mathewhe/aqua_rat huggingface dataset:
Question: In a factory, there are 40% technicians and 60% non-technicians. If the 60% of the technicians and 40% of non-technicians are permanent employees, then the percentage of workers who are temporary is?
(A) 32%
(B) 42%
(C) 52%
(D) 62%
(E) 72%
Rationale: Total = 100
T= 40 NT= 60
40*(60/100)=24 60*(40/100)=24
24 + 24 = 48 => 100 - 48 = 52%
ANSWER:C
Answer: (C) 52%
Question: A man buys an article for rs.27.50 and sells it for rs.28.50. find his gain %.
(A) 4%
(B) 5%
(C) 3.5%
(D) 5.5%
(E) 4.5%
Rationale: sol. cp=rs27.50, sp=rs 28.50
gain=rs(28.50 –27.50)=rs1.10
so gain%={(1.10/27.50)*100}=4%
Answer is A.
Answer: (A) 4%
Question: 1/2+[(2/3*3/8)+4]-7/16=
(A) 29/16
(B) 19/16
(C) 69/16
(D) 9/13
(E) 0
Rationale: 1/2+[(2/3*3/8)+4]-7/16=
1/2+[(1/4)+4]-7/16=
1/2+[17/4]-7/16=
8/16 + 68/16 - 7/16 = 69/16
C
Answer: (C) 69/16
Question: In a certain company, the ratio of the number of managers to the number of non-managers in any department must always be greater than 7 : 32. In the company, what is the maximum number of non-managers in a department that has 9 managers?
(A) 39
(B) 40
(C) 41
(D) 42
(E) 43
Rationale: 9/7 * 32 = 41.1
The answer is C.
Answer: (C) 41
Question: Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar?
(A) Rs. 1(2/9)
(B) Rs. 2(2/9)
(C) Rs. 2(1/9)
(D) Rs. 3(2/7)
(E) Rs. 4(2/9)
Rationale: Here r = 10 % ,x = 100 and A = 5 kg
Actual price of sugar = 10*100/((100-10 )*5) = Rs. 2(2/9)
B
Answer: (B) Rs. 2(2/9)
Question: A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?
(A) 100
(B) 277
(C) 2987
(D) 278
(E) 271
Rationale: Relative speed of the thief and policeman = 11 - 10 = 1 km/hr.
Distance covered in 6 minutes = 1/60 * 6 = 1/10 km = 100 m.
Distance between the thief and policeman = 200 - 100 = 100 m.
Answer: A
Answer: (A) 100
Question: Difference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103?
(A) 2500 m^2
(B) 2510 m^2
(C) 2520 metre sq
(D) 2540 m^2
(E) 2590 m^2
Rationale: Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m^2
C
Answer: (C) 2520 metre sq
Question: A credit card number has 6 digits (between 1 to 9). The first two digits are 12 in that order, the third digit is bigger than 8, the forth is divisible by 3 and the fifth digit is 3 times the sixth. How many different credit card numbers exist?
(A) 27
(B) 9
(C) 72
(D) 112
(E) 422
Rationale: {1}{2}{greater than 6}{divisible by 3}{3x}{x}:
The third digit can take 1 values: 9.
The fourth digit can take 3 values: 3, 6, or 9.
The fifth and sixth digits can take 3 values: 31, 62, or 93.
Total = 1*3*3 = .
Answer: B.
Answer: (B) 9
Question: Set S consists of 5 values, not necessarily in ascending order: {4, 8, 12, 16, x}. For how many values of x does the mean of set S equal the median of set S?
(A) Zero
(B) One
(C) Two
(D) Three
(E) More than three
Rationale: There could be 3 medians of this set.
8 , when x <8
x , when 8<=x<=12
and
12, when x>12
There could be 1 mean = (40+x)/5
Now, we can solve (40+x)/5 = 8 , x, 12 to find out values.. and if valid values are found that solution counts.
We get x= 0 ,10, 20. Hence 3 solutions.
Ans D
Answer: (D) Three
Question: An inspector rejects 0.02% of the meters as defective. How many will he examine to reject 2?
(A) A)1500
(B) B)10000
(C) C)2500
(D) D)3000
(E) E)3100
Rationale: Let the number of meters to be examined be x
Then, 0.02% of x = 2
(2/100)*((1/100)*x = 2
x = 10000
Answer is B
Answer: (B) B)10000
Question: A train travels from station A to station B. If the train leaves station A and makes 75 km/hr, it arrives at station B 48 minutes ahead of scheduled. If it made 50 km/hr, then by the scheduled time of arrival it would still have 40 km more to go to station B. Find the distance between the two stations.
(A) 210
(B) 200
(C) 220
(D) 230
(E) 240
Rationale: Let x be the scheduled time for the trip from A to B. Then the distance between A and B can be found in two ways. On one hand, this distance equals 75(x−4860) km. On the other hand, it is 50x+40 km. So we get the equation:
75(x−4860)=50x+40
x=4 hr is the scheduled travel time. The distance between the two stations is 50⋅4+40=240 km.
Answer is E.
Answer: (E) 240
Question: A train , having a length of 330 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that of the train
(A) 10 sec
(B) 18 sec
(C) 6 sec
(D) 4 sec
(E) 2 sec
Rationale: Explanation:
Distance = 330 m
Relative speed = 60+6 = 66 kmph (Since both the train and the man are in moving in opposite direction)
= 66×10/36 mps = 110/6 mps
Time = distance/speed =330/(110/6) = 18 s
Answer: Option B
Answer: (B) 18 sec
Question: When a certain number X is divided by 143, the remainder is 45. Which of the following numbers, if added to X, would result in a number divisible by 40?
(A) 7
(B) 21
(C) 34
(D) 47
(E) 55
Rationale: Số thẻ number given is N = 143Q + 45
If this number is divided by 13, the remainder would be R[(143Q + 45)/13]
Since 143 is divisible by 13 , the product 143Q gives no remainder
This means the remainder of 45/13 should be the remainder of the entire number N
which is 6
To make it divisible by 13 , the smallest number that can be added =40 - 6 = 34
Correct Option : C
Answer: (C) 34
Question: Mariah has decided to hire three workers. To determine whom she will hire, she has selected a group of 20 candidates. She plans to have one working interview with 3 of the 20 candidates every day to see how well they work together. How many days will it take her to have working interviews with all the different combinations of job candidates?
(A) 520
(B) 120
(C) 300
(D) 30
(E) 333
Rationale: 520.
Answer A
Answer: (A) 520
Question: The tax on a commodity is diminished by 20% and its consumption increased by 25%. The effect on revenue is?
(A) 2% decrease
(B) 8% decrease
(C) 9% decrease
(D) 0% No change
(E) 2% decrease
Rationale: 100 * 100 = 10000
80 * 125 = 10000
-----------
10000-----------0
100-----------? => 0% No change
Answer: D
Answer: (D) 0% No change
Question: A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?
(A) 78.2 km/hr
(B) 89.2 km/hr
(C) 73.2 km/hr
(D) 79.2 km/hr
(E) 73.7km/hr
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 264)/20 = y
y = 22
Speed = 22 m/sec = 22 * 18/5 = 79.2 km/hr.
Answer: D
Answer: (D) 79.2 km/hr
Question: A telephone company needs to create a set of 3-digit area codes. The company is entitled to use only digits 2, 4 and 5, which can be repeated. If the product of the digits in the area code must be odd, how many different codes can be created?
(A) 20
(B) 22
(C) 24
(D) 1
(E) 30
Rationale: Total # of codes possible is 3*3*3 = 27. Oit of those 27 codes only the product of 555 will be odd, the remaining 26 will have either 2 or 4 in them, which ensures that their product will be even. Therefore the number of codes where the product of the digits is even = (total) - (restriction) = 27 - 26 = 1.
Answer: D.
Answer: (D) 1
Question: A salesman commission is 5% on all sales upto $10000 and 4% on all sales exceeding this. He remits $31100 to his parent company after deducting his commission. Find the total sales?
(A) $30000
(B) $32500
(C) $35120
(D) $41520
(E) $25460
Rationale: Let his total sales be x
Total sales - commission = $31100
x - [(5% of 10000)+4% of (x-10000)] = 31100
x-500-(x-10000)/25 = 31100
x = 32500
Answer is B
Answer: (B) $32500
Question: Irin, Ingrid and Nell bake chocolate chip cookies in the ratio of 9.18: 5.17: 2.05. If altogether they baked a batch of 170 cookies, what percent of the cookies did Nell bake?
(A) 0.125%
(B) 1.25%
(C) 11.7%
(D) 125%
(E) 0.152%
Rationale: 9.18x+5.17x+2.05x = 16.4x = 170 cookies
x= 170/16.4 = 10 (approx)
So, Nell baked 10*2.05 cookies or 20 cookies (approx)
% share = 20/170 = 11.7 approx
Hence, answer is C.
Answer: (C) 11.7%
Question: Shreyas bought an article and sold it for 112% of its cost price. What was the cost price of the article, if Shreyas sold it for Rs.42750/-?
(A) Rs.24600
(B) Rs.38169
(C) Rs.38989
(D) Rs.23200
(E) None of these
Rationale: Explanation:
112% of CP = Rs.42750
:. CP = Rs.42750x100/112 = Rs.38169.
Answer: Option B
Answer: (B) Rs.38169
Question: If x and y are perfect squares, then which one of the following is not necessarily a perfect square?
(A) x^2
(B) xy
(C) 4x
(D) x+y
(E) x^5
Rationale: If x=y=1^2=1, then each option but D is a perfect square, therefore D is NOT necessarily a perfect square.
Answer: D.
Answer: (D) x+y
Question: A certain university will select 1 of 4 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
(A) 42
(B) 70
(C) 140
(D) 180
(E) 315
Rationale: 1 of 7 will be chosen for the math
2 of 10 will be chosen for the computer
None of the 3 chosen people can be in more thn one deparments.
We can choose any of the 4 candidates for the math dep., which gives as 4 selections.
We can choose 2 of the 10 candidates for the computer dep., which gives us 2 selections and 8 rejections.
So, the way to find how many different selections of 2 candidates we can have for the computer dep., we do:
10! /2!*8!= (9*10) / 2 = 90 / 2 = 45.
We are multiplying our individual selections: 4*45 = 180
In the bolded part, we don't have to multiply all of the numbers, as those in 8! are included in 10!, so we simplify instead.
Ans D
Answer: (D) 180
Question: A family consists of six members P, Q, R, S, T and U. There are two married couples. Q is a doctor and the father of T. U is grandfather of R and is a contractor. S is grandmother of T and is a housewife. There is one doctor, one contractor, one nurse, one housewife and two students in the family. Which of the following is definitely a group of male members ?
(A) QU
(B) UU
(C) QI
(D) QH
(E) HS
Rationale: Explanation:
Q, the Doctor, is the father of T. S, the Housewife, is the grandmother of T and hence the mother of Q. Since there are only two married couples one being that of Q, the grandfather of R. i.e, U must be married to S. Thus, R and T will be both children of Q and these must be the students So, P, who remains, shall be the wife of Q and she alone can be the nurse. Thus, U must be the contractor
Clearly, for definite the males are Q, the father and U, the grandfather
Answer: A) QU
Answer: (A) QU
Question: What is the area of square field whose side of length 7 m?
(A) 225
(B) 662
(C) 772
(D) 882
(E) 49
Rationale: 7 * 7
= 49 sq m
Answer:E
Answer: (E) 49
Question: What is 5 2/3 - 3 5/4 divided by 5/2 - 7/6 ?
(A) 2
(B) 6
(C) 4
(D) 5
(E) 1
Rationale: 5 2/3 - 3 5/4 = 17/3 - 20/4 = (68 - 60 )/12 = 8/12 = 4/3
5/2 - 7/6 = (15-7)/6 = 8/6 = 4/3
So 4/3/4/3 = 1
Answer - E
Answer: (E) 1
Question: √6 percent of 6√6 =
(A) 0.3
(B) 0.25
(C) 0.1
(D) 0.95
(E) 0.35
Rationale: The other solutions are great, but here's one more approach.
First, we scan the answer choices to see that they are quite spread apart. This means we can also use someAPPROXIMATION
All test-takers must memorize the following approximations:
√2 ≈ 1.4
√3 ≈ 1.7
√5 ≈ 2.2
√6 ≈ 2.4
So, √6 percent of 6√6 ≈ 2.4 percent of (6)(2.4)
≈ (2.4/100)(14.4)
≈ 34.56/100
≈ 0.34
Check the answer choices to see that E is the only answer that's close.
Answer: E
Answer: (E) 0.35
Question: The probability that A speaks truth is 1/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
(A) 16/35
(B) 16/37
(C) 16/39
(D) 16/33
(E) 18/31
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 1/5 * 4/7 + 4/5 * 3/7
= 16/35
Answer:A
Answer: (A) 16/35
Question: A sum of money place at compound interest doubles itself in 3 years. In how many years will it amount to eight times itself?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: 100 ---- 200 ---- 3
400 ---- 3
800 ---- 3
------
9 years
Answer: C
Answer: (C) 9
Question: The cost of the paint is Rs. 36.50 per kg. If 1 kg of paint covers 16 squares feet, how much will it cost to paint outside of a cube having 8 feet each side?
(A) Rs. 692
(B) Rs. 768
(C) Rs. 876
(D) Rs. 972
(E) None
Rationale: Solution
Surface area of the cube	= (6 ×82)sq.ft
= 384 sq.ft.
Quantity of paint required	= (384 / 16)kg
‹=›24 kg.
Cost of painting	= Rs.(36.50 ×24)
= Rs. 876.
Answer C
Answer: (C) Rs. 876
Question: The amount of water (in ml) that should be added to reduce 15 ml. Lotion, containing 50% alcohol, to a lotion containing 30% alcohol, is?
(A) 8 ml
(B) 5 ml
(C) 4 ml
(D) 6 ml
(E) 10 ml
Rationale: 7.5 7.5
30% 70%
30% ----- 7.5
70% ------? => 17.5 - 7.5 = 10 ml
Answer:E
Answer: (E) 10 ml
Question: CP of one kg apple is Rs.9 and thereby loses 20%. At what price per kg, we should have sold them to make a profit of 5%?
(A) 10
(B) 11.81
(C) 11.92
(D) 12.4
(E) 12.56
Rationale: SP=9Loss=20%CP=100(100−Loss%)×SP=100(100−20)×9=10080×9=54×9to make a profit of 5%,SP=100+Gain%100×CP=(100+5)100×CP=105100×54×9=105100×54×9=2120×54×9=214×14×9=18916=11.81
B
Answer: (B) 11.81
Question: 517 + 5.017 + 0.517 + 5.0017 = ?
(A) 558.3657
(B) 527.5357
(C) 229.6357
(D) 629.5637
(E) 629.6753
Rationale: 517
5.017
0.517
+ 5.0017
--------
527.5357
---------
Answer is B.
Answer: (B) 527.5357
Question: A large tanker can be filled by two pipes A and B in 60 and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half ?
(A) 30 min
(B) 23 min
(C) 25 min
(D) 28 min
(E) 40 min
Rationale: (A+B) in 1 min = 1/60 + 1/40 = 1/24
x min then x/2(1/24+1/40) = 1
(x/2) x (1/15) = 1 ==> x = 30 min
ANSWER A
Answer: (A) 30 min
Question: A clock loses a minute every three hours for 4 days and gains 1% in the subsequent 6 days. If it was set right on Friday at 09 AM, what will be the time at the end of 10 days?
(A) 09:54:40 AM
(B) 09:56:24 AM
(C) 10:16:40 AM
(D) 10:06:36 AM
(E) 09:54:24 AM
Rationale: Loses 8 minutes each day.
so total loss = 4×8 = 32min
subsequent 6 days = 6×24×60 minutes
1% gain = ( 6×24×60)/100 = 86.4 minutes
so, total gain = 86.4 - 32 = 54.4 min = 54 + 0.4 min = 54 minutes + 0.4 × 60 seconds = 54min + 24seconds
10 days later the clock should be 54 min and 24seconds fast.
so time , 09:54:24 am (Answer E)
Answer: (E) 09:54:24 AM
Question: If the average of 9 digits is 18 and the average of 4 of them is 8, calculate the average of the remaining 5 numbers?
(A) 21
(B) 26
(C) 27
(D) 22
(E) 29
Rationale: Explanation:
Total of the 9 digits - 9*18 = 162
Total of the 4 digits - 4*8 = 32
Total of the remaining 5 digits - 162-32 = 130
average of the remaining 3 numbers = 130/5 = 26
ANSWER: B
Answer: (B) 26
Question: 4 weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 6 weavers in 6 days?
(A) 6
(B) 9
(C) 12
(D) 15
(E) 18
Rationale: 1 weaver can weave 1 mat in 4 days.
6 weavers can weave 6 mats in 4 days.
6 weavers can weave 9 mats in 6 days.
The answer is B.
Answer: (B) 9
Question: If y is 40 percent greater than x, then x is what percent less than y?
(A) 18%
(B) 21%
(C) 25%
(D) 29%
(E) 35%
Rationale: y = 1.4x
x = y/1.4 = 10y/14 = y - (2/7)*y
2/7 is about 29%.
The answer is D.
Answer: (D) 29%
Question: If an object travels at sixty feet per minute, how many feet does it travel in one hour?
(A) 60
(B) 3000
(C) 2400
(D) 1800
(E) 3600
Rationale: If an object travels at 60 feet per minute it covers covers 60x60 feet in in one hour.
Answer = 3600 Answer:E
Answer: (E) 3600
Question: Siddharth wants to borrow Rs.8000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction?
(A) s.28.80
(B) s.21.68
(C) s.21.18
(D) s.21.98
(E) s.21.29
Rationale: Amount of money Siddharth borrowed at S.I at 6% p.a. for two years = Rs.8,000
He lend the same amount for C.I at 6% p.a. for two years.
=> Siddharth's income = C.I - S.I
= p[1 + r/ 100]n - p - pnr/100
= p{ [1 + r/ 100]2 - 1 - nr/100
= 8,000{ [1 + 6/100]2 - 1 - 12/100}
= 8,000 {(1.06)2- 1 - 0.12} = 8,000(1.1236 - 1 - 0.12)
= 8,000 (0.0036) = 8 * 3.6
= Rs.28.80
Answer: A
Answer: (A) s.28.80
Question: A company’s four cars running 10 hrs a day consume 1500 lts of fuel in 10 days. In the next 6 days, the company will need to run 9 cars for 12 hrs each so it rents 5 more cars which consume 20% less fuel than the company’s four cars. How many lts of fuel will be consumed in the next 6 days?
(A) 1200 lt
(B) 1555 lt
(C) 1664 lt
(D) 1728 lt
(E) 2160 lt
Rationale: Given that
4 cars running 10 hrs a day consume 1200 lts. of fuel in 10 days.
1 car consumption per hour per day = 1500 /4 *10 *10 = 3.75 litre
Now question say new car consume 20% less fuel than the company’s four cars = 80/100 of 3.75 = 3 ( 20 percent less than 3.75)
Hence we calculate total consumption for next 6 days, the company will need to run 5 new cars for 12 hrs = 3 *12 *6*5 =1080
similarly = old 4 car consumption for next 6 days for 12 hrs = 3.75*6*12*4 = 1080
hence total is = 1080+1080= 2160 lt
Ans is E .
Answer: (E) 2160 lt
Question: In a sample of college students, 50 percent are third year students and 70 percent are not second-year students. What fraction of those students who are not third-year students are second-year students?
(A) 2/3
(B) 1/4
(C) 2/5
(D) 3/7
(E) 2/9
Rationale: required answer= 40/60. = 2/3
Answer is A
Answer: (A) 2/3
Question: A firm has 5 senior partners and 6 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner? (Note that two groups are considered different if at least one group member is different.)
(A) 130
(B) 135
(C) 140
(D) 145
(E) 150
Rationale: The number of ways to form a group of 3 is 11C3 = 165
The number of groups with no senior partner is 6C3 = 20
The number of groups with at least one senior partner is 165-20 = 145
The answer is D.
Answer: (D) 145
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?
(A) 20%
(B) 33.0%
(C) 22%
(D) 77%
(E) 54%
Rationale: Explanation:
SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 --- 20 => 20%
Answer: Option A
Answer: (A) 20%
Question: The price of a car is Rs. 3,25,000. It was insured to 85% of its price. The car was damaged completely in an accident and the insurance company paid 90% of the insurance. What was the difference between the price of the car and the amount received?
(A) Rs.32.500
(B) Rs.48,750
(C) Rs.76,375
(D) Rs.81,250
(E) None
Rationale: Solution
Amount paid to car owner	= 90% of 85% of Rs. 3,25,000.
= Rs. (90/100 ×85/100 ×325000)
= Rs. 2,48,625.
Required differene	= Rs. (325000 - 248625)
= Rs. 76,375.
Answer C
Answer: (C) Rs.76,375
Question: 90, 180, 12, 50, 100, 160, ?, 3, 40, 4, 25, 2, 6, 30, 3
(A) 100
(B) 150
(C) 180
(D) 120
(E) 220
Rationale: 30*3=90
6*30=180
6*2=12
25*2=50
4*25=100
40*4=160
3*40=120 ans is 120
ANSWER:D
Answer: (D) 120
Question: Pipe A can fill a tank in 6 hours. Due to a leak at the bottom, it takes 10 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
(A) 13
(B) 17
(C) 15
(D) 19
(E) 12
Rationale: Let the leak can empty the full tank in x hours 1/6 - 1/x = 1/10
=> 1/x = 1/6 - 1/10 = (5 - 3)/30 = 2/30 = 1/15
=> x = 15.
Answer: C
Answer: (C) 15
Question: What is the place value of 7 in the numeral 2734?
(A) 70
(B) 7
(C) 700
(D) 7.0
(E) 800
Rationale: Explanation:
7 × 100 = 700
Answer: Option C
Answer: (C) 700
Question: WINK, Inc. follows a certain procedure that requires two tasks to be finished independently in order for a job to be done. On any given day, there is a 7/8 probability that task 1 will be completed on time, and a 1/5 probability that task 2 will be completed on time. On a certain day, what is the probability that task 1 will be completed on time, but task 2 will not?
(A) 1/20
(B) 3/40
(C) 13/40
(D) 7/10
(E) 13/22
Rationale: P(1 and not 2)=7/8*(1-1/5)=7/10.
Answer: D.
Answer: (D) 7/10
Question: When Greenville State University decided to move its fine arts collection to a new library, it had to package the collection in 20-inch by 20-inch by 12-inch boxes. If the university pays $0.50 for every box, and if the university needs 2.16 million cubic inches to package the collection, what is the minimum amount the university must spend on boxes?
(A) $155
(B) $225
(C) $510
(D) $850
(E) $1250
Rationale: The volume of each box is 20*20*12 = 4800 cubic inches.
Number of boxes = 2,160,000/4800 = 450 boxes
Total cost = 450×$0.5=$225
The answer is B.
Answer: (B) $225
Question: Evaluate (12 + 22 + 32 + ... + 102)
(A) 430
(B) 720
(C) 385
(D) 265
(E) 295
Rationale: We know that (12 + 22 + 32 + ... + n2) =	1/6	n(n + 1)(2n + 1)
Putting n = 10, required sum =1/6 x 10 x 11 x 21 =385
Option C
Answer: (C) 385
Question: A train met with an accident 70km away from station A. It completed the remaining journey at 5/6th of the original speed and reached station B 1hr 12mins late. Had the accident taken place 60km further, it would have been only 1hr late. what was the original speed of the train?
(A) 60 km/hr
(B) 55 km/hr
(C) 65 km/hr
(D) 70 km/hr
(E) 48 km/hr
Rationale: let the original speed be 6x. A/q, traveling 70 km at 5/6th of original speed costs him 12 minutes etc
70/5x =70/6x +12/70 -> x =10 , 7x= 70.
Ans D
Answer: (D) 70 km/hr
Question: If R, x, y, and z are positive integers and (x)×(y)×(z)=R^2, which of the following could be the values of x, y, and z?
(A) 3, 16, 25
(B) 9, 25, 24
(C) 2, 9, 32
(D) 2, 9, 16
(E) 8, 16, 36
Rationale: This is one of those questions where using the given options is fastest way to get the solution. We need to find a set where 3 numbers can be paired into 2 pairs of some numbers because we need a product which is a square number.
C fits the bill. 2*9*32 = 2*3*3*8*4 = 3*3*8*8
ans C
Answer: (C) 2, 9, 32
Question: The average of 5 quantities is 8. The average of 3 of them is 4. What is the average of remaining 2 numbers?
(A) 14
(B) 10
(C) 8
(D) 9.5
(E) None of these
Rationale: ANSWER: A
(5x8-3x4)/2=14
Answer: (A) 14
Question: In the first 10 overs of a cricket game, the run rate was only 2.1. What should be the rate in the remaining 30 overs to reach the target of 282 runs?
(A) 6.25
(B) 8.28
(C) 6.11
(D) 8.7
(E) 8.11
Rationale: Required run rate
= [282 - (2.1 * 10)]/30
= 261/30
= 8.70
Answer:D
Answer: (D) 8.7
Question: The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?
(A) 388
(B) 800
(C) 277
(D) 126
(E) 191
Rationale: Area of the square = s * s = 5(125 * 64)
=> s = 25 * 8 = 200 cm
Perimeter of the square = 4 * 200 = 800 cm.
Answer: B
Answer: (B) 800
Question: A is twice as good a work man as B and together they finish the work in 14 days. In how many days A alone can finish the work?
(A) 23
(B) 21
(C) 77
(D) 92
(E) 61
Rationale: WC = 2:1
2x + x = 1/14 => x = 1/42
2x = 1/21
A can do the work in 21 days.
Answer: B
Answer: (B) 21
Question: A bag contains 18 purple jellybeans, 12 green jellybeans, and 16 yellow jellybeans; these jellybeans are the only items in the bag. If a person picks a jellybean at random out of the bag, what is the probability that the jellybean will be green?
(A) 15%
(B) 20%
(C) 26%
(D) 30%
(E) 35%
Rationale: Probability of green beans = 12 / (18 + 12 + 16) = 12/46 = 26%
Answer is C
Answer: (C) 26%