mathewhe/aqua_rat huggingface dataset:
Question: A works twice as fast as B.If B can complete a work in 12 days independently,the number of days in which A and B can together finish the work is :
(A) 4 days
(B) 6 days
(C) 8 days
(D) 18 days
(E) None of these
Rationale: Solution
Rates of worktio of raing of A and B = 2: 1.So, ratio of times taken = 1: 2
∴ A’s 1 day’s work = 1/6 B’s 1 day’s work =1/12
(A + B)'s 1 day’s work =(1/6 + 1/12)= 3/12=1/4
So,A and B together can finish the work in 4 days.
Answer A
Answer: (A) 4 days
Question: The total of the ages of Amar, Akbar and Anthony is 66 years. What was the total of their ages four years ago ?
(A) 71
(B) 44
(C) 54
(D) 16
(E) 18
Rationale: Explanation:
Required sum = (66 - 3 x 4) years = (66 - 12) years = 54 years.
Answer: C
Answer: (C) 54
Question: what is rate of interest if principal.amount be 400,simple interest 100 and time 2year.
(A) 10
(B) 12.5
(C) 25
(D) 12
(E) 14.5
Rationale: s.i=(p*r*t)/100
100=800r/100
r=100/8=12.5%
answer B
Answer: (B) 12.5
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 purple?
(A) 15%
(B) 20%
(C) 25%
(D) 43%
(E) 52%
Rationale: p = 26 , g=15 , y=9
total = 50
p(purple)=(26/50)*100 = 52% . Ans = E
Answer: (E) 52%
Question: If x and y are positive integers, Choose which of the following CANNOT be the greatest common divisor of 15x and 20y?
(A) 5
(B) 5(x-y)
(C) 20x
(D) 20y
(E) 35x
Rationale: We are looking for a choice that CANNOT be the greatest common divisor of 15x and 20y ...which means 15x and 20y when divided by the answer choice the quotient should not be a integer.
lets check
a. 5 15x/5 = 3x and 20y/5 = 4y both are integers so eliminate
b. 5(x-y) when x = 2 and y = 1 it could be be the greatest common divisor ..so eliminate
c. 20x when x = 1 its 20 and 20 cannot be the greatest common divisor of 35x and 20y ...
or 15x/20x = 3/4 which is not a integer.
so answer is C.
Answer: (C) 20x
Question: If (x/y)=(6/5), find the value (x^2+y^2)/(x^2-y^2)
(A) 61/11
(B) 59/11
(C) 51/77
(D) 41/11
(E) None of them
Rationale: = (x^2+y^2)/(x^2-y^2) = ( x^2 /y^2+ 1)/ ( x^2 /y^2-1) = [(6/5)^2+1] / [(6/5)^2-1]
= [(36/25)+1] / [(36/25)-1] = (61*25)/(25*11) = 61/11
Answer is A.
Answer: (A) 61/11
Question: Q:Robert purchased $1500 worth of US saving bonds. If bonds are sold in $50 or $100 denominations only, which of the following CANNOT be the number of US saving bonds that Robert purchased?
(A) 10
(B) 20
(C) 27
(D) 30
(E) 40
Rationale: I started off with looking at the answer choices... 10-20-27-30 are in a tight range, so my guess was to look and rule out the bigger numbers.
The total amount is $1500. So with 40 bonds, each $50 = $2000 , we already exceed the $1500 limit. Hence E is the answer.
Answer: (E) 40
Question: The smallest number which when diminished by 7, is divisible by 12, 16, 18, 21 and 28 is
(A) 1008
(B) 1015
(C) 1022
(D) 1032
(E) None
Rationale: Solution
Required numbers	=(L.C.M of 12,16,18,21,28) + 7
‹=›1008 + 7
= 1015.
Answer B
Answer: (B) 1015
Question: There are 12 teams in a certain league and each team plays each of the other teams exactly once. What is the total number of games played?
(A) 55
(B) 66
(C) 77
(D) 88
(E) 99
Rationale: 12C2 = 66
The answer is B.
Answer: (B) 66
Question: Difference between the length &breadth of a rectangle is 26 m. If its perimeter is 208 m, then the ratio of area and perimeter is?? We have: (l - b) = 26 and 2(l + b) = 208 or (l + b) = 104?
(A) 315:26
(B) 315:25
(C) 315:30
(D) 415:35
(E) 425:35
Rationale: Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m^2 The required ratio is 2520 :208 =315 :26
A
Answer: (A) 315:26
Question: Miraa is making telescopes, each consisting of 2 lenses, 1 tube, and 1 eyepiece. Lenses can be purchased only in packs of 50, tubes only in packs of 10, and eyepieces only in packs of 30. However, half of the lenses in each pack are not usable for telescopes. If all parts are used only for the telescopes, what is the minimum number of lenses Miraa must purchase to make a set of telescopes with no leftover components other than the unusable lenses?
(A) 75
(B) 150
(C) 3000
(D) 600
(E) 7,500
Rationale: I'd use backsolving for this question.
Check C:
3000 lenses = 1500 usable lenses = 750 tubes = 750 eyepieces. We CAN buy 750 tubes and 750 eyepieces, so that not to have leftovers.
Answer: C.
Answer: (C) 3000
Question: A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:
(A) No profit, no loss
(B) 5%
(C) 8%
(D) 10%
(E) 11%
Rationale: Explanation:
C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600.
S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.
Gain =80/100X100%=5%
ANSWER IS B
Answer: (B) 5%
Question: The Arnolds purchased 550 square feet of Kentucky Gem sod at $1.79 per square foot and 270 square feet of Zelzea Blue sod at $1.38 per square foot. What was the approximate average price per square foot paid for all the sod?
(A) $1.63
(B) $1.64
(C) $1.66
(D) $1.72
(E) $1.76
Rationale: Average price = (550*1.79)+(270*1.38)/550+270=1.66 (Approx)
Answer C
Answer: (C) $1.66
Question: find value for x from below equation? x + 1 = 4
(A) -5
(B) -4
(C) 4
(D) 3
(E) 2
Rationale: 1. Subtract 1 from both sides:
x + 1 - 1 = 4 - 1
2. Simplify both sides:
x = 3
D
Answer: (D) 3
Question: Today my car meter reads as 72527 kms. I notes that this is a palindrome. How many minimum kms i need to travel so my car meter find another palindrom.
(A) 100 kms
(B) 115 kms
(C) 110 kms
(D) 210 kms
(E) 100 kms
Rationale: E
100 kms
72527+100 = 72627 , a palindrome
Answer: (E) 100 kms
Question: Working alone at its constant rate, pump M pumped out ¼ of the water in a tank in 2 hours. Then pumps N and O started working and the three pumps, working simultaneously at their respective constant rates, pumped out the rest of the water in 3 hours. If pump N, working alone at its constant rate, would have taken 18 hours to pump out the rest of the water, how many hours would it have taken pump O, working alone at its constant rate, to pump out all of the water that was pumped out of the tank?
(A) 6
(B) 12
(C) 15
(D) 18
(E) 24
Rationale: Rate of pump M = 1/8
3 hours are required to pump out the remaining (3/4)ths of tank --> 1 hr to pump out 1/4
Rate of M + Rate of N + Rate of O = 1/4
Rate of N + Rate of O = 1/4 - 1/8 = 1/8
N takes 18 hours to pump out the remaining (3/4)ths of tank --> 6 hrs per (1/4)ths --> 24 hrs to pump out fully.
Rate of N = 1/24
1/24 + Rate of O = 1/8
Rate of O = 1/8 - 1/24 = 1/12
Time required to pump out all the water by O = 12 hrs
Answer: B
Answer: (B) 12
Question: A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the cycle?
(A) Rs. 1090
(B) Rs. 1160
(C) Rs. 1190
(D) Rs. 1202
(E) Rs. 1406
Rationale: S.P. = 85% of Rs. 1400 = Rs. (85/100)	x 1400 = Rs. 1190
Answer: Option C
Answer: (C) Rs. 1190
Question: What is the units digit of (6!*4! + 6!*5!)/6?
(A) 1
(B) 0
(C) 2
(D) 3
(E) 4
Rationale: (6!*4! + 6!*5!)/6
=6!(4! + 5!)/6
=720 ( 24 + 120)/6
=(720 * 144)/6
= 720 * 24
Units digit of the above product will be equal to 0
Answer B
Answer: (B) 0
Question: How many of the following numbers are divisible by 132?
264, 396, 462, 792, 968, 2178, 5808, 6336
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: A number is divisible by 132, if it is divisible by each one of 11, 3 and 4.
Clearly, 968 is not divisible by 3. None of 462 and 2178 is divisible by 4.
Each one of remaining 5 is divisible by each one of 11, 3 and 4 and therefore, by 132.
ANSWER:B
Answer: (B) 5
Question: Little John had $8.50. He spent $1.25 on sweets and gave to his two friends $1.20 each. How much money was left?
(A) $3.85
(B) $4.85
(C) $5.85
(D) $2.85
(E) $1.85
Rationale: John spent and gave to his two friends a total of
1.25 + 1.20 + 1.20 = $3.65
Money left
8.50 - 3.65 = $4.85
correct answer is B) $ 4.85
Answer: (B) $4.85
Question: On his deathbed, a father called upon his three sons and told them to distribute all his assets worth Rs. 52,500 in the ratio of 1/15 : 1/21 : 1/35 amongst themselves. Find the biggest share amongst the three portions.
(A) Rs. 2,75,000
(B) Rs. 2,45,000
(C) Rs. 1,10,500
(D) Rs. 1,13, 250
(E) Rs. 1,15, 250
Rationale: The ratio of distribution should be:
21 x 35 : 15 x 35 : 15 x 21
= 147 : 105 : 63
= 7 : 5 : 3
The largest share will be worth:
7/15 x 525000 = Rs. 2,45,000
ANSWER:B
Answer: (B) Rs. 2,45,000
Question: In what proportion must rice at Rs 3.10 per kg be mixed with rice at Rs 3.75 per kg, so that the mixture be worth Rs 3.25 a kg?
(A) 7/3
(B) 5/3
(C) 10/3
(D) 3/7
(E) 11/5
Rationale: C.P of 1 kg of cheaper rice = Rs 3.10
C.P of 1 kg of expensive rice = Rs 3.75
the mixture be worth for 1 kg = Rs 3.25
By the alligation rule : Quantity of cheaper rice / Quantity of expensive rice
= (3.75 - 3.25)/(3.25 - 3.10)
= (0.50)/(0.15)
= 10/3
C
Answer: (C) 10/3
Question: If {x} is the product of all even integers from 1 to x inclusive, what is the greatest prime factor of {26} + {24}?
(A) 23
(B) 20
(C) 27
(D) 5
(E) 2
Rationale: Soln:
{26} + {24} = 26*{24} +{24} = 27*{24}
ANSWER:C
Answer: (C) 27
Question: Find the number that fits somewhere into the middle of the series. Some of the items involve both numbers and letters
Look at this series: J14, L16, __, P20, R22, ... What number should fill the blank?
(A) S16
(B) B29
(C) N18
(D) T34
(E) M45
Rationale: C
N18
In this series, the letters progress by 2, and the numbers increase by 2.
Answer: (C) N18
Question: If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players?
(A) 986
(B) 1000
(C) 1200
(D) 1230
(E) 1365
Rationale: A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players.
=. Required number of ways = 14C10 = 14C4
= 14!/4!x19! = 1365
E
Answer: (E) 1365
Question: A man can row upstream at 45 kmph and downstream at 55 kmph, and then find the speed of the man in still water?
(A) 32 kmph
(B) 34 kmph
(C) 30 kmph
(D) 50 kmph
(E) 65 kmph
Rationale: US = 45
DS = 55
M = (45 + 55)/2 = 50
Answer:D
Answer: (D) 50 kmph
Question: If j and k are integers whose product is 400, which of the following statements must be true?
(A) n + k > 0
(B) n is not equal to k.
(C) Either n or k is a multiple of 10.
(D) If n is even, then k is odd.
(E) If j is odd, then k is even.
Rationale: If j and k are integers whose product is 400, which of the following statements must be true?
A.n + k > 0n and k should have the same sign, but that means that they can also both be negative
B.n is not equal to k.20 x 20 = 400[i]
C.Either n or k is a multiple of 10. [i]25 x 16 = 400
D.If n is even, then k is odd.k can also be even since even x even will be even
E. If j is odd, then k is even.k must be even since odd x even = even
Answer: (E) If j is odd, then k is even.
Question: A reduction of 40% in the price of bananas would enable a man to obtain 50 more for Rs.40, what is reduced price per dozen?
(A) 1.34
(B) 2.84
(C) 3.84
(D) 4.34
(E) 5
Rationale: 40*(40/100) = 16 --- 50
? --- 12 => Rs.3.84
Answer: C
Answer: (C) 3.84
Question: What least whole no. should be added to 532869 to make it divisible by 9?
(A) 5
(B) 6
(C) 9
(D) 10
(E) 11
Rationale: If a number is divisible by 9, the sum of its digits must be a multiple of 9.
Here, 5+3+2+8+6+9=33, the next multiple of 9 is 36.
3 must be added to 532869 to make it divisible by 9
C
Answer: (C) 9
Question: In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
(A) 63
(B) 12
(C) 45
(D) 72
(E) 36
Rationale: Required number of ways = (7C5 x 3C2) = (7C2 x 3C1) = = 63.
Ans: A
Answer: (A) 63
Question: Find the least number which when divided by 18,32,48,52 leaves remainder 14,28,44,48 respectively.
(A) 2845
(B) 3250
(C) 3740
(D) 4150
(E) 5140
Rationale: The difference of 18-14= 4 , 32-28 = 4 , 48-44= 4 , 52-48 = 4
LCM of 18,32,48,52 = 3744
Required number = 3744 - 4 = 3740
Answer is C
Answer: (C) 3740
Question: If x is an even integer and y = 5x + 1, which of the following CANNOT be a divisor of y?
(A) 11
(B) 31
(C) 21
(D) 41
(E) 30
Rationale: x takes even values as 2,4,6,8.,
y=5x+1
x is an even term so 5x must be an even term when it adds with 1 so it must be a odd integer
30 didn't follows this condition ans is E
Answer: (E) 30
Question: Find the compound interest and the amount on Rs.8000 at 5% per annum for 4 years when C.I is reckoned yearly?
(A) s.1261.05
(B) s.1440.05
(C) s.1185.05
(D) s.1346.05
(E) s.1724.05
Rationale: A = 8000(21/20)4
= 9724.05
= 8000
---------
1724.05
ANSWER:E
Answer: (E) s.1724.05
Question: M is a certain set of numbers with an average (arithmetic mean) of 10 and a standard deviation of 1.5. 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, 7, 7, 10, 12}
(C) {3, 5, 5, 10, 16}
(D) {1, 5, 7, 10, 18}
(E) {5, 6, 7, 10, 12}
Rationale: Exactly 80% of the numbers in Q, so 4 out of 5 numbers are from 10 - 2*{SD} = 7 to 10 + 2*{SD} = 13.
A. {3, 4,5, 10, 14} --> only 3 numbers are in this range. Discard.
B. {3,7, 7, 10, 12} --> 4 numbers are in this range. OK.
C. {3,5, 5, 10, 16} --> only 1 number is in this range. Discard.
D. {1,5, 7, 10, 18} --> only 2 numbers are in this range. Discard.
E. {5, 6, 7, 10, 12} --> only 3 numbers are in this range. Discard.
Answer: B.
Answer: (B) {3, 7, 7, 10, 12}
Question: How many numbers from 10 to 50 are exactly divisible by 9?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 14
Rationale: 10/9 = 1 and 50/9 = 5 ==> 5 - 1 = 4. Therefore 4
Answer : E
Answer: (E) 14
Question: 3^11 + 3^11 + 3^11 =
(A) 3^12
(B) 3^13
(C) 3^30
(D) 9^10
(E) 9^30
Rationale: Since we have 3^11 added together 3 times, we can factor out a 3 and we get 3(3^11) which is equal to 3^12.
The answer is A.
Answer: (A) 3^12
Question: Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?
(A) 600
(B) 881
(C) 767
(D) 261
(E) 121
Rationale: Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus.
BE2 + AE2 = AB2
252 = 152 + AE2 AE = √(625 - 225) = √400 = 20,
AC = 20 + 20 = 40 cm.
Area of a rhombus = 1/2 * d1d2
= 1/2 * 40 * 30 = 600 sq.cm.
Answer:A
Answer: (A) 600
Question: Two family reunions are happening at the Taj hotel, the Oates reunion and the Hall reunion. All 150 guests at the hotel attend at least one of the reunions. If 70 people attend the Oates reunion and 52 people attend the Hall reunion, how many people attend both reunions?
(A)  2
(B)  5
(C)  10
(D)  16
(E)  28
Rationale: No of people in Oates reunion=70
No of people in Hall reunion=52
Attending both=x
All guests attend at least one.
Therefore, 150=70+52-(Both)
Both=28
Answer E
Answer: (E)  28
Question: A certain company has budgeted $1320 for entertainment expenses for the year, divided into 12 equal monthly allocations. If by the end of the third month, the total amount spent on entertainment was $400, how much was the company under budget or over budget?
(A) $70 under budget
(B) $30 under budget
(C) $30 over budget
(D) $70 over budget
(E) $180 over budget
Rationale: The budget for 3 months is (3/12)*$1320 = $330
The company is $70 over budget.
The answer is D.
Answer: (D) $70 over budget
Question: On his drive to work, Leo listens to one of three radio stations A, B or R. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns it to B. If B is playing a song he likes, he listens to it; if not, he turns it to R. If R is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.30 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?
(A) 0.027
(B) 0.09
(C) 0.417
(D) 0.657
(E) 0.9
Rationale: Probability he hears a song is like:
Tune to A and likes what he is hearing = 0.3
Tune to A, don't find he like what they are airing, then tune to B and likes what he finds there = 0.7 * 0.3 = 0.21
Tune to A, finds crap there, Tune to B, hears a similar crap, Tune to R and finally falls in love with the program = 0.7^2 * 0.3 = 0.147
Total = 0.657
Ans D
Answer: (D) 0.657
Question: For which of the following does n(a)−n(b)=n(a−b) for all values of a and b?
(A) n(x)=x^2
(B) n(x)=x/2
(C) n(x)=x+5
(D) n(x)=2x−1
(E) n(x)=|x|
Rationale: To solve this easiest way is just put the value and see that if it equals or not.
with option 1. n(a) = a^2 and n(b) = b^2
so L.H.S = a^2 - b^2
and R.H.S = (a-b)^2 ==> a^2 + b^2 -2ab.
so L.H.S not equal to R.H.S
with option 2. n(a) = a/2 and n(b) = b/2
L.H.S = a/2 - b/2 ==> 1/2(a-b)
R.H.S = (a-b)/2
so L.H.S = R.H.S which is the correct answer.
answer:B
Answer: (B) n(x)=x/2
Question: How many factors greater than 50, which are multiples of 3, are possible in 8400?
(A) 41
(B) 31
(C) 21
(D) 11
(E) 01
Rationale: Prime factorisation of 8400- 2^4∗3∗5^2∗7
Number of factors of 8400 =
5*2*3*2=60
Number of factors of 8400 which are not multiple of 3
5*2*3=30
Number of factors of 8400 which are multiple of 3
60-30 = 30
Factors which are multiple of 3 but less than 50-
3,6,12,15,21,24,30,42,48
Total-9
Number of factors of 8400 which are multiple of 3 but more than 50 are
30-9 = 21
Answer:- C
Answer: (C) 21
Question: How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 23 sec
(B) 30 sec
(C) 27 sec
(D) 28 sec
(E) 29 sec
Rationale: Speed of train relative to man = 63 - 3
= 60 km/hr.
= 60 * 5/18
= 50/3 m/sec.
Time taken to pass the man = 500 * 3/50
= 30 sec.
Answer:B
Answer: (B) 30 sec
Question: If X,Y is 20%,25% greater than Z then how much percentage is X smaller than Y?
(A) 3 1/13%
(B) 3%
(C) 3 11/13%
(D) 4%
(E) None of these
Rationale: Explanation:
X = 125%
Y = 130%
Z = 100%
X-Y/Y * 100 = 5/130 * 100
= 500/130 %
= 3 11/13% smaller than Y
Answer: Option C
Answer: (C) 3 11/13%
Question: Which of the following inequalities has a solution set, when graphed on the number line, is a single line segment of finite length?
(A) 2 <= 3x+4 <= 6
(B) 24 <= 34x+4 <= 6
(C) 2 <= 356x+4 <= 6
(D) 2 <= 378x+4 <= 6
(E) 2 <= 357x+4 <= 6
Rationale: The key words in the stem are:a singleline segment offinite length
Now, answer choices A, B, and C can not be correct answers as solutions sets for these exponential functions are not limited at all (>= for even powers and <= for odd power) and thus can not be finite (x can go to + or -infinity for A and C and x can got to -infinity for B). As for D: we have thatabsolute valueof x is between two positive values, thus the solution set for x (because of absolute value) will be two line segments which will be mirror images of each other.
Answer: A.
Answer: (A) 2 <= 3x+4 <= 6
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions.
(A) 287 m
(B) 704 m
(C) 168 m
(D) 278 m
(E) 107 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 500 * 2 * 22/7 * 22.4
= 70400 cm
= 704 m
Answer: B
Answer: (B) 704 m
Question: The speed of a car is 70 km in the first hour and 90 km in the second hour. What is the average speed of the car?
(A) 79 kmph
(B) 80 kmph
(C) 34 kmph
(D) 23 kmph
(E) 14 kmph
Rationale: S = (70 + 90)/2
= 80 kmph
Answer:B
Answer: (B) 80 kmph
Question: A loan has a variable interest rate that fluctuates between 7% and 10% of the base payment per month. If base payments remain at $300 each month and an additional monthly surcharge of 1% is added to the combined (base + interest), what would be the greatest possible payment due in any given month?
(A) $330.00
(B) $331.00
(C) $332.30
(D) $333.30
(E) $334.60
Rationale: The maximum interest in one month is 10%*$300=$30.
The combined payment (base plus interest) is $300 + $30 = $330.
The greatest possible payment is: 1.01*$330=$333.30.
The answer is D.
Answer: (D) $333.30
Question: 4 bells first begin to toll together with an intervals of 5, 10, 15 & 20 sec. How many times does they toll together in an hr?
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: 5|5, 10, 15, 20
2|1, 2, 3, 4
|1, 1, 3, 2
L.C.M of 5, 10, 15, 20 is 60
60 times
B
Answer: (B) 60
Question: Find 30 % of 240
(A) 72
(B) 94
(C) 86
(D) 74
(E) 110
Rationale: We know that R % of m is equal to R/100 × m.
So, we have 30 % of 240
30/100 × 240
= 72
Answer:A
Answer: (A) 72
Question: If X is to be chosen at random from the set {5,7,4,3,8} and Y is to be chosen at random from the set {6,3,4,2}, what is the probability that XY will be odd?
(A) 12
(B) 8
(C) 11
(D) 6
(E) 1
Rationale: Method-1
xy will be odd when
1) x is odd and y is even, Probability of x odd is (3/5) and Probability of y even is (3/4), so Probability of Case(1) = (3/5)*(3/4) = (15/20)=(3/4)
2) x is even and y is odd, Probability of x even is (2/5) and Probability of y odd is (1/4), so Probability of Case(2) = (2/5)*(1/4) = (2/20)
3) x is odd and y is odd, Probability of x odd is (3/5) and Probability of y odd is (1/4), so Probability of Case(1) = (3/5)*(1/4) = (3/20)
Total Favorable Probability = (15/20)+(2/20)+(3/20) = (20/20) = 1
Answer: option E
Answer: (E) 1
Question: In an entrance exam, 3 marks is awarded for every correct answer and (-1) for every wrong answer. If a student gets 38 marks after attempting all questions, find the number of questions answered correctly if the total questions were 70.
(A) 38
(B) 40
(C) 27
(D) 43
(E) 56
Rationale: Explanation:
Let x be the number of questions answered correctly. Hence, number of questions whose answer were wrong = (70 – x)
3*x + (70 – x)*(-1) = 38
4x = 38 + 70 = 108
x = 27
ANSWER C
Answer: (C) 27
Question: On 8th Feb, 2005 it was Tuesday. What was the day of the week on 8th Feb, 2004?
(A) Sunday
(B) Friday
(C) Saturday
(D) Monday
(E) Tuesday
Rationale: Given that 8th Feb, 2005 was Tuesday
Number of days from 8th Feb, 2004 to 7th Feb, 2005 = 366 (Since Feb 2004 has 29 days as it is a leap year)
366 days = 2 odd days
Hence 8th Feb, 2004 = (Tuesday - 2 odd days) = Sunday
Answer:A
Answer: (A) Sunday
Question: A box contains 6 black, 8 red and 4 green marbles. 2 marbles are drawn from the box at random. What is the probability that both the marbles are of the same color?
(A) 49/153
(B) 18/153
(C) 49/153
(D) 40/153
(E) 24/72
Rationale: Explanation:
Total marbles in a box = 6 black + 8 red +4 green marbles = 18 marbles
2 marbles are drawn from 18 marbles at random. Therefore,
n(S) = 18C2 = 153 ways
Let A be the event that 2 marbles drawn at random are of the same color. Number of cases favorable to the event A is
n(A) = 6C2 + 8C2 + 4C2 = 15+28+6= 49
Therefore, by definition of probability of event A,
P(A) = n(A)/n(S) = 49/153
ANSWER:A
Answer: (A) 49/153
Question: The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 3 years?
(A) 14300
(B) 17280
(C) 14500
(D) 14600
(E) 15400
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
10000 × 120/100^3 = 17280
B)
Answer: (B) 17280
Question: There was a match to be held.And 100 nations were to participate in that match.It was totally an elimination match,that is if a team loses a match it must be eliminated.Find out the total number of matches played to find out the grand winner?
(A) 96
(B) 97
(C) 98
(D) 99
(E) 92
Rationale: 100-1=99 as every match will eliminate one team.
ANSWER:D
Answer: (D) 99
Question: Find the missing figures :
?% of 60 = 2.125
(A) 8.54
(B) 6.54
(C) 8.7
(D) 3.54
(E) 4.54
Rationale: (i)	Let x% of 60 = 2.125. Then , (x/100)*60 = 2.125
X = (2.125 * 100/60) = 3.54
Answer is E.
Answer: (E) 4.54