mathewhe/aqua_rat huggingface dataset:
Question: M = {-6, -5, -4, -3, -2}
T = {-2, -1, 1, 2, 3}
If an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative?
(A) 0
(B) 1/3
(C) 2/5
(D) 1/2
(E) 3/5
Rationale: Answer E.
Total # of outcomes: 5*5= 25
# of outcomes where Product is -ve : (-6,1) ,(-6,2), (-6,3)... Hence, total: 15
Probability: 15/25 = 3/5
Answer: (E) 3/5
Question: When positive integer x is divided by positive integer y, the result is 59.32. What is the sum T of all possible 2-digit remainders for x/y?
(A) 560
(B) 616
(C) 672
(D) 728
(E) 784
Rationale: ans B 616...
remainders = .32=32/100=8/25=16/50 and so on..
so two digit remainders are 16+24+32+....+96..
T=8(2+3+4....+12)=616.B
Answer: (B) 616
Question: A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 4 hours. Working alone, the outlet pipe can empty out the tank in 10 hours. If it is desired that the tank should be filled, from empty, exactly 6 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ?
(A) 8:30am
(B) 9:30am
(C) 10:00am
(D) 10:30am
(E) 11:30am
Rationale: In 6 hours the inlet pipe will pump in water equal to 6*1/4 = 6/4 of the pool. So, 2/4 more than necessary, which should be compensated by the outlet pipe. To pump out 2/4 of the water the outlet pipe needs 20/4 = 5 hours.
Therefore, the outlet pipe should be opened at 9:30am + 6 hours - 5 hours = 10:30am.
Answer: D
Answer: (D) 10:30am
Question: In a mixture of 60 liters, the ratio of milk and water is 2:1. What amount of water must be added to make the ratio of milk and water as 1:2?
(A) 60
(B) 88
(C) 77
(D) 66
(E) 44
Rationale: 2:1 --- 60
1:2
2:4
---------------
3
3 ----------- 60
3 ----------- ? => 60 liters
Answer:A
Answer: (A) 60
Question: If st > 0, which of the following must be negative?
(A) -s/t
(B) st
(C) -s*-t
(D) -s/-t
(E) s+t
Rationale: Given st> 0 So both will be the positive integers. If both are positive, then B,C,D,E also positive.
Answer :A
Answer: (A) -s/t
Question: If the cost price is 92% of sp then what is the profit %
(A) 8.70%
(B) 8.60%
(C) 8.10%
(D) 8.30%
(E) 8.27%
Rationale: Sol. sp=Rs100 : then cp=Rs 92:profit =Rs 8.
Profit={(8/92)*100}%=8.70%
Answer is A.
Answer: (A) 8.70%
Question: What is the are of an equilateral triangle of side 10 cm?
(A) 66âˆš3 cm2
(B) 25âˆš3 cm2
(C) 64âˆš3 cm2
(D) 64âˆš5 cm2
(E) 14âˆš3 cm2
Rationale: Area of an equilateral triangle = âˆš3/4 S2
If S = 10, Area of triangle = âˆš3/4 * 10 * 10 = 25âˆš3 cm2;
Answer:B
Answer: (B) 25âˆš3 cm2
Question: The product of HCF and LCM of 18 and 15 is
(A) 120
(B) 150
(C) 175
(D) 270
(E) 190
Rationale: HCF of 18 and 15
18 = 2 x 3 x 3
15 = 3 x 15 = 3
LCM of 18 and 15 = 2 x 3 x 3 x 5 = 90
∴ Product of HCF and LCM of both numbers = 3 x 90 = 270
ANSWER :D
Answer: (D) 270
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red?
(A) 12/455
(B) 12/458
(C) 12/487
(D) 12/456
(E) 12/4512
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
When three marbles are drawn, the probability that one is yellow and two are red
= (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13)
= 12/455
Answer:A
Answer: (A) 12/455
Question: When a student Joe, weighing 45 kg, joins a group of students whose average weight is 30 kg, the average weight goes up by 1 kg. Subsequently, if two students, excluding Joe, leave the group the average weight comes back to 30 kg. What is the difference between the average weight of the two students who left and the weight of Joe?
(A) 7.5 kg
(B) 11 kg
(C) 30 kg
(D) 36.5 kg
(E) 71 kg
Rationale: After two persons leave the group the average remains the same. That means the weight of the two persons = 45+30 = 75
So, the average the two persons = 37.5
That gives the answer 45-37.5 = 7.5
ANswer A
Answer: (A) 7.5 kg
Question: A number when divided by a certain divisor left remainder 251, when twice the number was divided by the same divisor, the remainder was 112. Find the divisor?
(A) 370
(B) 365
(C) 390
(D) 456
(E) 460
Rationale: Easy solution:
N= Dq1+251
2N = 2Dq1 + 502 - (1)
2N = Dq2 + 112 - (2)
As (1) = (2) = 2N
D*(q2-2q1) = 390
D * Some integer = 390
Checking all options only (C) syncs with it.
Answer C
Answer: (C) 390
Question: A man sold 20 articles for $60 and gained 20%. How many articles should he sell for $60 to incur a loss 20%?
(A) 30
(B) 36
(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%: $60*(100% + 20%) = $72
Number of articles to be sold for $72 to incur a 20% loss: $72 / $2.40 = 30
Thus, solution A is correct.
Answer: (A) 30
Question: How many shots of 1cm radius can be prepared from a sphere of 4cm radius?
(A) 33
(B) 88
(C) 27
(D) 64
(E) 99
Rationale: 4/3 Ï€ * 4 * 4 * 4 = 4/3 Ï€ * 1 * 1 * 1 * x
x = 64
Answer: D
Answer: (D) 64
Question: A man purchased a cow for Rs. 3000 and sold it the same day for Rs. 3600, allowing the buyer a credit of 2 years. If the rate of interest be 10% per annum, then the man has a gain of:
(A) 0%
(B) 1%
(C) 2%
(D) 3%
(E) 4%
Rationale: C.P. = Rs. 3000.
S.P. = Rs.	(3600 x 100)/(100 + (10 x 2))= Rs. 3000.
Gain = 0%.
answer :A
Answer: (A) 0%
Question: Four usual dice are thrown on the ground. The total of numbers on the top faces of these four dice is 13 as the top faces showed 4, 3, 1 and 5 respectively. What is the total of the faces touching the ground?
(A) 22
(B) 37
(C) 15
(D) 99
(E) 26
Rationale: Explanation:
In a usual dice, the sum of the numbers on any two opposite faces is always 7. Thus, 1 is opposite 6, 2 is opposite 5 and 3 is opposite 4.
Consequently, when 4, 3, 1 and 5 are the numbers on the top faces, then 3, 4, 6 and 2 respectively are the numbers on the face touching the ground. The total of these numbers = 3 + 4 + 6 + 2 = 15.
Answer: C) 15
Answer: (C) 15
Question: M is a certain set of numbers with an average (arithmetic mean) of 10 and a standard deviation of 1. Q is a subset of M consisting of 5 terms. Exactly 80% of the numbers in Q are located within 2 standard deviations from the average of M. Which of the following could Q be?
(A) {3, 4, 5, 10, 14}
(B) {3, 6, 7, 10, 12}
(C) {3, 5, 5, 10, 16}
(D) {1, 5, 7, 10, 12}
(E) {5, 8, 9, 10, 12}
Rationale: Exactly 80% of the numbers in Q, so 4 out of 5 numbers are from 10 - 2*{SD} = 8 to 10 + 2*{SD} = 12.
A. {3, 4,5, 10, 14} --> only 1 number is in this range. Discard.
B. {3,6, 7, 10, 12} --> only 2 numbers are in this range. Discard.
C. {3,5, 5, 10, 16} --> only 1 number is in this range. Discard.
D. {1,5, 7, 10, 12} --> only 2 numbers are in this range. Discard.
E. {5, 8, 9, 10, 12} --> 4 numbers are in this range. OK.
Answer:E.
Answer: (E) {5, 8, 9, 10, 12}
Question: On increasing the number of lines in a page by 100, they become 240. What is the % of increase in the no. of lines in the page?
(A) 20%
(B) 305
(C) 50%
(D) 71.4%
(E) 60%
Rationale: Explanation : Number of pages increased = 100
Now , the number of pages of book = 240
Number of pages of the books before increase = 240 – 100 = 140
% increase in the number of pages in the book = 100 /140
x 100% = 71.4%
D
Answer: (D) 71.4%
Question: A man has $480 in the denominations of one-Dollar, five-Dollar notes and ten-Dollar. The number of Dollars of each denomination is equal. What is the total number of Dollar that he has ?
(A) 50
(B) 60
(C) 90
(D) 48
(E) 67
Rationale: C
$90
Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
16x = 480
x = 30.
Hence, total number of notes = 3x = 90.
Answer: (C) 90
Question: Car A runs at the speed of 65km/hr & reaches its destination in 8hr. Car B runs at the speed of 72 km/h & reaches its destination in 4h. What is the respective ratio of distances covered by Car A & Car B?
(A) 11 : 6
(B) 12 : 7
(C) 13 : 7
(D) 65 : 36
(E) 13 : 6
Rationale: Sol. Distance travelled by Car A = 65 Ã— 8 = 520 km
Distance travelled by Car B = 72 Ã— 4 = 288 km
Ratio = 520/288 = 65 : 36
D
Answer: (D) 65 : 36
Question: The side of a square is increased by 25% then how much % does its area increases?
(A) 55.2 %
(B) 10 %
(C) 15 %
(D) 56.25 %
(E) 18 %
Rationale: Explanation:
a = 100 a2 = 10000
a = 125 a2 = 15625
----------------
10000 --------- 5625
100 -------? => 56.25 %
Answer : D
Answer: (D) 56.25 %
Question: When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 24, what is the remainder when k is divided by 7?
(A) 2
(B) 5
(C) 6
(D) 3
(E) 8
Rationale: Cant think of a straight approach but here is how I solved it:
K is divided by 5 and remainder is 2. This means k = 5n + 2 (n is an integer)
so the possible values of K = {2, 7, 12, 17, 22} (less than 24)
Secondly, if K is divided by 6, the remainder is 5 => k= 6m + 5
so the possible value set for k = {5, 11, 17, 23} (less than 24)
17 is the only common number in both the sets. Hence k = 17
Answer : D
Answer: (D) 3
Question: Health insurance Plan C requires the insured to pay $1000 or 50% of total cost, whichever is lower. Plan B requires the insured to pay the initial $300, but then pays 80% of the cost over $300. Which of the following is a cost level for which both insurance plans pay out the same amount?
(A) $600
(B) $1000
(C) $3800
(D) $5300
(E) $6200
Rationale: 0.5 * 600 = 300 where C = B.
Answer: (B) $1000
Question: Which of these fractions is equivalent to 15
25?
(A) 3/4
(B) 2/3
(C) 3/5
(D) 1/2
(E) 5/7
Rationale: Both the numerator and the denominator are divisible by 5.
Dividing, we get 15/25 = 15/5/25/5 = 3/5 . Therefore, 15/25 is equivalent to 3/5 .
correct answer C
Answer: (C) 3/5
Question: The average of 10 numbers is calculated as 15. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
(A) 16
(B) 18
(C) 19
(D) 22
(E) 24
Rationale: Explanation:
10 * 15 + 36 – 26 = 160/10 = 16
A)
Answer: (A) 16
Question: In an examination 40% failed in Hindi, 45% failed in English. If 25% students failed in both the subjects. Then the percentage of failed students is?
(A) 60
(B) 20
(C) 25
(D) 30
(E) 40
Rationale: 15+25+20 = 60
ANSWER A
Answer: (A) 60
Question: If A lends Rs.3500 to B at 10% per annum and B lends the same sum to C at 14% per annum then the gain of B in a period of 3 years is?
(A) 400
(B) 410
(C) 460
(D) 420
(E) 430
Rationale: (3500*4*3)/100 => 420
Answer: D
Answer: (D) 420
Question: 4/[(1/0.03) + (1/0.37)] = ?
(A) 0.004
(B) 0.11111
(C) 2.775
(D) 3.6036
(E) 36.036
Rationale: Approximate.
1/.03 = 100/3 = 33
1/.37 = 100/37 = 3
Denominator becomes 33 + 3 = 36
4/36 = .1111
Answer (B)
Answer: (B) 0.11111
Question: In an examination 60% failed in Math and 40% failed in French. If 32% failed in both. What % of students passed in both.
(A) 25%
(B) 15%
(C) 20%
(D) 32%
(E) 10%
Rationale: Passed in Math = 100 - 60 = 40%
Passed in French = 100 - 40 = 60%
Students who passed Math or French = 100 -32 = 68%
Students passed in Math and French = (Passed in Math) + (Passed in French) - (Students who passed Math or French) = 60+40-68 =32%
ANSWER:D
Answer: (D) 32%
Question: If y exceeds x by 30%, then x is less than y by?
(A) 23 2/8%
(B) 16 8/3%
(C) 23 1/13%
(D) 76 2/3%
(E) 23 2/3%
Rationale: X=100	y=130
130------30
100-------? => 23 1/13%
Answer:C
Answer: (C) 23 1/13%
Question: The average of 11 results is 40, if the average of first five results is 49 and that of the last seven is 52. Find the fifth result?
(A) 165
(B) 166
(C) 167
(D) 168
(E) 169
Rationale: 1 to 11 = 11 * 40 = 440
1 to 5 = 5 * 49 = 245
5 to 11 = 7 * 52 = 364
5th = 245 + 364 – 440 = 169
ANSWER:E
Answer: (E) 169
Question: John started a business, investing Rs.18000. After 3 months and 4 months respectively, Rose and Tom joined him with capitals of 12000 and 9000. At the end of the year the total profit was Rs.3982. What is the difference between Rose ’s and Tom ’s share in the profit?
(A) Rs.340
(B) Rs.362
(C) Rs.370
(D) Rs.382
(E) Rs.390
Rationale: John : Rose : Tom
Ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8
= 6 : 3: 2
The difference between Rose’s and Tom’s share = 1 share
:.i.e. = Rs. 3982 × 1/11 = Rs.362.
B)
Answer: (B) Rs.362
Question: A computer factory produces 6048 computers per month at a constant rate, how many computers are built every 30 minutes assuming that there are 28 days in one month?
(A) 2.25.
(B) 3.125.
(C) 4.5.
(D) 5.225.
(E) 6.25.
Rationale: Number of hours in 28 days = 28*24
Number of 30 mins in 28 days = 28*24*2
Number of computers built every 30 mins = 6048/( 28*24*2) = 4.5
Answer C
Answer: (C) 4.5.
Question: The volume of a cube is 1000 cc. Find its surface.
(A) 864
(B) 556
(C) 255
(D) 600
(E) 267
Rationale: a3 = 1000 => a = 10
6a2 = 6 * 10 * 10 = 600
Answer:D
Answer: (D) 600
Question: A thief goes away with a SANTRO car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start?
(A) 22 hours
(B) 21 hours
(C) 23 hours
(D) 20 hours
(E) 28 hours
Rationale: D
20 hours
|-----------20--------------------|
50 40
D = 20
RS = 50 – 40 = 10
T = 20/10 = 2 hours
Answer: (D) 20 hours
Question: A 2015 model car had an average mileage of 38 miles per gallon, when the car wight was 180 kilograms. An upgraded version of the car in 2016 gave a mileage of 43 miles per gallon and the car weight was reduced to 150 kilograms. By approximately what percent did the mileage of the car to the weight of the car improve?
(A) 28
(B) 43
(C) 36
(D) 19
(E) 37
Rationale: Initial mileage/weight ratio = 38/180 = 190/900
Revised mileage/weight ratio = 43/150 = 258/900
Answer: C
Answer: (C) 36
Question: A and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 11 a.m.?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 15
Rationale: Relative speed = Speed of A + Speed of B (? they walk in opposite directions)
= 2 + 3 = 5 rounds per hour
=> They cross each other 5 times in 1 hour
Time duration from 8 am to 11 am = 3 hours
Hence they cross each other 15 times before 11 am
Answer is E
Answer: (E) 15
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 1100 m long?
(A) 200 Sec
(B) 230 Sec
(C) 167 Sec
(D) 197 Sec
(E) 179 Sec
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 2300 m
T = D/S
T = 2300/10
T = 230 Sec
Answer: B
Answer: (B) 230 Sec
Question: A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What is the probability that first is white and second is black?
(A) 21/115
(B) 36/145
(C) 31/111
(D) 11/154
(E) 11/151
Rationale: The probability that first ball is white:
=12C130C1=12C130C1
=1230=1230
=25=25
Since, the ball is not replaced; hence the number of balls left in bag is 29.
Hence, the probability the second ball is black:
=18C129C1=18C129C1
=1829=1829
Required probability,
=(25)×(1829)=(25)×(1829)
=36/145
B
Answer: (B) 36/145
Question: The ratio between the sale price and the cost price of an article is 9:5. What is the ratio between the profit and the cost price of that article?
(A) 23
(B) 1:2
(C) 4:5
(D) 3:5
(E) 25
Rationale: C.P. = Rs. 5x and S.P. = Rs. 9x.
Then, Gain = Rs. 4x
Required ratio = 4x : 5x = 4:5
C
Answer: (C) 4:5
Question: John purchased a grinder and a mobile for Rs. 15000 &Rs. 8000 respectively. He sold the grinder at a loss of 4% and the mobile phone at a profit of 20%. Overall how much he make aprofit.
(A) s. 190
(B) s. 1120
(C) s. 1200
(D) s. 1250
(E) s. 1290
Rationale: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 4/100) = 15000 - 600
m = 8000(1 + 20/100) = 8000 + 1600
Total SP - Total CP = r + m - (15000 + 8000) = -600 + 1600 = Rs. 1200
As this is positive, an overall profit of Rs. 1200 was made.
C
Answer: (C) s. 1200
Question: How many numbers from 10 to 47 are exactly divisible by 3?
(A) 12
(B) 15
(C) 16
(D) 17
(E) 18
Rationale: 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45,.
12 Numbers.
10/3 = 3 and 47/3 = 15 ==> 15 - 3 = 12. Therefore 12 digits
A)
Answer: (A) 12
Question: If n is an integer and 101n^2 is less than or equal to 3600, what is the greatest possible value of n?
(A) 7
(B) 5
(C) 9
(D) 10
(E) 11
Rationale: 101 * n^2 <=3600
n^2 <=3600/101 which will be less than 81 since 3600/100 = 36 which is the square of 9
Next closest value of n where n^2<=36 is 5
Ans B
Answer: (B) 5
Question: A man saves Rs 350 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 1159.54
(B) Rs 1158.54
(C) Rs 1158.78
(D) Rs 1158.88
(E) None of these
Rationale: Explanation:
=[350(21/20Ã—21/20Ã—21/20)+350(21/20Ã—21/20)+350(21/20)]=1158.54
Option B
Answer: (B) Rs 1158.54
Question: A farmer is planting a row consisting of 3 unique apple trees and 3 unique orange trees. How many ways are there for the farmer to plant the trees such that no apple tree is adjacent to another apple tree and no orange tree is adjacent to another orange tree?
(A) 72
(B) 576
(C) 1,024
(D) 1,152
(E) 10,080
Rationale: 2 possible arrangements are possible
AOAOAOAO
OAOAOAOA
2 unique type of trees are present consisting of 4 trees each
4 apple trees can be arranged in 4! ways
4 orange trees can be arranged in 4! ways
as 2 arrangements are possible
total arrangements = 2 *3! * 3! = 72
correct answer option A
Answer: (A) 72
Question: .The price of commodity P increases by 40 paise every year, while the price of commodity Q increases by 15 paise every year. If in 2001, the price of commodity P was Rs. 4.20 and that of Q was Rs. 6.30, in which year commodity P will cost 40 paise more than the commodity Q ?
(A) 2008
(B) 2009
(C) 2010
(D) 2011
(E) None of these
Rationale: Explanation :
Let the commodity P costs 40 paise more than the commodity Q after n years
Price of the commodity P in 2001 = Rs.4.20
Since the price of the commodity P increases by Rs 0.40 every year,
Price of the commodity P after n years from 2001 = Rs.4.20 + (n × .40)
Price of the commodity Q in 2001 = Rs.6.30
Since the price of the commodity Q increases by Rs 0.15 every year,
price of the commodity Q after n years from 2001 = Rs.6.30 + (n × .15)
Since the commodity P costs Rs. 0.40 more that the commodity Q after n years from 2001,
4.20 + (n × .40) = 6.30 + (n × .15) + 0.40
=> (40n - .15n) = 6.30 - 4.20 + 0.40 = 2.5
=> .25n = 2.5
⇒ n = 2.5/.25 = 250/25 = 101.15¯
=> Commodity P costs Rs.0.40 more that the commodity Q after 10 years from 2001. i.e., in 2011. Answer : Option D
Answer: (D) 2011
Question: If f(2, 4) = 24 and f(1, 5) = 26, what is the value of f(2, 6)?
(A) 107
(B) 127
(C) 44
(D) None of these
(E) Cannot be determined
Rationale: Solution:
The function f(a, b) = a3 + b2
f(2, 4) therefore is = 8 + 16= 24 and
f(1,5) = 1 +25= 26
Therefore, f(2, 6) = 8 + 36 = 44
Answer C
Answer: (C) 44
Question: At what rate percent of simple interest will a sum of money double itself in 12 years?
(A) 8 1/7 %
(B) 8 1/3 %
(C) 8 7/3 %
(D) 6 1/3 %
(E) 8 9/3 %
Rationale: Let sum = x. Then, S.I. = x.
Rate = (100 * S.I.) / (P * T) = (100 * x) / (x * 12)
= 25/3 = 8 1/3 %
Answer: B
Answer: (B) 8 1/3 %
Question: For all numbers a and b, the operationis defined by ab = (a + 2)(b – 3).
If 3x = –25, then x =
(A)  –15
(B)  –2
(C)  -3
(D)  6
(E)  15
Rationale: (3+2)(x-3)=-25..
x-3=-5..
x=-2
B
Answer: (B)  –2
Question: A person travels from P to Q a speed of 60 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips?
(A) 33
(B) 75
(C) 48
(D) 99
(E) 21
Rationale: Speed on return trip = 150% of 60 = 90 km/hr.
Average speed of trip = 60 + 90 /2 = 150/2 = 75 km/hr
Answer : B
Answer: (B) 75
Question: There are 8 books in a shelf that consist of 1 paperback books and 7 hardback books. If 4 books are selected at random without replacement, how many different combinations are there that at least one paperback book is selected?
(A) 35
(B) 45
(C) 50
(D) 55
(E) 60
Rationale: 8C4 [Select any four] - 7C4 [Select all hard backs] = 35.
A
Answer: (A) 35
Question: At an upscale fast-food restaurant, Shin can buy 3 burgers, 7 shakes, and one cola for $120. At the same place it would cost $158.50 for 4 burgers, 10 shakes, and one cola. How much would it cost for a meal of one burger, one shake, and one cola?
(A) $21
(B) $27
(C) $31
(D) $43
(E) It cannot be determined
Rationale: let's suppose that the price of a burger is BB, of a shake - SS and that of a cola is CC. We can then construct these equations:
3B+7S+C=120
4B+10S+C=158.5
Subtracting the first equation from the second gives us B+3S=38.5
Now if we subtract the new equation two times from first or 3 times from second we will get B+S+C=43. In any case, there is no necessity to know each item's price, just the sum.
Answer: D
Answer: (D) $43
Question: In a group of buffaloes and ducks, the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: let no. of buffaloes be x & no. of ducks be y
buffaloes have 4 legs while ducks have 2
4x + 2y = 2*(x + y) + 24
=> 4x + 2y - 2x - 2y = 24
=> x = 12
number of buffaloes in the group = 12
ANSWER:A
Answer: (A) 12
Question: The distance between Delhi and Mathura is 110 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?
(A) 10.30 a.m.
(B) 10.00 a.m.
(C) 9.30 a.m.
(D) 9.00 a.m.
(E) 9.45 a.m.
Rationale: Explanation:
D = 110 â€“ 20 = 90
RS = 20 + 25 = 45
T = 90/45 = 2 hours
8 a.m. + 2 = 10 a.m.
ANSWER IS B
Answer: (B) 10.00 a.m.
Question: After decreasing 80% in the price of an article costs Rs.320. Find the actual cost of an article?
(A) 2777
(B) 2987
(C) 1200
(D) 9977
(E) 1600
Rationale: CP* (20/100) = 320
CP= 16* 100 => CP = 1600
Answer: E
Answer: (E) 1600
Question: After M students took a test, the average score was 74%. If the test has 50 questions, what is the least number of questions that the next student has to get right to bring the average score up to 75%?
(A) 0.5M + 37
(B) M + 0.74
(C) 0.75M - 0.5
(D) 0.5M + 37.5
(E) 37-0.5M
Rationale: The total number of correct answers for M students is (0.74)*50*M=37*M
For an average of 75%: (total correct answers) / (M+1) = 0.75*50=37.5
Let x be the number of correct answers for the next student.
(x + 37M) / M+1 = 37.5
x + 37M= 37.5M+37.5
x = 0.5M + 37.5
The answer is D.
Answer: (D) 0.5M + 37.5
Question: A can do a piece of work in 12 days. He worked for 15 days and then B completed the remaining work in 10 days. Both of them together will finish it in?
(A) 12 1/2 days
(B) 12 1/8 days
(C) 12 6/2 days
(D) 16 1/2 days
(E) 12 2/2 days
Rationale: 15/25 + 10/x = 1 => x = 25
1/25 + 1/25 = 2/25
25/2 = 12 1/2 days
Answer: A
Answer: (A) 12 1/2 days
Question: A class contains five juniors and five seniors. If one member of the class is assigned at random to present a paper on a certain subject, and another member of the class is randomly assigned to assist him, what is the probability Q that both will be juniors?
(A) 1/10
(B) 1/5
(C) 2/9
(D) 2/5
(E) 1/2
Rationale: I think you're right. The other way to do it (but the long way) is to figure out the probability that it is not two Juniors.
2 seniors = P(Senior) * P(Senior) = 2/9
1 Senior and 1 Junior = (1/2) *(5/9)*2 = 5/9
Probability that it is not two Juniors is 5/9+2/9 = 7/9 so the probability Q that it is two juniors is 1- (7/9) = 2/9.C
Answer: (C) 2/9
Question: A certain chocolate bar manufacturer reduced the weight of Chocolate Bar M by 20 percent buy left the price unchanged. What was the resulting percent increase in the price per ounce of chocolate Bar M?
(A) 20
(B) 24
(C) 25
(D) 28
(E) 30
Rationale: assume 1oz candy cost $1 before.
now price remain same $1 but weight of candy reduces to 0.8 oz
new price of candy = 1/0.8 =1.25
price increase 25 %
C
Answer: (C) 25