mathewhe/aqua_rat huggingface dataset:
Question: With out any halt a train travels a certain distance with an average speed of 55 km ph , and with halts it covers the same distance at an average speed of 40 kmph. When it is traveling with halts, how many minutes/per hour does the train halt on an average ?
(A) 48 min.
(B) 6min.
(C) 15min.
(D) 18min.
(E) 19min.
Rationale: With halt in 1 hour the train travels 60km
With out halt for traveling same distance it take 55/50 = 11/10 = 66 minutes
:. 6 minutes is the halting time per hour
ANSWER:B
Answer: (B) 6min.
Question: What will be the difference between simple and compound interest at 14% per annum on a sum of Rs. 1000 after 4 years?
(A) 129
(B) 130
(C) 124
(D) 133
(E) 145
Rationale: S.I. = (1000 * 14 * 4)/100 = Rs. 560
C.I. = [1000 * (1 + 14/100)4 - 1000] = Rs. 689 Difference = (689 - 560) = Rs. 129
Answer: A
Answer: (A) 129
Question: If a coin is tossed three times, what is the probability that on the first toss the coin lands heads, on the second toss the coin lands tails, and on the third toss the coin lands heads.
(A) 1/2
(B) 1/8
(C) 1/4
(D) 3/8
(E) 1/16
Rationale: Since there are two options for how a coin can land (heads or tails), that means there is a 1/2 chance to land on tails and a 1/2 chance to land heads. To solve this problem you multiply each probability for each flip together. (1/2) chance to land heads the first time * (1/2) chance to land tails the second time * (1/2) chance to land heads the third time = (1/8) chance to land heads the first time, tails the second time, and heads the third time.
Answer: B
Answer: (B) 1/8
Question: If 3 people can do 3 times of a particular work in 3 days, then how many days would it take 8 people to do 8 times of that particular work?
(A) 1
(B) 2
(C) 3
(D) 8
(E) 11
Rationale: 3 people can do the work one time in one day.
1 person can do 1/3 of the work in one day.
8 people can do 8/3 of the work in one day.
8 people can do 8 times the work in 3 days.
The answer is C.
Answer: (C) 3
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 0.5 kmph, find his average speed for the total journey?
(A) 4
(B) 3.5
(C) 3
(D) 3.1
(E) 2.8
Rationale: M = 4.5
S = 2.5
DS = 7
US = 2
AS = (2 * 7 * 2) /9 = 3.1
Answer: D
Answer: (D) 3.1
Question: The ratio of red boxes to blue boxes in a certain warehouse is 12 to 20. If the number of the red boxes were doubled and the number of blue boxes were increased by 150 the ratio would be halved. How many total boxes are in the warehouse?
(A) 80
(B) 74
(C) 111
(D) 148
(E) 244
Rationale: Ratio = R/B = 12/20 or R = 12/20 B -----------(1)
2R/B+150 = 12/20*1/2 = 6/20 or we can say that 20R=3B+450 -------------(2)
solving (1) and (2) we get
B=50 and R = 30
so total boxes is B + R = 50+30=80
Hence A. 80 is the correct answer
Answer: (A) 80
Question: Find the average of first 30 natural numbers.
(A) 12
(B) 15.5
(C) 14.5
(D) 16
(E) 17
Rationale: Explanation:
Sum of first n natural numbers = n(n+1)/2
Hence, sum of first 30 natural numbers = (30 x 31)/2 = 465
Therefore, required average of = 465/30 = 15.5
ANSWER B
Answer: (B) 15.5
Question: 3 red and 4 blue balls are in a basket. A member of PPTeam is drawing balls from the basket. What is the probablity of getting the 3 red balls simultaneously?
(A) 1/35
(B) 2/35
(C) 3/35
(D) 4/35
(E) 5/35
Rationale: (3C3)/(7C3)=1/35
ANSWER:A
Answer: (A) 1/35
Question: What is the area of a square field whose diagonal of length 20 m?
(A) 10 sq m
(B) 200 sq m
(C) 400 sq m
(D) 500 sq m
(E) 156 sq m
Rationale: Explanation:
d^2/2 = (20 * 20)/2 = 200 sq m
Answer : B
Answer: (B) 200 sq m
Question: A single discount equivalent to the discount series of 20%, 10% and 5% is?
(A) 31.8
(B) 31.1
(C) 31.6
(D) 31.2
(E) 31.9
Rationale: Explanation:
100*(80/100)*(90/100)*(95/100) = 68.4
100 - 68.4 = 31.6
Answer: C
Answer: (C) 31.6
Question: A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr. find the time taken by the boat to go 72 km downstream?
(A) 2 hours
(B) 4 hours 12 minutes
(C) 4 hours
(D) 5 hours
(E) None
Rationale: Solution
Speed Downstream	= (13 + 4) km/hr
= 17 km/hr.
Time taken to travel 72 km downstream	=(72 / 17)hrs
= 4 hrs 12 minutes.
Answer B
Answer: (B) 4 hours 12 minutes
Question: A store reported total sales of $385 million for February of this year. If the total sales for the same month last year was $320 million, approximately what was the percent increase W in sales?
(A)  2%
(B)  17%
(C)  20%
(D)  65%
(E)  83%
Rationale: Last year's sales = $320 million;
This year's sales = $385 million;
Increase W = $65 million.
Now, 20% of $320 million is $64 million, which is very close to actual increase of $65 million.
Answer: C.
Answer: (C)  20%
Question: If -4 and -8 are negative integers, then -4*-8 + 2 is
(A) -32
(B) -30
(C) 34
(D) -24
(E) -10
Rationale: Answer : C
Answer: (C) 34
Question: Cole drove from home to work at an average speed of 50 kmh. He then returned home at an average speed of 110 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work?
(A) 66.5
(B) 70.5
(C) 72.5
(D) 75.5
(E) 82.5
Rationale: Let the distance one way be x
Time from home to work = x/50
Time from work to home = x/110
Total time = 2 hrs
(x/50) + (x/110)= 2
Solving for x, we get x = 275/4
Time from home to work in minutes= (275/4)*60/50 = 82.5 minutes
Ans= E
Answer: (E) 82.5
Question: log3 N+log5 N what is 3 digit number N that will be whole number
(A) 629
(B) 729
(C) 829
(D) 125
(E) 727
Rationale: No of values N can take is 1
5^3=125
ANSWER:D
Answer: (D) 125
Question: There were 35 students in a hostel. Due to the admission of 7 new students, he expenses of the mess were increased by Rs. 42 per day while the average expenditure per head diminished by Rs 1. What was the original expenditure of the mess?
(A) 125
(B) 321
(C) 561
(D) 852
(E) 420
Rationale: Let the original average expenditure be Rs. x. Then,
42 (x - 1) - 35x=42;	7x= 84;	x =12.
Original expenditure = Rs. (35 x 12) =Rs. 420. .
Ans: E
Answer: (E) 420
Question: In a certain growth fund, 3/5 of the investment capital is invested in stocks, and of that portion, 1/3 is invested in preferred stocks. If the mutual fund has $843,000 invested in preferred stocks, what is the total amount of money invested in the fund?
(A) $1,974,000
(B) $2,538,000
(C) $3,264,000
(D) $3,826,000
(E) $4,215,000
Rationale: Portion invested in preferred stock = 3/5 * 1/3 = 1/5
1/5 of fund = 843---
Fund = 5 * 843---
Here, we can avoid the math and simply look at 5 * 3 -> 15. Only option E has 15 in it.
Answer (E).
Answer: (E) $4,215,000
Question: A retail item is offered at a discount of a percent (where a > 10), with a 5% state sales tax assessed on the discounted purchase price. If the state sales tax were not assessed, what percent discount from the item’s original retail price, in terms of a, would result in the same final price?
(A) p+5/1.05
(B) p/1.05 +5
(C) 1.05a-5
(D) a-5/1.05
(E) 1.05(a – 5)
Rationale: Let x be the price of the item.
Final price after discount and sales tax = x * (1 - a/100) * 1.05
Let b be the percent discount which would result in the same final price.
Then,
x * (1 - a/100) * 1.05 = x * (1 - b/100)
=> 1.05 - 1.05a/100 = 1 - b/100
=> b/100 = 1.05a/100 - .05
=> b = 1.05a - 5
Hence ,option C is correct.
Answer: (C) 1.05a-5
Question: A can do a job in 18 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days?
(A) 22 1/8
(B) 22 1/2
(C) 22 1/1
(D) 22 1/5
(E) 22 1/9
Rationale: 1/18 + 1/30 = 8/90 = 4/45
45/4 = 11 ¼ *2 = 22 1/2 days
Answer:B
Answer: (B) 22 1/2
Question: A man spends 20% of his income in house rent, 10% of the rest on his children’s education, 15% of the rest miscellaneous causes. If he now posses Rs. 6352 then his income is?
(A) A)Rs.10379
(B) B)Rs.40598
(C) C)Rs.45699
(D) D)Rs.30379
(E) E)Rs.59879
Rationale: X * (80/100) * (90/100) * (85/100) = 6352
X * 0.8 * 0.9 * 0.85=6352
X = 6352/0.612
X = 10379
ANSWER:A
Answer: (A) A)Rs.10379
Question: Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn
randomly. If it is known that the number on the drawn card is more than 3, what is the probability
that it is an even number?
(A) 3/7
(B) 3/11
(C) 4/7
(D) 5/8
(E) 5/9
Rationale: Let A be the event ‘the number on the card drawn is even’ and B be the
event ‘the number on the card drawn is greater than 3’. We have to find P(A|B).
Now, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Then A = {2, 4, 6, 8, 10}, B = {4, 5, 6, 7, 8, 9, 10}
and A n B = {4, 6, 8, 10}
Also P(A) = 5/2, P(B) = 7/10 and P(A n B) = 4/10
Then P(A|B) = P(A n B)/P(B) = (4/10)/(7/10)	= 4/7
C)
Answer: (C) 4/7
Question: Two size of envelope having color of red,blue, purple ,green..company made packages of three envelopes either same size same color or same size different color...how many packages possible if sequence of color doesn't matters?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: For same colour four combinations are possible GGG,RRR,BBB,PPP
Four diff color four combinations r possible
GBR,GRP,GBP,RBP
So total 8 combination for each size
So no. Of package=16
ANSWER:E
Answer: (E) 16
Question: If log2X +log2Y ≥ 6, then the least value of XY is?
(A) 4
(B) 8
(C) 64
(D) 32
(E) 16
Rationale: Given : log2X + log2Y ≥ 6
=> log2(XY)≥6
=> XY ≥ 64
ANSWER:C
Answer: (C) 64
Question: The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides?
(A) 3
(B) 7
(C) 5
(D) 3
(E) 4
Rationale: S = (1 + 2 + 3)/2
= 3
Answer: A
Answer: (A) 3
Question: How many words can be formed by using all letters of the word ‘DAUGHTER’ so that the vowels always come together?
(A) 42
(B) 420
(C) 470
(D) 540
(E) 4320
Rationale: Given word contains 8 different letters. When the vowels AUE are always together, we may suppose them to form an entity, treated as one letter.
Then, the letters to be arranged are DGNTR (AUE).
Then 6 letters to be arranged in 6p6 = 6! = 720 ways.
The vowels in the group (AUE) may be arranged in 3! = 6 ways.
Required number of words = (720x6) = 4320.
ANSWER E 4320
Answer: (E) 4320
Question: The length and breadth of a rectangle is increased by 10% and 25% respectively. What is the increase in the area?
(A) 37.7%
(B) 37.5%
(C) 36.5%
(D) 27.5%
(E) 47.5%
Rationale: 100 * 100 = 10000
110 * 125 = 13750
-----------
3750
10000 ------ 3750
100 ------- ? => 37.5%
Answer:B
Answer: (B) 37.5%
Question: If a and s are positive integers such that (2^a)(4^s) = 16, then 2a + s =
(A)  2
(B)  3
(C)  4
(D)  5
(E)  6
Rationale: lets get the eq into simplest orm..
(2^a)(4^s) = 16..
(2^a)(2^2s) = 2^4..
or a+2s=4..
since a and s are positive integers, only a as 2 and s as 1 satisfy the Equation..
so 2a+s=2*2+1=5..
D
Answer: (D)  5
Question: The average age 9 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
(A) 12
(B) 18
(C) 22
(D) 24
(E) 26
Rationale: 9 * 2 = 18 years
B
Answer: (B) 18
Question: At exactly what time past 10:00 will the minute and hour hands of an accurate working clock be precisely perpendicular to each other for the first time?
(A) 20 13/21 minutes past 7:00
(B) 20 13/17 minutes past 7:00
(C) 21 3/23 minutes past 10:00
(D) 21 9/11 minutes past 7:00
(E) 22 4/9 minutes past 7:00
Rationale: A1 = hour angle
A2 = minute angle
A1-A2 = 90
Assume the minutes = M
A1 = (10*60+M)/12*60 )*360
A2 = M*360/60
Solving all three equation , results in the answer C
Answer: (C) 21 3/23 minutes past 10:00
Question: Kim has 9 pairs of shoes; each pair is a different color. If Kim randomly selects 2 shoes without replacement from the 18 shoes, what is the probability that she will select 2 shoes of the same color?
(A) 2/5
(B) 11/5
(C) 1/9
(D) 1/17
(E) 1/5
Rationale: Can be tackled in this way as well: Probability of selecting any 1 out of 10 shoes = 18/18 = 1
Probability of selecting the next shoe (out of 18 available) having the same color = 1/18 (as after selecting the 1st one, there is only 1 another shoe left with the same color).
Thus the total probability = 1*1/17=1/17.
D is the correct answer.
Answer: (D) 1/17
Question: x and y are positive integers. If y + x is odd, then which of the following must be even?
(A) x
(B) y
(C) x + y
(D) xy − x
(E) x^2 − y
Rationale: Given that y + x is odd,
Hence x is odd, Answer will be C.
Answer: (C) x + y
Question: A car traveling at a certain constant speed takes 15 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 60 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?
(A) 48
(B) 50
(C) 52
(D) 54
(E) 56
Rationale: 60 * T = 1 km => T = 1/60 km/h
V*(T+15/3600) = 1
V (1/60 + 15/3600) = 1
V (75/3600) = 1
V = 48 km/h
The answer is A.
Answer: (A) 48
Question: A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?
(A) 350 m
(B) 250 m
(C) 300 m
(D) 148 m
(E) 150 m
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 9 = 150 m
Answer:E
Answer: (E) 150 m
Question: Let Raj be 3 years older than Ravi and Hema be two years younger than Ravi. Raj is three times as old as Rahul
who is Hema’s brother. The ratio of the ages of Hema and Her brother is 3:2. Find by how much percentage Raj’s age
is more than Hema’s when Raj will be 20 years old.
(A) 33.33
(B) 27.33
(C) 28.38
(D) 29.37
(E) 28.31
Rationale: Answer: 33.33
Answer: (A) 33.33
Question: A is twice as good a work man as B and together they finish the work in 12 days. In how many days A alone can finish the work?
(A) 23
(B) 18
(C) 77
(D) 92
(E) 61
Rationale: WC = 2:1
2x + x = 1/12 => x = 1/36
2x = 1/18
A can do the work in 18 days.
Answer: B
Answer: (B) 18
Question: Monica planned her birthday party. She prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra. After the party, it turned out that one of the guests didn't come but every one of the guests that did come ate six muffins and 2 muffins remained. How many guests did Monica plan on?
(A) 3.
(B) 4.
(C) 6.
(D) 8.
(E) 7.
Rationale: 5N +2 = 2 + 6(N-1)
Solving N= 6
Hence C
Answer: (C) 6.
Question: In a certain mathematical activity, we have five cards with five different prime numbers on them. We will distribute these five cards among three envelope: all could go in any envelope, or they could be broken up in any way among the envelopes. Then in each envelop, we find the product of all the cards in that envelope: that is the “number” of the envelope. An envelope containing no cards has the number 1. We then put the three envelope numbers in order, from lowest to highest, and that is our set. How many different W sets can be produced by this process?
(A)  41
(B)  89
(C)  125
(D)  243
(E)  512
Rationale: Case 1: 1 used envelope => 1 way
Case 2: 2 used envelopes
- 4-1-0: Choose 4 from 5 cards: 5 ways
- 3-2-0: Choose 3 from 5 cards: 10 ways
Case 3: All envelopes used
- 3-1-1: Choose 3 from 5 andno need to choose 1 from 2: 10 ways
- 2-2-1: Choose 2 from 5 and choose 2 from 3, but two groups are the same => (10X3):2 = 15
Total W: 1+5+10+10+15=41 => Answer: A
Answer: (A)  41
Question: In a single throw of a die what is the probability of getting a number greater than 2 ?
(A) 2/3
(B) 1/4
(C) 2/5
(D) 1/3
(E) 1/5
Rationale: when a die is thrown S={1,2,3,4,5,6}
E = event of getting a number greater than 2 = {3,4,5,6}
P(E) = n(E)/n(S) = 4/6 = 2/3
Answer is A
Answer: (A) 2/3
Question: 34 men can complete a piece of work in 18 days. In how many days will 17 men complete the same work?
(A) 36
(B) 26
(C) 97
(D) 26
(E) 19
Rationale: Explanation:
Let the required number of days be A.
Then, Less men, More days (Indirect Proportion)
17 : 34 : : 18 : A
17 x A = 34 x 18
A = (34 x 18) / 17
A = 36
ANSWER: A
Answer: (A) 36
Question: A fruits marks his fruit baskets 40% more than the real price and allows 15% discount. His profit is:
(A) 16%
(B) 17%
(C) 18%
(D) 19%
(E) 20%
Rationale: Let the CP = 100 Rs.
Mark Price = 140
Discount = 15%
Selling price 85/100 Ã— 140
Hence profit = 19%
Answer: D.
Answer: (D) 19%
Question: Two trains move in the same direction at speeds 50 kmph and 32 kmph respectively. A man in the slower train observes that 15 seconds elapse before the faster train completely passes by him. What is the length of faster train?
(A) 100m
(B) 75m
(C) 120m
(D) 50m
(E) 40m
Rationale: As both trains move in same direction, the relative velocity is (50-32)Km/hr
=> Velocity = 18Km/hr = 18*(5/18) m/s = 5m/s
As 15seconds is the total time taken by the train,
=> Length of train = 5*15 = 75m
ANSWER:B
Answer: (B) 75m
Question: If –2 < x < 2 and x ≠ 0, which of the following inequalities must be true?
I. x^3 < x
II. x^2 < |x|
III. x^4 – x^5 > x^3 – x^2
(A)  I only
(B)  II only
(C)  III only
(D)  II and III only
(E)  I, II, and III
Rationale: Answer is D. Let's look at the statements one by one
Stmt I. x^3 < x
if 0<x<1 then x^3< x but if -1<x<0 then x^3>x
So this statement is not always true
Stmt II. x^2 < |x|
Because we know that x is a number less than one but not equal to zero then x^2 will always be less than |x|.
Why? think of positive fractions (and you can think in terms of positive fractions because the inequality is in regards to |x|). Lets set x = 1/2, then x^2 = 1/4 and 1/4<1/2
So Stmt II is always true
Stmt III. x^4 – x^5 > x^3 – x^2
This one may seem tricky but lets break it down. x^4 – x^5 > x^3 – x^2 = x^4(1-x)>x^2(x-1).
Because lets concentrate on (1-x) and (x-1). We are given that -1<x<1 which means that (1-x)>0 and (x-1)<0. x^4 will always be positive and x^2 will always be positive so without doing any math we are looking at positive > negative... which is always true.
So Stmt III is always true
C
Answer: (C)  III only
Question: The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is:
(A) 21
(B) 20
(C) 25
(D) 30
(E) 27
Rationale: Let the total number of workers be x. Then,
8000x = (12000 * 7) + 6000(x - 7)
= 2000x = 42000
= x = 21.
ANSWER A
Answer: (A) 21
Question: Enrollment in City College in 1980 was 210 percent of enrollment in 1990. What was the percent increase in the college’s enrollment from 1980 to 1990?
(A) - 10%
(B) - 16 2/3 %
(C) - 52.38%
(D) - 25%
(E) - 183 1/3%
Rationale: Assume 100 enrollments present in 1990
210 % of 1990 = enrollments on 1980
enrollments on 1980 = 210
% change = (enrollment in 1990 - enrollment in 1980)*100/(enrollment in 1980)
=(100 - 210) *100 / 210
= -11000 / 210
= - 52.38 %
Ans - C
Answer: (C) - 52.38%
Question: Set S is the prime integers between 0 and 30. If three numbers are chosen randomly from set S, what is the probability that the sum of these three numbers is odd?
(A) 15/56
(B) 3/8
(C) 15/28
(D) 7/10
(E) 3/4
Rationale: Total number of combinations=10C3=120...............(1)
Total number of combinations including2and two other numbers=9C2=36......................(2)
Therefore the difference ie. (1)-(2) is the set of 3 primes without 2=(120-36)=84
So, probability=84/120=7/10
D
Answer: (D) 7/10
Question: Divide Rs. 1301 between A and B, so that the amount of A after 7 years is equal to the amount of B after 9 years, the interest being compounded at 4% per annum.
(A) 625
(B) 367
(C) 288
(D) 209
(E) 198
Rationale: Explanation:
Let the two parts be Rs. x and Rs. (1301 - x).
625x=676(1301-x) 1301x=676 x 1301x=676.
So,the parts are rs.676 and rs.(1301-676)i.e rs.676 and rs.625
Answer: A) Rs.625
Answer: (A) 625
Question: If T < y < -1, which of the following is true?
(A) T/y > Ty
(B) y/t > t+y
(C) y/t > Ty
(D) y/T < T+y
(E) y/T > T/y
Rationale: Consider :
T= -3
y= -2
then put for every option. U'll get ans B.
Answer: (B) y/t > t+y
Question: A, B and C started a business by investing Rs. 1,20,000, Rs. 1,35,000 and ,Rs.1,50,000 respectively. Find the share of each, out of an annual profit of Rs. 56,700.
(A) 16800;18900;21000
(B) 17800;19800;22500
(C) 15500;17600;20500
(D) 16400;17200;18900
(E) None of them
Rationale: Ratio of shares of A, Band C = Ratio of their investments
= 120000 : 135000 : 150000 = 8 : 9 : 10.
A’s share = Rs. (56700 x (8/27))= Rs. 16800.
B's share = Rs. ( 56700 x (9/27)) = Rs. 18900.
C's share = Rs. ( 56700 x (10/27))=Rs. 21000.
Answer is A.
Answer: (A) 16800;18900;21000
Question: If a and b are both prime numbers greater than 10, which of the following CANNOT be true?
I. ab is an even number.
II. The difference between a and b equals 117.
III. The sum of a and b is even.
(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II and III
Rationale: CONCEPT: Prime Numbers greater than 10 will all be ODD
I. ab is an even number - Can't be True because both a and b are ODD
II. The difference between a and b equals 117 - Can't be True because both a and b are ODD and Difference of two Odd No. must be EVEN
III. The sum of a and b is even - This will be True because both a and b are ODD and Sum of two Odd No. must be EVEN
ANSWER:B
Answer: (B) I and II only
Question: Two trains, one from P to Q and the other from Q to P, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is
(A) 4:1
(B) 4:2
(C) 4:5
(D) 4:3
(E) 4:6
Rationale: Ratio of their speeds = Speed of first train : Speed of second train
= 16−−√9√
= 4:3
Answer is D.
Answer: (D) 4:3
Question: It is given that 2^32 + 1 is exactly divisible by a certain number. Which one of the following is also divisible by the same number B?
(A) a. 2^96 + 1
(B) b. 2^16 - 1
(C) c. 2^16 + 1
(D) d. 7 * 2^33
(E) e. 2^64 + 1
Rationale: a³ + b³ =(a+b)(a² -ab +b²)
Now, let (2^32 + 1) be (a+b)
a³ + b³ = (2^96 + 1)
Now, as mentioned in formula above,
a³ + b³ is always divisible by (a+b)
So any factor of B= (a+b) is a factor of (a³ + b³)
Henca A
Answer: (A) a. 2^96 + 1
Question: If two numbers, a and b, are to be chosen from a set of 4 consecutive integers starting with 1 and a set of three consecutive even integers starting with 6, respectively, what is the probability that b/a will not be an integer?
(A) 1/6
(B) 1/4
(C) 1/3
(D) 1/2
(E) 2/3
Rationale: a is from the following set {1,2,3,4}
b is from the following set {6,8,10}
The total number of ways of choosing 2 integers, one from each set is 4*3 = 12 ways.
The possibilities where b/a is not an integer is for the following outcomes:
{b,a} = {6,4},{8,3},{10,3},{10,4} = 4 ways
Thus the probability is 4/12 = 1/3
The answer is C.
Answer: (C) 1/3
Question: If |x| = 7x - 5, then x = ?
(A) 1
(B) 1/2
(C) 1 and 1/2
(D) 2
(E) -1
Rationale: Answer: A
Approach:
Substituted option A i.e x=1. Inequality satisfied.
D
Answer: (D) 2
Question: The maximum number of students among them 1048 pens and 828 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is:
(A) 4
(B) 8
(C) 16
(D) 1911
(E) None of these
Rationale: Explanation:
Required number of students = H.C.F of 1048 and 828 = 4. Answer: A
Answer: (A) 4
Question: An art gallery owner is hanging paintings for a new show. Of the eight paintings she has to choose from, she can only hang two on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings?
(A) 18
(B) 30
(C) 56
(D) 120
(E) 216
Rationale: Arrangment means permutations questions..
8P2 = 8!/2! = 56.
IMO option C is correct answer..
Answer: (C) 56
Question: A watch passes through three hands and each person gains 25%. If the third person sells it for $125, what did the first person pay for it?
(A) $54
(B) $60
(C) $64
(D) $72
(E) $80
Rationale: 1.25*1.25*1.25 * original price = 125
(5/4)^3 * original price = 125
original price = 64*125 / 125 = $64
The answer is C.
Answer: (C) $64
Question: The distance between Delhi and Mathura is 140 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) 10.50 a.m.
(B) 10.40 a.m.
(C) 10.30 a.m.
(D) 11.40 a.m.
(E) 1.40 a.m.
Rationale: D = 140 – 20 = 120
RS = 20 + 25 = 45
T = 120/45 = 2 2/3 hours
8 a.m. + 2 hrs 40 min = 10.40 a.m.
ANSWER:B
Answer: (B) 10.40 a.m.