mathewhe/aqua_rat huggingface dataset:
Question: A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 35,000, what will be the amount A receives?
(A) 14700
(B) 15700
(C) 16700
(D) 18700
(E) 24700
Rationale: Total amount invested = 50000
Assume that investment of C = x.
Then investment of B = 5000 + x ,
Investment of A = 4000+5000+x = 9000+x
x + 5000+x + 9000+x = 50000
=> 3x + 14000 = 50000
=> 3x = 50000 – 14000 = 36000
=> x = 36000/3 = 12000
=> Investment of C = x = 12000 ,
Investment of B = 5000 + x = 17000,
Investment of A = 9000+x = 21000
Ratio of the investment of A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12
Share of A = Total Profit * 21/50 = 35000 * 21/50 = 700*21 = 14700
Answer is A
Answer: (A) 14700
Question: Suppose f(x) is an odd function for which f(x + 2) = f(x) for all x, and
f(x) = x2nd for xε2 (0,1). Compute f(-3/2) + f(1).
(A) -1
(B) -1/2
(C) -1/4
(D) 1/4
(E) 1/2
Rationale: Because f is periodic, we know that f(-3/2) = f(1/2) = (1/2)2 = 1/4. Because f
is odd, we know that f(1) = -f(-1), but because f is periodic, f(1) = f(-1). Therefore,
f(1) = 0 and the answer is 1/4.
correct answer D
Answer: (D) 1/4
Question: Six men and six women have to sit around a circular table so that no 2 women are together. In how many ways can that be done?
(A) 5!*6!
(B) 6!*6!
(C) 5!*7!
(D) 6!*7!
(E) 7!*7!
Rationale: The number of arrangements of n distinct objects in a row is given by n!.
The number of arrangements of n distinct objects in a circle is given by (n-1)!.
The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have: n!/n=(n-1)!
Now, 6 men in a circle can be arranged in (6-1)! ways and if we place 6 women in empty slots between them then no two women will be together. The # of arrangement of these 6 women will be 6! and not 5! because if we shift them by one position we'll get different arrangement because of the neighboring men.
So the answer is indeed 5!*6!.
A
Answer: (A) 5!*6!
Question: A man saves Rs 250 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years.
(A) Rs 827.53
(B) Rs 862.01
(C) Rs 822.02
(D) Rs 862.03
(E) None of these
Rationale: Explanation:
=[250(21/20Ã—21/20Ã—21/20)+250(21/20Ã—21/20)+250(21/20)]=827.53
Option A
Answer: (A) Rs 827.53
Question: A certain candy manufacturer reduced the weight of Candy Bar M by 40 percent buy left the price unchanged. What was the resulting percent increase in the price per ounce of Candy Bar M?
(A) 66.66
(B) 62.5
(C) 58
(D) 60
(E) 62
Rationale: assume 1oz candy cost $1 before.
now price remain same $1 but weight of candy reduces to 0.6 oz
new price of candy = 1/0.6 =1.6666
price increase 66.66 %
A
Answer: (A) 66.66
Question: What are the maximum value and minimum values of f(x) = |2sin(2x - pi/3) - 5| + 3
(A) max10-min6
(B) max11-min7
(C) max12-min8
(D) max13-min9
(E) max14-min10
Rationale: -1 <= sin(2x - pi/3) <= 1 : range of a sine function
-2 <= 2sin(2x - pi/3) <= 2 : mulitply all terms of the double inequality by 2
-2 - 5 <= 2sin(2x - pi/3) - 5 <= 2 - 5 : add -5 to all terms of the inequality.
-7 <= 2sin(2x - pi/3) - 5 <= -3
3 <= |2sin(2x - pi/3) - 5| <= 7 : change the above using absolute value.
3 + 3 <= |2sin(2x - pi/3) - 5| + 3 <= 7 + 3 : add 3 to all terms of the double inequality.
The maximum value of f(x) is equal to 10 and the minimum value of f(x) is equal to 6.
correct answer is A)max10-min6
Answer: (A) max10-min6
Question: A train 125 m long passes a man, running at 8 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
(A) 53
(B) 50
(C) 99
(D) 288
(E) 12
Rationale: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 8) km/hr. x - 8 = 45 ==> x = 53 km/hr.Answer: A
Answer: (A) 53
Question: Of the 5 numbers, whose average is 100, the first is one-fourth of the sum of the last 4. The first number is?
(A) 83.3
(B) 80
(C) 78.63
(D) 56.98
(E) 67.85
Rationale: Let the first number be x
sum of the 5 numbers = x+5x = 6x
6x/5 = 100
x = 100*5/6 = 83.3
Answer is A
Answer: (A) 83.3
Question: In how many different number of ways 4 men and 3 women can sit on a bench such that girls always sit together.
(A) 720
(B) 740
(C) 750
(D) 770
(E) 780
Rationale: 720
A)
Answer: (A) 720
Question: A division of a company consists of four men and six women. If two of these ten employees are randomly selected as representatives of the division, what is the probability that both representatives will be female?
(A) 1/6
(B) 1/5
(C) 1/4
(D) 1/3
(E) 1/2
Rationale: The total number of ways to choose two representatives is 10C2=45.
The number of ways to choose two females is 6C2=15.
P(choosing two female representatives)=15/45=1/3
The answer is D.
Answer: (D) 1/3
Question: If an item that originally sold for A dollars was marked up by x percent and then discounted by L percent, which of the following expressions represents the final price of the item?
(A) (10,000z + 100z(x – y) – xyz)/10,000
(B) (10,000z + 100z(y – x) – xyz)/10,000
(C) (100z(x – y) – xyz)/10000
(D) (100z(y – x) – xyz)/10000
(E) 10000 /(x – y)
Rationale: value of item =A ..marked up by x% = Ax/100
total value = A +ax/100 .discounted by L% on Total L/100 * ( A+Ax/100)
Final price =(A+ Ax/100) - L/100 ( A +Ax/100)
C
Answer: (C) (100z(x – y) – xyz)/10000
Question: The sum of the non-prime numbers between 40 and 50, non-inclusive, is
(A) 131
(B) 176
(C) 274
(D) 405
(E) 495
Rationale: The sum of the non-prime numbers between 40 and 50, non-inclusive, are {42, 44, 45, 46, 48, 49}.
6 times 40 something is approx north of 240
Hence the answer is (C) 274
Answer: (C) 274
Question: If 75 percent of a class answered the first question on a certain test correctly, 35 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?
(A) 10%
(B) (8) 20%
(C) 30%
(D) 50%
(E) 65%
Rationale: I didn't understand how to connect 20 percent with the whole equation.
Why 20 is out of the percentile diagram (circles) but inside of 100?
20% appeared in the exam; however did not answer Question AQuestion B correctly
So they are out of the two circles, however as they have appeared in the exam, they have to be taken into consideration for calculation purpose
I am doing it this way:
Suppose the total class size is 100, then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both.
Now,
100 - [(75 - x) + x + (35 - x)] = 20 .......... values are in percent
x = 20 - 100 + 110
x = 30
Ans: C
Answer: (C) 30%
Question: A bag contains 3 red, 2 green balls. 3 balls are drawn randomly. What is the probability that balls drawn contain exactly two green balls?
(A) 1/7
(B) 2/9
(C) 3/11
(D) 4/17
(E) 3/10
Rationale: Total number of balls = 3+2 = 5
n(S) = 5C3 = 5*4*3 / 3*2 = 10
n(E) = 2C2* 3C1 = 3
Probability = 3/10
Answer is E
Answer: (E) 3/10
Question: If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions uses all four of the digits 1, 2, 3, and 6, what is the greatest number of four-digit extensions that the company can have?
(A) 4
(B) 6
(C) 12
(D) 16
(E) 24
Rationale: The four digits available are 1,2,3 and 6
as the extensions can only be even numbers, the last digit has to be either 2 or 6
If it is 2...it leaves 1,3 and 6 for the first three digits...these can be arranged in 3! ways
If the last digit is 6...it leaves 1,2 and 3 for the first three digits...these can be arranged in 3! ways
Thus answer is 2*3! = 12 C
Answer: (C) 12
Question: We have 10 people and 3 chairs. In how many ways chairs can be occupy?
(A) 650
(B) 720
(C) 810
(D) 790
(E) 915
Rationale: no. of ways they can be occupy = 10*9*8 = 720
Answer is B
Answer: (B) 720
Question: In a certain appliance store, each model of television is uniquely designated by a code made up of a particular ordered pair of letters. If the store has 80 different models of televisions, what is the minimum number of letters that must be used to make the codes?
(A) 6
(B) 7
(C) 9
(D) 8
(E) 10
Rationale: If n is the number of distinct letters used to create the two lettered codes, then a total of n∗n=n^2 different codes can be created. We need n2≥80. The smallest n which fulfills this condition is n = 9.
Answer C
Answer: (C) 9
Question: A taxi leaves Point A 2 hours after a bus left the same spot. The bus is traveling 20 mph slower than the taxi. Find the speed of the taxi, if it overtakes the bus in two hours.
(A) 42
(B) 48
(C) 44
(D) 50
(E) 40
Rationale: Let the speed of bus be v - 20, speed of taxi be v
The bus travelled a total of 4 hrs and taxi a total of 2 hrs.
Hence 4 * (v-20) = 2v
4v - 80 = 2v
2v = 80
v = 40 mph
E
Answer: (E) 40
Question: X, Y, and Z are different prime numbers. The product X^2*Y^2*Z^2 is divisible by how many different positive numbers?
(A) 9
(B) 18
(C) 27
(D) 36
(E) 45
Rationale: The exponents of X^2*Y^2*Z^2 are 2, 2, and 2.
The number of factors is (2+1)(2+1)(2+1) = 27
The answer is C.
Answer: (C) 27
Question: 75% of the guestrooms at the Stagecoach Inn have a queen-sized bed, and each of the remaining rooms has a king-sized bed. Of the non-smoking rooms, 60% have a queen-sized bed. If 20% of the rooms at the Stagecoach Inn are non-smoking rooms with king-sized beds, what percentage of the rooms permit smoking?
(A) 25%
(B) 30%
(C) 50%
(D) 55%
(E) 75%
Rationale: Let x be the number of non-smoking rooms.
Let N be the total number of rooms at the inn.
40% of non-smoking rooms have a king-sized bed.
0.4x = 0.2N
x = 0.5N
The percentage of rooms which permit smoking is 1 - 0.5 = 50%
The answer is C.
Answer: (C) 50%
Question: Right triangle ABC is the base of the prism in the figure above. If AB=AC=âˆš10 and the height of the prism is 4, what is the volume of the prism?
(A) 40
(B) 85
(C) 20
(D) 60
(E) 45
Rationale: Volume of prism = Area of base * height = 1/2* (square root of 10) * (square root of 10)*4= 20
Answer: C
Answer: (C) 20
Question: Jacob bought a scooter for a certain sum of money.He spent 10% of the cost on repairs and sold the scooter for a profit of Rs.1100. How much did he spend on repairs if he made a profit of 20% ?
(A) Rs.400
(B) Rs.440
(C) Rs.500
(D) Rs.550
(E) Rs.650
Rationale: Total Profit = Rs. 1100.
%Profit = 20.
20% = 1100,
So,
100% = 5500.
Rs. 5500 would be the cost price for Jacob.
He spends 10% on repairing. So,
Initial Cost + Repair Cost = 5500.
Let Initial Cost was X. then
X + 10% of X = 5500
1.1X = 5500
X = 5500/1.1
X = 5000.
The initial cost price was Rs. 5000. Thus, he spends Rs. 500 on repairing.
ANSWER : OPTION C
Answer: (C) Rs.500
Question: Two trains running in opposite directions cross a man standing on the platform in 25 seconds and 18 seconds respectively and they cross each other in 20 seconds. The ratio of their speeds is:
(A) 3 : 1
(B) 3 : 2
(C) 3 : 8
(D) 2 : 5
(E) 3 : 4
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 25 x meters, and length of the second train = 18 y meters. (25 x + 18 y) / (x + y) = 20 ==>
25 x + 18 y = 20 x + 20 y ==> 5 x = 2 y ==> x/y = 2/5
Answer: Option D
Answer: (D) 2 : 5
Question: How many 3 digit positive integers Q exist that when divided by 7 leave a remainder of 5?
(A) 128
(B) 142
(C) 143
(D) 141
(E) 129
Rationale: Minimum three digit number is 100 and maximum three digit number is 999.
The first three digit number that leaves remainder 5 when divided by 7 is 103.
14 * 7 = 98 +5 = 103
The second three digit number that leaves remainder 5 when divided by 7 is 110.
15 * 7 = 105 +5 =110
The third three digit number that leaves remainder 5 when divided by 7 is 117
and so on
The last three digit number that leaves remainder 5 when divided by 7 is 999
142 * 7 = 994 + 5 = 999
Therefore, we identify the sequence
103,110,117.....999
use the formula of last term
Last term = first term + (n - 1) * common difference
you will get the answer 129 that is definitely E.
Answer: (E) 129
Question: A man invests Rs. 4,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum?
(A) Rs. 1200
(B) Rs. 1300
(C) Rs. 1500
(D) Rs. 2000
(E) None of these
Rationale: Explanation :
Interest on Rs.4000 at 5% per annum = ( 4000 × 5 × 1) / 100 = Rs. 200
Let his additional investment at 8% = x
Interest on Rs.x at 8% per annum = ( x × 8 × 1 ) / 100 = 2x/25.
To earn 6% per annum for the total, interest = (4000 + x) × 6 × 1/100.
=> 200 + 2x/25 = (4000 + x) × 6 × 1/100.
=> 20000 + 8x = (4000 + x) × 6.
=> 20000 + 8x = 24000 + 6x.
=> 2x=4000.
=> x=2000.
Answer : D
Answer: (D) Rs. 2000
Question: 96% of 5/8 =
(A) 0.2
(B) 0.5
(C) 0.6
(D) 0.75
(E) 1.0
Rationale: Should be simple.
0.96*5/8 = 4.8/8 = 0.6
Correct Option : C
Answer: (C) 0.6
Question: A man travelled from the village to the post office at the rate of 10kmph and walked backed at the rate of 5 kmph. If the whole journey took 3hours, find the distance of the post office from the village?
(A) 10km
(B) 15km
(C) 20km
(D) 25km
(E) 30km
Rationale: Average speed = 2xy/x+y = 2*10*5/10+5 = 20/3km/hr
Distance travelled in 3hours = 20/3 * 3 = 20km
Distance of the post office from the village = 20/2 =10km
Answer is A
Answer: (A) 10km
Question: A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is?
(A) 7/19
(B) 7/17
(C) 7/18
(D) 7/11
(E) 7/15
Rationale: Drawing two balls of same color from seven green balls can be done in ways.
Similarly from eight white balls two can be drawn in ways.
7/15
Answer: E
Answer: (E) 7/15
Question: In two triangle, the ratio of the areas is 4:3 and that of their heights is 3:4 the ratio of their bases is
(A) 16:9
(B) 9:16
(C) 9:12
(D) 16:12
(E) 4:12
Rationale: Explanation:
Given a1/a2 =4/3, h1/h2=3/4
also, we know that
a1/a2=(1/2×b1×h1)/(1/2×b2×h2)
on substituting in above equation, we get
b1/b2= 16/9
therefore b1:b2= 16:9
Answer: Option A
Answer: (A) 16:9
Question: seven friends met for lunch at an expensive restaurant, and everyone decided to contribute equally to the total bill of $530. If one of the friends had a coupon for 32% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay?
(A) $90
(B) $70
(C) $51
(D) $37
(E) $35
Rationale: 530 * 0,32 = 169
530 - 169 = 361
361 / 7 = 51
Answer C
Answer: (C) $51
Question: If a traveller was offered 5 city in asia and 11 city in europe and asked to chose atleast 3 city in asia and overall a 11 city. How many ways can he travel
(A) 2854
(B) 2958
(C) 3156
(D) 3762
(E) 6835
Rationale: 5c3*11c8+5c4*11c7+5c5*11c6=3762 ways
ANSWER:D
Answer: (D) 3762
Question: A trader sells 2 oranges per rupee, calculate the profit loss percentage if the trader bought the oranges at 3 per rupee.
(A) 22 %
(B) 55 %
(C) 35 %
(D) 40 %
(E) 50 %
Rationale: Let he total number of oranges bought by the shopkeeper be 12.
If he buys 3 a rupee, his CP = 2
He selling at 2 a rupee, his SP = 3
Profit = SP - CP = 3 - 2 = 1
Profit Percent = 1/2 * 100 = 50 %
Answer: E
Answer: (E) 50 %
Question: An eccentric casino owner decides that his casino should only use chips in $3 and $5 denominations. Which of the following amount cannot be paid out using these chips?
(A) $19
(B) $21
(C) $14
(D) $9
(E) $11
Rationale: Yes, the number of 3 or/and 5 dollar chips can be zero, however both being zero mean that the casino is paying out $0, which is not realistic.
Each option but E can be represented as the sum of a multiple of 3 and a multiple of 5:
A. $19 = 3*3 + 5*2
B. $21 = 3*2 + 5*3
C. $14 = 3*3 + 5*1
E. $9 = 3*3
Answer: E.
Answer: (E) $11
Question: An airplane travels 4362 km against the wind in 6 hours and 5322 km with the wind in the same amount of time. What is the rate of the plane in still air?
(A) 344 km/hr
(B) 767 km/hr
(C) 807 km/hr
(D) 908 km/hr
(E) 555 km/hr
Rationale: Let the speed of the air plane in still air be x km/hr
And the speed of the wind be y km/hr.
Then speed of the airplane going with the wind = (x + y) km/hr
and speed of the airplane going against the wind = (x - y) km/hr.
We know that,
Distance = Speed ? Time
or, Speed = Distance
Time
According to the problem,
An airplane travels 4362 km against the wind in 6 hours
x - y = 4362/6
or, x - y = 727 ----------- (1)
Again, the airplane travels 5322 km with the wind in the same amount of time i.e. 6 hours
x + y = 5322/6
or, x + y = 887 ----------- (2)
Now add (1) and (2) we get,
x - y = 727
x + y = 887
2x = 1614
or, 2x/2 = 1614/2, (Divide both sides by 2)
or, x = 807
Now substitute the value of value of x = 807 in equation (2) we get,
807 + y = 887
-807 -807, (Subtract 407 from both sides)
y = 80
Answer: Rate of the plane in still air = 807 km/hr
correct answer C
Answer: (C) 807 km/hr
Question: Which of the following describes all values of x for which 16-x^2 ≥ 0 ?
(A) x ≥ 1
(B) x ≤ -1
(C) 0 ≤ x ≤ 1
(D) x ≤ -1 or x ≥ 1
(E) -4 ≤ x ≤ 4
Rationale: 16-x^2 >= 0 ---> x^2-16<=0
--> (x+4)(x-4)<=0
Above equation true for
i) x+4<=0 and x-4>=0 ---> x<= -4 and x>=4 ---> this is not possible ---Strike out this solution
ii) x+4>=0 and x-4<=0 ---> x>=-4 and x<=4 --> -4<=x<=4
answer E
Answer: (E) -4 ≤ x ≤ 4
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 33 kmph. Of how many minutes does the train stop per hour?
(A) 73
(B) 83
(C) 16
(D) 83
(E) 28
Rationale: Explanation:
T = 12/45 * 60 = 16
Answer: Option C
Answer: (C) 16
Question: A tank is filled in SIX hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?
(A) 56 hours
(B) 28 hours
(C) 55 hours
(D) 66 hours
(E) 21 hours
Rationale: 1/A + 1/B + 1/C = 1/6 (Given)
Also given that A = 2B and B = 2C
=> 1/2B + 1/B + 2/B = 1/6
=> (1 + 2 + 4)/2B = 1/6
=> 2B/7 = 6
=> B = 21 hours.
Answer: E
Answer: (E) 21 hours
Question: Kelly and Jody packed boxes with books. If Jody packed 80% of the total number of boxes, what was the ratio of the number of boxes Kelly packed to the number that Jody packed?
(A) 1 to 6
(B) 1 to 4
(C) 2 to 5
(D) 3 to 5
(E) 2 to 3
Rationale: Explanation:
If Jody packed 80% of the boxes then Kelly packed 20%. The ratio of the number of boxes Kelly packed to the number Jody packed is thus 20%/80%=1/4
Answer: Option B
Answer: (B) 1 to 4
Question: 65% of x = 20% of 552.50. Find the value of x?
(A) 100
(B) 170
(C) 150
(D) 180
(E) 199
Rationale: 65% of x = 20% of 552.50
Then, 65/100 * x = 20/100 * 5525/10
x = 170
Answer is B
Answer: (B) 170
Question: Jim’s Taxi Service charges an initial fee of $2.05 at the beginning of a trip and an additional charge of $0.35 for each 2/5 of a mile traveled. What is the total charge for a trip of 3.6 miles?
(A) $5.20
(B) $4.45
(C) $4.80
(D) $5.05
(E) $5.40
Rationale: Let the fixed charge of Jim’s Taxi Service = 2.05 $
and charge per 2/5 mile(.4 mile) = .35$
Total charge for a trip of 3.6 miles = 2.05 + (3.6/.4) * .35
= 2.05 + 9*.35
= 5.2 $
Answer A
Answer: (A) $5.20
Question: A person travels first 100km at 40km/hr and the next 100km at 60km/hr. The average speed for the first 200km of the tour is?
(A) 36km/hr
(B) 50km/hr
(C) 48km/hr
(D) 60km/hr
(E) 55km/hr
Rationale: Total time taken = 100/40 + 100/60 = 25/6 hrs
Average speed = 200*6/25 = 48km/hr
Answer is C
Answer: (C) 48km/hr
Question: The area of the largest circle that can be drawn inside a square of side 56 Cm in length is:
(A) 2464
(B) 2052
(C) 3201
(D) 4202
(E) 1200
Rationale: Radius of required circle = 28 Cm
its area = 22/7 × 28 × 28
88 × 28 = 2464 Cm(power)2
Answer is A.
Answer: (A) 2464
Question: Number N is randomly selected from a set of all primes between 10 and 40, inclusive. Number D is selected from a set of all multiples of 5 between 10 and 40 inclusive. What is the probability that N+D is odd?
(A)  1/2
(B)  2/3
(C)  3/4
(D)  4/7
(E)  5/8
Rationale: All primes except 2 are odd, thus N must be odd. For N + D = odd + D to be odd, D must be even.
There are 7 multiples of 5 between 10 and 40, inclusive: 10, 15, 20, 25, 30, 35, and 40. Out of them 3 (15, 25, and 35) are odd.
Therefore the probability that N + D is odd is 4/7.
Answer: D.
Answer: (D)  4/7
Question: What is the units digit of the product of the first 100 odd numbers?
(A) 1
(B) 3
(C) 0
(D) 5
(E) 7
Rationale: 1*3*5*7 ................... will end up in 5 in the units place
Answer : D
Answer: (D) 5
Question: A rectangular floor is covered by a rug except fo a strip q meters along each of the four edges. If the floor is m meters by n meteres, What is the area of the rug in square meters?
(A) mn - p(m+n)
(B) mn – 2p(m+n)
(C) mn – p^2
(D) (m - p)(n - p)
(E) (m - 2q)(n - 2q)
Rationale: The answer must be E.
Plug in M 100
N 50
q 10=E
Answer: (E) (m - 2q)(n - 2q)
Question: Equal amount of water were poured into two empty jars of different capacities, which made one jar 1/5 full and other jar 1/4 full. If the water in the jar with lesser capacity is then poured into the jar with greater capacity, what fraction of the larger jar will be filled with water?
(A) 1/7
(B) 2/5
(C) 1/2
(D) 7/12
(E) 2/3
Rationale: Same amount of water made bigger jar 1/5 full, then the same amount of water(stored for a while in smaller jar) were added to bigger jar, so bigger jar is 1/5+1/5=2/5 full.
Answer: B.
Answer: (B) 2/5
Question: A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10% protein and food Y contains 15% protein. If the rabbit's diet provides exactly 39 grams of protein daily, how many grams of food X are in the mixture.
(A) 120
(B) 140
(C) 150
(D) 160
(E) 200
Rationale: Let x be the amount of food X.
0.1x + 0.15(300-x) = 39
0.05x = 6
x = 120
The answer is A.
Answer: (A) 120
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 13 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
(A) 11
(B) 408
(C) 2881
(D) 287
(E) 221
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 13 + 21 = 34
T = 12
D = 34 * 12 = 408
Answer:B
Answer: (B) 408
Question: Water boils at 212°F or 100°C and ice melts at 32°F or 0°C . If the temperature of a pot of water is 60°C, what is the temperature of the pot of water in °F?
(A) 132°F
(B) 140°F
(C) 148°F
(D) 156°F
(E) 164°F
Rationale: Let F and C denote the temperature in Fahrenheit and Celsius respectively.
(F - 32) /(212 - 32) = (C - 0)/(100 - 0)
F = 9C/5 + 32
F = 9(60)/5 + 32 = 140°F
The answer is B.
Answer: (B) 140°F
Question: A person invested in all Rs. 2600 at 4%, 6% and 8% per annum simple interest. At the end of the year, he got the same interest in all the three cases. The money invested at 4% is?
(A) 3477
(B) 2688
(C) 2699
(D) 1200
(E) 2671
Rationale: Let the parts be x, y and [2600 - (x + y)].
Then,
(x * 4 * 1)/100 = (y * 6 * 1)/100 = {[2600 - (x + y)] * 8 * 1}/100
y/x = 4/6 = 2/3 or y = 2/3 x
So, (x * 4 * 1)/100 = [(2600 - 5/3 x) * 80/100
52x = (7800 * 8) => x = 1200
Money invested at 4% = Rs. 1200.
Answer:D
Answer: (D) 1200
Question: A bag contains 26 purple jellybeans, 15 green jellybeans, and 9 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 yellow?
(A) 18%
(B) 20%
(C) 25%
(D) 30%
(E) 35%
Rationale: p = 26 , g=15 , y=9
total = 50
p(yellow)=(9/50)*100 = 18% . Ans = A
Answer: (A) 18%
Question: In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 48. What is the total number of students in the school?
(A) 72
(B) 80
(C) 120
(D) 100
(E) 150
Rationale: Let the number of students be x. Then,
Number of students above 8 years of age = (100 - 20)% of x = 80% of x.
80% of x = 48 +2/3of 48
(80/100)x = 80
x = 100.
ANSWER D
Answer: (D) 100