mathewhe/aqua_rat huggingface dataset:
Question: If q and r are both odd numbers C , which of the following must also be odd?
(A) q – r
(B) (q + r)^2
(C) q(q + r)
(D) (qr)^2
(E) q/r
Rationale: We're told that q and r are both ODD numbers C. We're asked which of the following must also be odd.
IF...
q = 1
r = 3
Answer A) q – r = 1-3 = -2 NOT odd
Answer B) (q + r)^2 = (1+3)^2 = 16 NOT odd
Answer C) q(q + r) = (1)(4) = 4 NOT odd
Answer D) (qr)^2 = (3)^2 = 9 This IS ODD
Answer E) q/r = 1/3 NOT odd
Final Answer:
D
Answer: (D) (qr)^2
Question: 23, 25, 53, 163, 657, 3291, ?
(A) 19853
(B) 18753
(C) 17753
(D) 19753
(E) 17532
Rationale: 23*1+2=25
25*2+3=53
53*3+4=163
163*4+5=657
657*5+6=3291
3291*6+7=19753
ANSWER:D
Answer: (D) 19753
Question: If you have 5 New Year greeting cards and you want to send them to 3 of your friends, in how many ways can this be done?
(A) 60
(B) 720
(C) 20
(D) 70
(E) None
Rationale: Solution
We have to find number of permutations of 3 objects out of 5 objects. This number is 5P3=5(5-1)(5-2)=5*4*3=60
Answer A
Answer: (A) 60
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 6 years the amount to be paid is?
(A) 3377
(B) 2688
(C) 2688
(D) 9490
(E) 1268
Rationale: A = 7500(26/25)^6 = 9490
Answer: D
Answer: (D) 9490
Question: A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
(A) 7.1
(B) 7.2
(C) 7.5
(D) 7.4
(E) 7.3
Rationale: distance = 600 meter
time = 5 minutes = 5 x 60 seconds = 300 seconds
Speed = distance/time=600/300=2m/s=2×18/5 km/hr=36/5 km/hr=7.2 km/hr
Answer is B.
Answer: (B) 7.2
Question: If a man can cover 14 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
(A) 189km
(B) 195km
(C) 197km
(D) 200km
(E) 205km
Rationale: 14 m/s = 14 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 14 * 18/5 * 15/4 km = 189 km.
Answer:A
Answer: (A) 189km
Question: For 2consecutive yrs, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the 2nd yr is Rs. 42000 & my expenses in the first yr in Rs.21000, my total savings for the two-year is
(A) Rs. 7000
(B) Rs. 8000
(C) Rs. 9000
(D) Rs. 9900
(E) Rs. 10000
Rationale: Sol. Income in first year = * x 42000 = Rs. 24000
Expenses in second year = \ x 21000 = Rs. 35000 Total savings = Total income - Total expenses = (42000 + 24000)- (21000 + 35000)
= 66000 - S6000 = Rs. 10000
E
Answer: (E) Rs. 10000
Question: 1!+2!+3!+4!+5!+.......100! is divided by 24. Find the remainder?
(A) 5
(B) 7
(C) 9
(D) 11
(E) 14
Rationale: By applying rule 2, we divide the terms of the above expression individually, and add them to get the final remainder. But from 4! onwards all the terms leave a remainder 0 when divided by 24.
So the remainder = 1 + 2 + 6 + 0 + 0....... = 9
C
Answer: (C) 9
Question: Joe’s average (arithmetic mean) test score across 4 equally weighted tests was 50. He was allowed to drop his lowest score. After doing so, his average test score improved to 55. What is the lowest test score that was dropped?
(A) 20
(B) 35
(C) 55
(D) 65
(E) 80
Rationale: The arithmetic mean of 4 equally weighted tests was 50. So what we can assume is that we have 4 test scores, each 50.
He dropped his lowest score and the avg went to 55. This means that the lowest score was not 50 and other three scores had given the lowest score 5 each to make it up to 50 too. When the lowest score was removed, the other 3 scores got their 5 back. So the lowest score was 3 *5 = 15 less than 50.
So the lowest score =50 - 15 = 35
Answer (B)
Answer: (B) 35
Question: A 18% stock yielding 8% is quoted at?
(A) 165
(B) 170
(C) 175
(D) 180
(E) 225
Rationale: Assume that face value = Rs.100 as it is not given
To earn Rs.8, money invested = Rs.100
To earn Rs.18, money invested = 100×18/8 = Rs.225
ie, market value of the stock = Rs.175
Answer is E.
Answer: (E) 225
Question: What is the sum of all consecutive multiples of 8 between 400 and 600, inclusive?
(A) 8000
(B) 10,400
(C) 12,500
(D) 13,000
(E) 15,000
Rationale: 400 is 8*50 and 600 is 8*75...
Average of 400 and 600= 500, extreme multiples of 8..
# of multiples of 8 =75-50+1=26..
Sum =#*avg= 26*500=13000
ANSWER:D
Answer: (D) 13,000
Question: P and Q can complete a work in 40 days and 24 days respectively. P alone started the work and Q joined him after 8 days till the completion of the work. How long did the work last?
(A) 5 days
(B) 10 days
(C) 14 days
(D) 20 days
(E) 26 days
Rationale: Explanation :
Work done by P in 1 day = 1/40
Work done by Q in 1 day = 1/24
Work done by P in 8 days = 8 Ã— (1/40) = 1/5
Remaining work = 1 â€“ 1/5 = 4/5
Work done by P and Q in 1 day = 1/40 + 1/24 = 1/15
Number of days P and Q take to complete the remaining work = (4/5) / (1/15) = 12
Total days = 8 + 12 = 20
Answer : Option D
Answer: (D) 20 days
Question: A certain quantity is measured on two different scales, the B-scale and the S-scale, that are related linearly. Measurements on the B-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the B-scale corresponds to a measurement of 100 on the S-scale?
(A)  20
(B)  36
(C)  48
(D)  60
(E)  84
Rationale: First, we have to understand what linearly means. It's not a straight ratio (since 6:30 does NOT equal 24:60). We need to look at the increases in each measurement to see what the scalar actually is.
From 6 to 24 we have an increase of 18. From 30 to 60 we have an increase of 30. Therefore, the increase ratio is 18:30 or 3:5. In other words, for every 3 that B increases, S increases by 5.
We know that S is 100. To get from 60 to 100, we went up by 40, or 8 jumps of 5; therefore, B will go up by 8 jumps of 3.
24 + 8(3) = 24 + 24 = 48=C
Answer: (C)  48
Question: Which one of the following is not a prime number?
(A) 31
(B) 61
(C) 71
(D) 91
(E) 93
Rationale: 91 is divisible by 7. So, it is not a prime number.
D)
Answer: (D) 91
Question: What sum of money will produce Rs.70 as simple interest in 4 years at 2 1/2 percent?
(A) 337
(B) 500
(C) 700
(D) 288
(E) 211
Rationale: 70 = (P*4*5/2)/100
P = 700
Answer: C
Answer: (C) 700
Question: There are 7 executives, including the CEO and CFO, that are asked to form a small team of 4 members. However, the CEO and CFO may not both be assigned to the team. Given this constraint, how many ways are there to form the team?
(A) 25
(B) 28
(C) 30
(D) 32
(E) 35
Rationale: The total number of ways to form a team of 4 is 7C4=35.
We need to subtract the number of teams that have both the CEO and the CFO.
The number of teams with both the CEO and CFO is 5C2=10.
The number of ways to form an acceptable team is 35-10=25.
The answer is A.
Answer: (A) 25
Question: The third proportional to 0.24 and 0.36 is :
(A) 48
(B) 64
(C) 54
(D) 58
(E) 66
Rationale: Explanation :
Solution: Let the third proportion to 0.24 and 0.36 be x.
Then, 0.24 : 0.36 : : 0.36 : x
=> x = 0.36*0.36/0.24 = 0.54
Answer : C
Answer: (C) 54
Question: What is the number of different committees of 9 people that can be selected from a group of 10 people?
(A) a) 20
(B) b) 40
(C) c) 80
(D) d) 10
(E) e)1
Rationale: 10c9 = 10
Answer is D.
Answer: (D) d) 10
Question: What are the last two digits of 35*37*82*71*41?
(A)  10
(B)  30
(C)  50
(D)  70
(E)  80
Rationale: We know that to find the last two digits, we need to find the remainder we get when we divide the product by 100.
Remainder of (63*35*37*82*71*41)/ 100
Note that we can simplify this expression by canceling out the 5 and 2 in the numerator and denominator. But before we do that, here is an important note:
Note: We cannot just cancel off the common terms in the numerator and denominator to get the remainder. But, if we want to cancel off to simplify the question, we can do it, provided we remember to multiply it back again.
So say, we want to find the remainder when 14 is divided by 10 i.e. 14/10 (remainder 4). But we cancel off the common 2 to get 7/5. The remainder here will be 2 which is not the same as the remainder obtained by dividing 14 by 10. But if we multiply 2 back by 2 (the number we canceled off), the remainder will become 2*2 = 4 which is correct.
Take another example to reinforce this – what is the remainder when 85 is divided by 20? It is 5.
We might rephrase it as – what is the remainder when 17 is divided by 4 (cancel off 5 from the numerator and the denominator). The remainder in this case is 1. We multiply the 5 back to 1 to get the remainder as 5 which is correct.
So keeping this very important point in mind, let’s go ahead and cancel the common 5 and 2.
We need the
Remainder of (63*7*37*41*71*41*5*2)/10*5*2
Remainder of (63*7*37*41*71*41)/10
Now using concept 2, let’s write the numbers in form of multiples of 10
Remainder of (60+3)*7*(30+7)*(40+1)*(70+1)*(40+1)/10
Remainder of 3*7*7*1*1*1/10
Remainder of 147/10 = 7
Now remember, we had canceled off 10 so to get the actual remainder so we need to multiply by 10: 7*10 = 70.
When 63*35*37*82*71*41 is divided by 100, the remainder is 70. So the last two digits of 63*35*37*82*71*41 must be 50.
Answer (C)
Answer: (C)  50
Question: A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A.
(A) 240
(B) 288
(C) 277
(D) 877
(E) 361
Rationale: (3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 630 = 240
Answer: A
Answer: (A) 240
Question: If k is an integer and 2 < k < 8, for how many different values of k is there a triangle with sides of lengths 3, 6, and k?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: (6-3) < k < (6+3)
3 < k < 9
Thus k = 4, 5, 6, 7, 8
Since 2 < k < 8, then k can be 4, 5, 6, or 7.
The answer is E.
Answer: (E) 4
Question: During a car trip, Maria stopped to rest after she traveled 1/2 of the total distance to her destination. she stopped again after she traveled 1/4 of the distance remaining between her first stop and her destination, and then she drove the remaining 150 miles to her detination. What was the total distance, in miles from Maria's starting point to her destination?
(A) 280
(B) 320
(C) 360
(D) 400
(E) 480
Rationale: Easy 400 is the answer.
3/4 ( x/2) = 150
x = 150 * 8 /3 = 400.
Answer D
Answer: (D) 400
Question: There is a 30% increase in the price of an article in the first year, a 20% decrease in the second year and a 10% increase in the next year. If the final price of the article is Rs.4576 , then what was the price of the article initially?
(A) Rs.5000
(B) Rs.3000
(C) Rs.4000
(D) Rs.2000
(E) Rs.6000
Rationale: Let the price of the article, four years age be Rs. 100 in the 1st year, price of the article = 100 + 30 = Rs. 130. In the 2nd year, price = 130 - 20% of 130 = 130 - 26 = Rs. 104.
In the 3rd year, price = 104 + 10% of 104 = 104 + 10.4 = Rs. 114.40.
But present price of the article is Rs. 4576
for 114.4 ---> 100 ; 4576 ---> ?
Required price = (4576 * 100)/114.4 = 40 * 100 = Rs.4000.
Answer:C
Answer: (C) Rs.4000
Question: At the Boonsoft Museum, 1 out of every 3 paintings are abstract. If 1 out of every 4 abstract paintings are by Van Heymoe, and there are 20 paintings by Van Heymoe in the museum, how many paintings total are there in the museum?
(A) 40
(B) 250
(C) 240
(D) 300
(E) 350
Rationale: Proportions: Let P = hats, and Pa = abstract paintings, and Pav = abstract paintings by Van Heymoe.
20Pav/xPa = 1Pav/4Pa
xPa = 80Pa
80Pa/yP = 1Pa/3P
yP = 240P
Answer: C
Answer: (C) 240
Question: If a certain sample of data has a mean of 11.0 and the value 20.0 is more than 2.5 standard deviations from the mean, which of the following could be the standard deviation of the sample
(A) 14.75
(B) 3.55
(C) 4.25
(D) 4.0
(E) 2.75
Rationale: 20.0 is more than 2.5 standard deviations from 11 --> 20 > 11 + 2.5*{SD} --> 2.5*{SD} < 9 --> {SD} < 3.6. Only option B offers the standard deviation less than 3.6.
Answer: B
Answer: (B) 3.55
Question: A man buys 10 lts of liquid which contains 20% of the liquid and the rest is water. He then mixes it with 15 lts of another mixture with 30% of liquid. What is the % of water in the new mixture?
(A) 74
(B) 84
(C) 94
(D) 49
(E) 47
Rationale: 20% in 10 lts is 2. So water = 10-2 = 8 lts. 30% of 15 lts = 4.5. So water in 2nd mixture = 15-4.5 = 10.5 lts. Now total quantity = 10 + 15 = 25 lts. Total water in it will be 8 + 10.5 = 18.5 lts. % of water = (100*18.5)/25 = 74
ANSWER:A
Answer: (A) 74
Question: The C.I. on a certain sum for 2 years at 10% per annum is Rs. 525. The S.I. on the same sum for double the time at half the rate percent per annum is?
(A) Rs. 400
(B) Rs. 500
(C) Rs. 600
(D) Rs. 800
(E) Rs. 900
Rationale: Let the sum be Rs. P. Then,
[P(1 + 10/100)2 - p] = 525
P[(11/10)2 - 1] = 525
P = (525 * 100) / 21 = 2500
Sum = Rs. 2500
So, S.I. = (2500 * 5 * 4)/100 = Rs. 500
ANSWER:B
Answer: (B) Rs. 500
Question: In a class of 140 students, 60% of them passed. By what percent is the number of students who passed more than the number of failed students?
(A) 70%
(B) 80%
(C) 58%
(D) 50%
(E) 53%
Rationale: Number of students passed
= 60% of 140 = 60/100 * 140 = 84
Number of students failed
= 140 - 84 = 56.
Required percentage
= 28/56 * 100 = 50%.
Answer:D
Answer: (D) 50%
Question: If y is the smallest positive integer such that 8,820 multiplied by y is the square of an integer, then y must be
(A) 2
(B) 5
(C) 6
(D) 7
(E) 14
Rationale: i just tried plugging in the numbers and found out that
5*8820 = 44, 100, which is a square of 210
B
Answer: (B) 5
Question: If 20 men take 15 days to to complete a job, in how many days can 25 men finish that work?
(A) 12
(B) 66
(C) 77
(D) 8
(E) 6
Rationale: Ans. 12 days
Answer: (A) 12
Question: What sum of money put at C.I amounts in 2 years to Rs.8820 and in 3 years to Rs.9261?
(A) 8000
(B) 2277
(C) 2678
(D) 1276
(E) 1871
Rationale: 8820 ---- 441
100 ---- ? => 5%
x *105/100 * 105/100 = 8820
x*1.1025=8820
x=8820/1.1025 => 8000
Answer:A
Answer: (A) 8000
Question: If m times the mth series of an A.P. is equal to n times its nth series, what is the (m+n)th term of the A.P. ?
(A) 0
(B) m
(C) n
(D) mn
(E) None of these
Rationale: Explanation :
Here's the solution :
mth term of an A.P.
Am = a + (m-1)d-------------------------------(1)
nth term of an A.P.
An = a + (n+1)d--------------------------------(2)
[Here a= First term of an A.P
d= difference between two consecutive terms ]
Now , According to the question;
m*Am = n*An
m(a + (m-1)d)= n(a + (n-1)d)
m(a + md - d)= n(a + nd - d)
am + m2d-md = an + n2d - nd
a(m-n)+ (m2-n2)d -(m-n)d = 0
a(m-n)+ (m-n)(m+n)d -(m-n)d= 0
(m-n)[a + (m+n)d - d ]= 0
[a + (m+n)d - d ]= 0
[a + (m+n-1)d ]= 0-------------------------------------(3)
Hence , According to equation (3)
Am+n = 0
Hence (A) is the correct answer
Answer : A
Answer: (A) 0
Question: If there are 200 questions in a 3 hr examination. Among these questions are 10 type A problems, which requires twice as much as time be spent than the rest of the type B problems. How many minutes should be spent on type A problems?
(A) 17.14286 min
(B) 62 min
(C) 70.1346 min
(D) 74 min
(E) 76.1346 min
Rationale: x=time for type B prolems
2x=time for type A problem
total time=3hrs=180min
190x+10*2x=180
x=180/210
x=0.72
time taken for type A problem=10*2*0.857143=17.14286min
ANSWER:A
Answer: (A) 17.14286 min
Question: Seven cards numbered from 1 to 7 are placed in an empty bowl. First one card is drawn and then put back into the bowl, and then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 9, what is the probability that one of the two cards drawn is numbered 5?
(A) 1/2
(B) 1/3
(C) 1/5
(D) 2/5
(E) 2/7
Rationale: There are 6 ways to get a total sum of 9.
2 of these ways include the number 5.
The probability that one of the cards is a 5 is 2/6 = 1/3
The answer is B.
Answer: (B) 1/3
Question: The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
(A) 8%
(B) 4%
(C) 6%
(D) 3%
(E) 2%
Rationale: 65*(90/100)*((100-x)/100)
= 56.16
x = 4%
Answer: B
Answer: (B) 4%
Question: If n is a natural number, then 6n^2 + 6n is always divisible by?
(A) 6 only
(B) 6 and 12 both
(C) 12 only
(D) 18 only
(E) 20 only
Rationale: 6n^2 + 6n = 6n(n+1), which is always divisible by 6 and 12 both, since n(n+1) is always even.
Answer is B
Answer: (B) 6 and 12 both
Question: A watch was sold at a loss of 10%. If it was sold for Rs.500 more, there would have been a gain of 10%. What is the cost price?
(A) 1000
(B) 2998
(C) 2500
(D) 2788
(E) 2991
Rationale: 90%
110%
--------
20% ---- 500
100% ---- ? => Rs.2500
Answer:C
Answer: (C) 2500
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:
(A) 14 years
(B) 19 years
(C) 33 years
(D) 38 years
(E) 42 years
Rationale: Let the son's present age be x years. Then, (38 - x) = x
2x = 38.
x = 19.
Son's age 5 years back (19 - 5) = 14 years.
Answer: Option A
Answer: (A) 14 years
Question: CONVERT 2.5 hectares in ares
(A) 130 ares.
(B) 160 ares.
(C) 180 ares.
(D) 230 ares.
(E) 250 ares.
Rationale: 2.5 hectares in ares
1 hectare = 100 ares
Therefore, 2.5 hectares = 2.5 × 100 ares
= 250 ares.
ANSWER- E
Answer: (E) 250 ares.
Question: Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 3% sugar by weight. To make a delicious and healthy mixture that is 5% sugar, what should be the ratio of Cereal A to Cereal B, by weight?
(A) 2:5
(B) 2:7
(C) 1:6
(D) 1:4
(E) 1:3
Rationale: Ratio of A / Ratio of B = (Average Wt of Mixture - Wt of B)/(Wt of A - Average Wt of Mixture)
=> Ratio of A / Ratio of B = (5 - 3)/(10 - 5) = 2/5
So they should be mixed in the ratio 2:5
Answer - A
Answer: (A) 2:5
Question: Given distinct positive integers 1, 12, 3, x, 2, and 9, which of the following could be the median?
(A) 1
(B) 3
(C) 6
(D) 8
(E) 9
Rationale: The median of a set with even number of terms is the average of two middle terms when arranged in ascending (or descending) order.
Arrange numbers in ascending order: 1, 2, 3, 9, 11, and x.
Now, x can not possibly be less than 3 as given that all integers are positive and distinct (and we already have 1, 2, and 3).
Next, if x is 3<x<9 then the median will be the average of 3 and x. As all answers for the median are integers, then try odd values for x:
If x=5, then median=(3+5)/2=4 --> not among answer choices;
If x=7, then median=(3+7)/2=5 --> not among answer choices;;
If x is more than 9 so 10 or more then the median will be the average of 3 and 9 so (3+9)/2=6 (the maximum median possible).
Answer: C
Answer: (C) 6
Question: Four faces of a fair die are Yellow, three faces red and one blue.The die is tossed three
times. The probability that the colours, yellow, red and blue appear in the first, second and
third tosses respectively is
(A) 1/36
(B) 1/18
(C) 1/32
(D) 1/37
(E) None of these
Rationale: Probability of getting yellow color = P(Y) = 4/6 = 2/3
Probability of getting red color = P(R) = 3/6 = 1/2
Probability of getting blue color = P(B) = 1/6
So, the probability that the colors yellow, red and blue appear in first, second and third toss respectively= P(Y ∩ R ∩ B) = P(Y) x P(R) x P(B) = 2/3 x 1/2 x 1/6 = 1/18
ANSWER:B
Answer: (B) 1/18
Question: A man buys a cycle for Rs.1400 and sells it at a loss of 20%. What is the selling price of the cycle?
(A) Rs.1090
(B) Rs.1160
(C) Rs.1120
(D) Rs.1202
(E) NONE
Rationale: Solution
S.P	= 80% of Rs.1400
= Rs.(80/100×1400)
Rs.1120.
Answer C
Answer: (C) Rs.1120
Question: How many seconds does Puja take to cover a distance of 500 m, if she runs at a speed of 30 km/hr?
(A) 60 sec
(B) 82 sec
(C) 95 sec
(D) 100 sec
(E) 120 sec
Rationale: Hint:
Time =	Distance / Speed
We see that the distance is given in metres while the speed is given in km/hr and the answer is asked in seconds.
So, convert km/hr into m/s by multiplying	5 /18	m/s to the given value of speed.
30	km / hr	= 30 x	5 /18	=	75 /9 m/sec
i.e. Place these values in the formula:
Time = 500 x	9 / 75= 60 sec
ANSWER IS A
Answer: (A) 60 sec
Question: If 1/a^2 + a^2 represents the diameter of circle O and 1/a + a = 5, which of the following best approximates the circumference of circle O?
(A) 28
(B) 22
(C) 20
(D) 16
(E) 12
Rationale: Given that (1/a)+a =3
Square both sides of the equation:
We get,
[(1/a)^2 + a^2 + 2*(1/a)*a] = 9
=> (1/a)^2 + a^2 + 2 = 9
=> (1/a)^2 + a^2 = 7 ----------------- (1)
Diameter D = (1/a)^2 + a^2
= 7 (From (1))
So Radius = D/2 = 7/2
Circumference = 2*Pi*r
= 2*(22/7)*(7/2)
=28
So the answer should be A.
Answer: (A) 28
Question: In how many different number of ways 5 men and 2 women can sit on a shopa which can accommodate persons?
(A) 170
(B) 180
(C) 200
(D) 210
(E) 220
Rationale: Option 'D'
7p3 = 7 × 6 × 5 = 210
Answer: (D) 210
Question: A certain junior class has 1,200 students and a certain senior class has 800 students. Among these students, there are 60 siblings pairs, each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected at will be a sibling pair?
(A) 3/40,000
(B) 1/3,600
(C) 9/2,000
(D) 1/60
(E) 1/16,000
Rationale: Total number of ways of choosing one student from each group is = 800 * 1200
Number of cases in which a sibling pair will be got is = 60
Thus the probability that the 2 students selected will be a sibling pair is
= 60 /(800 * 1200)
= 1/16,000
E
Answer: (E) 1/16,000
Question: The greatest number which on dividing 1657 and 2037 leaves remainders 10 and 7 respectively, is:
(A) 123
(B) 1
(C) 235
(D) 305
(E) 505
Rationale: Explanation:
Required number = H.C.F. of (1657 - 10) and (2037 - 7)
= H.C.F. of 1647 and 2030 = 1. Answer: B
Answer: (B) 1
Question: Find 6 + 9 + 12 + . . . + 30
(A) 162
(B) 165
(C) 167
(D) 169
(E) 171
Rationale: a = 6
l = 30
d = 9 – 6 = 3
ANSWER IS A
Answer: (A) 162
Question: The number of cars present at a particular time was measured at 4,999 different locations on Tuesday and on Wednesday. The number of locations that had more cars on Wednesday was 20% higher than the number of locations that had more cars on Tuesday. How many of the locations had more cars on Tuesday?
(A) 1,159
(B) 1,333
(C) 1,860
(D) 2,160
(E) 2,272
Rationale: The question states that all these 4,999 locations were measured twice, once on each day.
It also breaks the 4,999 into two groups, the higher-on-Tuesday locations and the higher-on-Wednesday locations, which we can call T and W.
Therefore, we can write two equations:
For each of the first and second day count of locations, T + W = 4999
But, for the second day count, W = 1.20 T
i.e. for Second day count, T + 1.20T = 4999
i.e. 2.20 T = 4999
i.e. T = 2272
E
Answer: (E) 2,272
Question: ind next number in the series
23 21 24 19 26 15 28 11 30 7 36 ?
(A) 12
(B) 20
(C) 5
(D) 40
(E) 34
Rationale: C
5
23-2=21
21+3=24
24-5=19
19+7=26
26-11=15
15+13=28
28-17=11
11+19=30
30-23=7
7+29=36
36-31=5
(2,3,5,7,11,13,17,19,23,29,31,37,41,43... are Prime Numbers)
Answer: (C) 5
Question: The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?
(A) 2500
(B) 2700
(C) 2200
(D) 2900
(E) 2400
Rationale: Let the price of a saree and a shirt be Rs. x and Rs. y respectively.
Then, 2x + 4y = 1600 .... (i)
and x + 6y = 1600 .... (ii)
Divide equation (i) by 2, we get the below equation.
=> x + 2y = 800. --- (iii)
Now subtract (iii) from (ii)
x + 6y = 1600 (-)
x + 2y = 800
----------------
4y = 800
----------------
Therefore, y = 200.
Now apply value of y in (iii)
=> x + 2 x 200 = 800
=> x + 400 = 800
Therefore x = 400
Solving (i) and (ii) we get x = 400, y = 200.
Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.
Answer is E.
Answer: (E) 2400
Question: Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/5 = 8 m/sec.
Relative speed = 12 + 8 = 20 m/sec.
Required time = (120 + 120)/20 = 12 sec.
Answer: Option B
Answer: (B) 12