123.
Difference
= Rs.[123-120]
= Rs. 3.
Answer: B
Answer: B
Question: Find the value of 2.5 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)]
Options:
A)2000
B)500
C)900
D)1600
E)None
Rationale: Answer
2.5 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)]
= 2.5 x [(36 x 48 x 250) / (12 x 9 x 5)]
= 2.5 x 4 x 4 x 50 = 2000
Correct Option: A
Answer: A
Question: A women purchased 3 towels @ Rs.100 each, 5 towels @ Rs.150 each and two towels at a certain rate which is now slipped off from his memory. But she remembers that the average price of the towels was Rs.145. Find the unknown rate of two towels?
Options:
A)A)400
B)B)450
C)C)500
D)D)550
E)E)600
Rationale: 10 * 145 = 1450
3 * 100 + 5 * 150 = 1050
1450 – 1050 = 400
A
Answer: A
Question: Calculate 85184 ÷ ? = 352
Options:
A)241
B)242
C)244
D)247
E)240
Rationale: Answer
Let 85184 ÷ X = 242
Then X = 85184/242 = 352.
Option: B
Answer: B
Question: A doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 115 pounds. If the typical dosage is 2 cubic centimeters per 15 pounds of the body weight, by what percent was the prescribed dosage greater than the typical dosage?
Options:
A)8%
B)9%
C)11%
D)12.5%
E)13.03%
Rationale: Typical dosage is Dose : weight :: 2: 15.
Now if weight is 115 :(115/15)) then typical dosage would be 2 *7.67 = 15.33 cc.
Dosage = 18 cc. Dosage is greater by 2 cc.
% dosage is greater: (2 / 15.33)*100 = 13.03 %
E is the answer.
Answer: E
Question: There are three places P, Q and R such that 3 roads connects P and Q and 4 roads connects Q and R. In how many ways can one travel from P to R?
Options:
A)41
B)36
C)25
D)54
E)12
Rationale: Number of ways in which one can travel from P to R
=3×4=12=3×4=12
Ans: E
Answer: E
Question: A train 900 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
Options:
A)200 m
B)379 m
C)400 m
D)589 m
E)600 m
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (900 + x)/60 = 65/3
x = 400 m.
Answer: C
Answer: C
Question: The sum of the present ages of father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be?
Options:
A)27 years
B)28 years
C)29 years
D)20 years
E)17 years
Rationale: Let the present ages of son and father be x and (60 - x) years respectively.
Then, (60 - x) - 6 = 5(x - 6)
6x = 84 => x = 14
Son's age after 6 years = (x + 6)
= 20 years.
Answer:D
Answer: D
Question: Bert and Rebecca were looking at the price of a condominium. The price of the condominium was 80% more than Bert had in savings, and separately, the same price was also 20% more than Rebecca had in savings. What is the ratio of what Bert has in savings to what Rebecca has in savings.
Options:
A)1:4
B)4:1
C)2:3
D)3:2
E)3:4
Rationale: Suppose bert had 100 so price becomes 180 , this 180 = 1.2 times R's saving .. so R's saving becomes 150
So required ratio is 100:150=2:3
ANSWER:C
Answer: C
Question: Of 70 players on a football team, 43 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?
Options:
A)54
B)59
C)61
D)71
E)92
Rationale: Total = 70
Thrower = 43
Rest = 70 - 43 = 27
Left Handed = 27/3 = 9
Right handed = 18
If all Thrower are right handed then total right handed is 43 + 18 = 61
so C. 61 is the right answer
Answer: C
Question: A jar contains only red, yellow, and orange marbles. If there are 3 red, 7 yellow, and 4 orange marbles, and 3 marbles are chosen from the jar at random without replacing any of them, what is the probability that 2 yellow, 1 red, and no orange marbles will be chosen?
Options:
A)1/60
B)1/45
C)2/45
D)3/22
E)5/22
Rationale: I started by finding the 2 probabilities, without calculation, like this:
P(YYR)
P(YRY)
P(RYY)
I calculated the first one and ended in 1/22. I looked at the answer choices at this point and saw answer D: 5/22.
This helped me realise that for the 3 possible orderings the probabbility is the same. So, it should be (1/22)*(5), which indeed is 5/22.
E
Answer: E
Question: A man sold 20 articles for $60 and gained 20%. How many articles should he sell for $90 to incur a loss 10%?
Options:
A)45
B)41.2
C)40
D)50
E)48
Rationale: Production cost per article: $60*(100%-20%) / 20 = $2.40
Required production costs for a loss of 20%: $90*(100% + 10%) = $99
Number of articles to be sold for $108 to incur a 20% loss: $99 / $2.40 = 41.2
Thus, solution B is correct.
Answer: B
Question: Vijay bought 160 shirts at the rate of Rs. 215 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?
Options:
A)s.225
B)s.288
C)s.485
D)s.273
E)s.282
Rationale: Total CP per shirt = 215 + 1400/160 + 1.75 + 320/160 = Rs. 227.5
SP = CP[(100 + profit%)/100]
= 227.5 * [(100 + 20)/100] = Rs.273.
Answer:D
Answer: D
Question: A car drove from Town A to Town B without stopping. The car traveled the first 60 miles of its journey at an average speed of 25 miles per hour. What was the car’s average speed, in miles per hour, for the remaining 100 miles if the car’s average speed for the entire trip was 40 miles per hour?
Options:
A)28.5
B)48.5
C)50.4
D)55.5
E)62.5
Rationale: KAPLAN OFFICIAL SOLUTION:
To solve this problem, you must remember that average speed means total distance divided by total time over an entire journey. This should not be confused with the average of the speeds. The total distance in this problem is 160 miles, but we will need to express the total time in a more complex way.
For the first 60 miles, the car traveled at 25 miles per hour. Therefore, we can say that the time this took was 60/25, because distance divided by rate equals time.
For the last 100 miles, we are trying to solve for the rate, so we can call this speed R. Thus, the time for the final 100 miles is 100/R.
If we put all of this together, knowing that the average speed over the entire journey is 40 miles per hour, we get the equation 160/(60/25 + 100/R) = 40. We can now solve for R and reach our answer.
160/(60/25 + 100/R) = 40
R = 62.5
50 is choice (E) and that’s our correct answer.
Answer: E
Question: 1, 13, 35, 67, 109, ____
Options:
A)161
B)154
C)216
D)158
E)none
Rationale: 1, 13, 35, 67, 109, .....
13=1+12
35=13+22
67=35+32
109=67+42
So 109+52=161
ANSWER:A
Answer: A
Question: For any number y, y* is defined as the greatest positive even integer less than or equal to y. What is the value of 9.2 – 9.2*?
Options:
A)0.2
B)1.2
C)1.8
D)2.2
E)4.0
Rationale: Since y* is defined as the greatest positive even integer less than or equal to y, then 9.2* = 8 (the greatest positive even integer less than or equal to 9.2 is 4).
Hence, 9.2 – 9.2* = 9.2 - 8 = 1.2
Answer: B.
Answer: B
Question: A sum of Rs.5800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
Options:
A)A)282
B)B)3770
C)C)8383
D)D)8383
E)E)3284
Rationale: Let A be the amount received at the end of the three years.
A = 5800[1 + 10/100][1 + 20/100][1 + 25/100]
A = 5800 * 1.65
A = Rs.9570
So the interest = 9570 - 5800 = Rs.3770
Answer: B
Answer: B
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?
Options:
A)228
B)278
C)48
D)27
E)21
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
Question: A walk 20m towards north east.B walk towards east 8m and then 12m south.Now calculate Distance between A and B?
Options:
A)30m
B)20m
C)35m
D)40m
E)38m
Rationale: its coming 30.4m
since 1st triangle we get 18.31
and extra 12 so 18.31+12=30.31=30m
ANSWER:A
Answer: A
Question: If m and n are whole numbers such that mn = 121, the value of (m 1)
n + 1 is:
Options:
A)1
B)10
C)121
D)100
E)1000
Rationale: If m and n are whole numbers such that mn = 121, the value of (m - 1)n + 1 is:
A.	1	B.	10
C.	121	D.	1000
sol.-We know that 112 = 121.
Putting m = 11 and n = 2, we get:
(m - 1)n + 1 = (11 - 1)(2 + 1) = 103 = 1000.
ANSWER:E
Answer: E
Question: There are 27 balls, of which 1 is heavier. given a balance how many times you need to weigh to find out the odd ball.
Options:
A)7 times
B)2 times
C)3 times
D)5 times
E)9 times
Rationale: first make 3 groups of 9 balls each...
then weight 2 group using balance which tells u which group is having the heavier ball...
then split dat group into 3 groups each containing 3 balls...
then follow same procedure...
in 3 times u get heavier ball
ANSWER:C
Answer: C
Question: The simple interest at c% for c years will be $c on a sum of
Options:
A)$ (1000)/c
B)$(100)c^2
C)$ c
D)$ (100)/c
E)$ 100c
Rationale: Principal =$(100*c)/(c*c)=$(100/c).
Answer is D
Answer: D
Question: In a fuel station the service costs $2.05 per car, every liter of fuel costs 0.8$. Assuming that you fill up 3 mini-vans and 2 trucks, how much money will the fuel cost to all the cars owners total, if a mini- van's tank is 65 liters and a truck's tank is 120% bigger and they are all empty-?
Options:
A)122.6$
B)228.9$
C)343.7$
D)395.05$
E)412.12$
Rationale: Service cost of 3 van and 2 truck = 2.05*(3+2)=10.5
Fuel in 3 Van = 3*65=195 litre
Fuel in 2 Trucks =2 * 65(1+120/100)= 286
Total fuel(Van+Truck) = 481 Litre
Total Fuel cost = 481*0.8 =384.8
TOTAL COST =FUEL+SERVICE=384.8+10.25=395.05
ANSWER IS D
Answer: D
Question: Solve the given two equations and find the inequality of X and Y. (a) 2x^2 + 11x + 14 = 0 and (b) 4y^2 + 12y +9 =0
Options:
A)If x>y
B)If x>y
C)If x<y
D)If x<=y
E)If x<=y
Rationale: Solution:-
X=-7/2 or -2
Y=-3/2
If x<y
C)
Answer: C
Question: If a boat is moving in upstream with velocity of 14 km/hr and goes downstream with a velocity of 40 km/hr, then what is the speed of the stream ?
Options:
A)13 km/hr
B)26 km/hr
C)34 km/hr
D)44 km/hr
E)none of these
Rationale: if the downstream is a km/hr and upstream is b km/hr then speed of stream is 1/2(a-b)
so, 1/2(40-14)=13 km/hr ANSWER:A
Answer: A
Question: If the integer N = 139k00 where k is the hundreds digit, N can always be divisible by which of the following?
Options:
A)2
B)4
C)3
D)6
E)9
Rationale: Apply the divisibility rule here that for a number to be divisible by 4 the last two digits must be divisible by 4
hence B is correct
Answer: B
Question: 5*2 is a three digit number with * is a missing digit. If the number is divisible by 6, the missing digit is
Options:
A)0
B)2
C)5
D)7
E)9
Rationale: Sol.
Let the number be 5x2. Clearly, it is divisible by 2.
Now, 5 + x + 2 = (7 + x) must be divisible by 3.
So, x = 2.
Answer B
Answer: B
Question: A cube of side 5.5 meter length is cut into small cubes of side 110 cm each. How many such small cubes can be obtained?
Options:
A)125
B)127
C)152
D)140
E)190
Rationale: Along one edge, the number of small cubes that can be cut
= 550/110 = 5
Along each edge 5 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut
= 5 * 5 * 5= 125
Answer:A
Answer: A
Question: 5 years ago Amith was three times as old as his daughter and 10 years hence, he will be two times as old as his daughter. Then Amith’s current age is,
Options:
A)10
B)50
C)40
D)20
E)60
Rationale: D
20
Amith’s age = A and
daughter’s age =B
Then, A – 5 = 3(B – 5)
=> A – 3B + 10 = 0 ……(1)
And, A + 10 = 2 (A + 10)
=> A – 2B – 10 = 0 ……(2)
Solving the 2 eqns, we will get
A = 50, B = 20.
Therefore,
Amith’s age is 50
And his Daughter’s age is 20
Answer: D
Question: The average age of X,Y & Z were 5 years ago was 25 years and the age of X and Y were 6 years ago was 18 years. The present age of the Z is?
Options:
A)52 Years
B)55 Years
C)42 Years
D)38 Years
E)22 Years
Rationale: Sum of the present ages of X,Y & Z = (25*3+5*3) = 90 years.
Sum of the present ages of X,Y = (18*2+6*2) = 48 years
Present age Z = (90- 48) = 42 years.
Answer : C
Answer: C
Question: 90 percent of your marbles are a solid color. 5 percent of your marbles are solid yellow. What percentage of your marbles are a solid color other than yellow?
Options:
A)5
B)15
C)85
D)90
E)95
Rationale: 90 percent are solid colors including solid yellow. 5 percent are solid yellow. 90% - 5% = 85%, so 85 percent are a solid color other than yellow => (C)
Answer: C
Question: The owner of an electronics shop charges his customer 25% more than the cost price. If a customer paid Rs.11,500 for a television set, then what was the cost price of the television set?
Options:
A)Rs.9200
B)Rs.7200
C)Rs.8600
D)Rs.9800
E)None of these
Rationale: Explanation:
SP = Rs.11500
i.e. 125% of CP.
:. CP = 11500x100/125
= Rs.9200/-
Answer: Option A
Answer: A
Question: A bowl has only 5 apples and 5 bananas. If one piece of fruit is selected from the bowl at random, and a second piece is selected from the bowl without replacing the first, what is the probability that both pieces of fruit chosen are apples?
Options:
A)1/10
B)1/5
C)2/9
D)2/5
E)1/2
Rationale: A bowl has only 5 apples and 5 bananas. If one piece of fruit is selected from the bowl at random, and a second piece is selected from the bowl without replacing the first, what is the probability that both pieces of fruit chosen are apples?
5/10 * 4/9
=2/9
C. 2/9
Answer: C
Question: The length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field?
Options:
A)73
B)32
C)34
D)43
E)42
Rationale: Explanation:
A/8 = 8 * 8 => A = 8 * 8 * 8
x * 2x = 8 * 8 * 8
x = 16 => 2x = 32
Answer: Option B
Answer: B
Question: AB
+BA
___
101
In the addition problem above, A and B represent digits in two different two-digit numbers. What is the sum of A and B?
Options:
A)6
B)8
C)10
D)11
E)14
Rationale: two ways to do it..
1) straight logic..
we can see that ones digit is 1 when units digit B and A are added..
only 10 fits in..
C
Answer: C
Question: An investor bought 200 shares of stock in ABCD company in 1990. By 1992, the investment was worth only 2/3 of its original value. By 1995, the 200 shares were worth only 3/5 of their value in 1990. By what percent did the value of the investment drop from 1992 to 1995?
Options:
A)16 2/3%
B)25%
C)33 1/3%
D)50%
E)10%
Rationale: Let price of each share in 1990 = X.
Total cost in 1990 = 200X
Now Price in 1992 = 2/3 * 200X = 400/3 * X
Now price in 1995 = 3/5 *200X= 120X
%Change in 1995 from 1992 = [(400/3* X -120X) / (400/3 *X) ] *100 = 10%
Answer E
Answer: E
Question: For any integer m greater than 1, $m denotes the product of all the integers from 1 to m, inclusive. How many prime numbers are there between $7 + 2 and $7 + 10, inclusive?
Options:
A)None
B)One
C)Two
D)Three
E)Four
Rationale: $ is basically a factorial of a number.
So, we are asked to find the number of primes between 7!+2 and 7!+10, inclusive.
From each number 7!+k were 2≤k≤102≤k≤10 we can factor out k, thus there are no pries in the given range.
For example:
7!+2=2(3*4*5*6*7+1) --> a multiple of 2, thus not a prime;
7!+3=3(2*4*5*6*7+1) --> a multiple of 3, thus not a prime;
...
7!+10=10(3*4*6*7+1) --> a multiple of 10, thus not a prime.
Answer: A.
Answer: A
Question: The value of a scooter depreciates in such a way that its value of the end of each year is 3/4 of its value of the beginning of the same year. If the initial value of the scooter is Rs.40,000, what is the value at the end of 5 years ?
Options:
A)3277
B)2977
C)9492
D)6077
E)17112
Rationale: Explanation: 40,000*(3/4)^5
Answer:C
Answer: C
Question: The tax on a commodity is diminished by 35% but its consumption is increased by 15%. Find the decrease percent in the revenue derived from it?
Options:
A)18%
B)72%
C)32%
D)25.25%
E)52.25%
Rationale: 100 * 100 = 10000
65 * 115 = 7475
10000------- 2525
100 ------- ? = 25.25%
Answer:D
Answer: D
Question: For the past 3 weeks, Rikki has gone to the gym an average of 2 times per week. After 1 more week, the average number of times Rikki goes to the gym increases to 3 times per week. How many times did Rikki visit the gym during the most recent week?
Options:
A)7
B)3
C)6
D)2
E)4
Rationale: Total times per week over 3 weeks = 3*2 = 6
Total times per week over 4 weeks = 4*3 = 12
Number of visits in most recent week = 12-6 = 6 visits
Answer is C
Answer: C
Question: If the sides of a triangle are 78 cm, 72 cm and 30 cm, what is its area?
Options:
A)120 cm2
B)765 cm2
C)1080 cm2
D)197 cm2
E)275 cm2
Rationale: The triangle with sides 78 cm, 72 cm and 30 cm is right angled, where the hypotenuse is 78 cm.
Area of the triangle
= 1/2 * 72 * 30
= 1080 cm2
Answer: C
Answer: C
Question: If the perimeter of a rectangular garden is 480 m, its length when its breadth is 100 m is?
Options:
A)299 m
B)140 m
C)200 m
D)167 m
E)128 m
Rationale: 2(l + 100) = 480 => l
= 140 m
Answer:B
Answer: B
Question: A bag contains 1 white,3 red and 2 blue balls.Three balls are drawn at random from the bag.the probability that all of them are red are????
Options:
A)1/6
B)3/6
C)1/20
D)2/20
E)3/20
Rationale: 3c3/6c3=1/20
ANSWER:C
Answer: C
Question: An article was sold after a discount of 20% and there was a gain of 20%. If the profit made on it was Rs. 6 less than the discount offered on it, find its selling price?
Options:
A)7
B)8
C)9
D)5
E)4
Rationale: Let CP = Rs. 100x
SP = Rs. 120x
MP = 120x/80 * 100 = Rs. 150x
D = Rs. 150x - Rs. 120x = Rs. 30x
D - P = 30x - 20x = Rs. 6, 10x = Rs. 6
120x = 120/10 * 6 = Rs. 7
Answer:A
Answer: A
Question: Two diagonals of a rhombus are 72 cm and 30 cm respectively. What is its perimeter?
Options:
A)136 CM
B)156 CM
C)144 CM
D)121 CM
E)126 CM
Rationale: ALL SIDES OF RHOMBUS ARE CONGRUENT LET PR = 72 SQ = 30 CM
PO = 0R = 72/1 = 36 CM SO = 0Q = 30/2 = 15 CM
PQ = QR = RS = SP
= ROOT( 36^2 + 15^2) = RPPT(1296+225)=ROOT(1521) = 39 CM
PERIMETER = 4 * 39 = 156 CM
ANSWER B
Answer: B
Question: The average salary of the employees in a office is Rs.120/month.The avg salary of officers is Rs.440 and of non officers is Rs 110. If the no.of officers is 15,then find the No of nonofficers in the office.
Options:
A)400
B)420
C)480
D)450
E)510
Rationale: Let no. of non- officers be x
15 * 440 + x * 110 = (x + 15) 120
x = 480
C
Answer: C
Question: In how many different ways can the letters of the word "FAME" be rearrangement?
Options:
A)26
B)24
C)28
D)12
E)30
Rationale: Option 'B'
The total number of arrangements is
4P4 = 4! = 24
Answer: B
Question: Each night before he goes to bed, Jordan likes to pick out an outfit to wear the next day. He has 11 different shirts, 10 different pairs of jeans, and 8 pairs of sneakers. If an outfit consists of 1 shirt, 1 pair of jeans, and 1 pair of sneakers, how many different outfits does Jordan have?
Options:
A)30
B)90
C)240
D)880
E)960
Rationale: Total # of outfits = 11 * 10 * 8 = 880
Answer - D
Answer: D
Question: A student chose a number, multiplied it by 5, then subtracted 275 from the result and got 135. What was the number he chose?
Options:
A)80
B)82
C)84
D)86
E)88
Rationale: Let x be the number he chose, then
5⋅x−275=135
5x=410
x=82
correct answer B
Answer: B
Question: Stephen likes to bike after school, and he has to get home before dark, so he only bike for five hours. His favorite route is a 45 mile loop starting from his house. In the first hour, he travels nine miles. For the next two hours, he travels at 7 miles per hour. Compute the average speed Stephen has to ride for the last three hours to get home before dark.
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: Stephen has to travel (45 - 9 - 7 * 2) = 22 miles in 2 hours
22 miles / 2 hours = 11 miles per hour
Correct answer B
Answer: B
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. What is the present age of the husband?
Options:
A)40
B)32
C)28
D)30
E)35
Rationale: Explanation:
Let the present age of the husband = h
Present age of the wife = w
Present age of the child = c
3 years ago, average age of husband, wife and their child = 27
=> Sum of age of husband, wife and their child before 3 years = 3 × 27 = 81
=> (h-3) + (w-3) + (c-3) = 81
=> h + w + c = 81 + 9 = 90 --- equation(1)
5 years ago, average age of wife and child = 20
=> Sum of age of wife and child before 5 years = 2 × 20 = 40
=> (w-5) + (c-5) = 40
=> w + c = 40 + 10 = 50 --- equation(2)
Substituting equation(2) in equation(1)
=> h + 50 = 90
=> h = 90 - 50 = 40
i.e., Present age of the husband = 40
Answer: Option A
Answer: A
Question: If a coin is tossed twice, what is the probability that on the first toss the coin lands tails and on the second toss the coin lands tails?
Options:
A)1/6
B)1/3
C)1/2
D)1/4
E)1
Rationale: Since there are two options for how a coin can land (heads or tails), that means there is a 1/2 chance to land on tails and a 1/2 chance to land heads. To solve this problem you multiply each probability for each flip together. (1/2) chance to land tails the first time * (1/2) chance to land tails the second time = (1/4) chance to land tails both times.
Answer: D
Answer: D
Question: A can do a piece of work in 4 days. B can do it in 6 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
Options:
A)87 days
B)12 days
C)66 days
D)77 days
E)44 days
Rationale: C = 1/2 - 1/4 - 1/6 = 1/12
=> 12 days
Answer: B
Answer: B
Question: The speed of a boat in still water is 80kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
Options:
A)60 kmph
B)40 kmph
C)16 kmph
D)15 kmph
E)18 kmph kmph
Rationale: Speed downstream = 80 + 20
= 100 kmph
Speed upstream = 80 - 20
= 60 kmph
Answer:A
Answer: A
Question: If the letters in the word RUTHENIUM are rearranged in the alphabatical order, which letter will be
second to the right of middle letter?
Options:
A)I
B)T
C)Y
D)H
E)F
Rationale: Alphabetical order of the letters of the word RUTHENIUM:
E H I M N R T U U
Middle Letter = N. will be second to the right of middle letter is T.
Answer: Option 'B'
Answer: B
Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit ?
Options:
A)24884
B)10500
C)23878
D)29988
E)27711
Rationale: Explanation:
Simran : Nanda = (50000 * 36) : (80000 * 30) = 3 : 4.
Simran's share = Rs. ( 24500 * 3/7) = Rs. 10500.
Answer: B) 10500
Answer: B
Question: If two numbers are in the ratio 5:3. If 10 is Reduced to both of the numbers then the ratio becomes 2:1 then find the smallest number?
Options:
A)15
B)20
C)30
D)34
E)36
Rationale: 5:3
5x - 10 : 3x - 10 = 2 : 1
1[5x - 10] = 2[3x - 10]
5x - 10 = 6x - 20
6x - 5x = 20 - 10
x = 10
the small number is = 3
3x = 30 (Answer = 30)
Short cut method:
a:b = 5:3
c:d = 2:1
1.Cross multiplication with both ratios
a * d ~ b * c = 5 * 1 ~ 3 * 2 = 5 ~ 6 = 1
2. If 10 is reduced both the number means 10 * 2 = 20 and 10 * 1 = 10,
Then 20 ~ 10 = 10
===> 1 -----> 10
===> 3 -----> 30 (Answer is = 30)
C
Answer: C