mathewhe/aqua_rat huggingface dataset:
Question: The difference between the squares of two consecutive odd integers
is a square<1000 whose root equals the combined sum of the digits
of the two integers. What is the sum of the digits of the larger integer?
(A) 2
(B) 5
(C) 8
(D) 10
(E) 11
Rationale: Assume two odd integers to be (2x-1) and (2x+1).
Difference of their squares = (2 x+1)^2 - (2x-1)^2
= 4x^2 + 1 + 4x - (4x^2 + 1 - 4x)
= 4x^2 + 1 + 4x - 4x^2 - 1 + 4x
= 8x
Now root of 8x needs to be an integer such that it is equal to the sum of the digits of the two odd integers.
8 = 2^3, so x needs to be such that it "completes" a perfect square.
If we find x, we can find the value of 2x+1 (larger integer) and then sum of its digits.
Let's check the options, starting with c.
For sum to be 8, few possibilities are: 17, 35, 53, 71
If we take 17, the pair is 15 and 17, meaning x = 8.
8x = 64
root of 64 = 4 but 4 is not equal to 1+5+1+7.
Reject.
If we take 35, the pair is 33 and 35, meaning x = 17.
8x = 8*17
Reject since perfect square is not possible.
If we take 53, the pair is 51 and 53, meaning x = 26.
8x = 8*26
Reject since perfect square is not possible.
If we take 71, the pair is 69 and 71, meaning x = 35.
8x = 8*35
Reject since perfect square is not possible.
I tried each option and the possibilities and then got lost.
Then, it occurred to me that I was only checking 2-digit integers. What about 3-digits?
Starting with option a, only 2-digit odd integer whose sum is 2 is 101.
If we take 101, the pair is 99 and 101, meaning x = 50.
8x = 8*50 = 400
root of 400 = 20 which is indeed equal to 9+9+1+1.
Answer (A).
Answer: (A) 2
Question: P , Q and R started a business by investing Rs 120000 , Rs 135000 & Rs 150000 respectively. Find the share of each, out of the annual profit of Rs 56700
(A) 16800 , 18900 , 21000
(B) 17850 , 18900 , 21000
(C) 16800 , 18900 , 22000
(D) 17850, 18500 , 22000
(E) None of these
Rationale: Explanation :
P : Q : R = 120000 : 135000 : 150000 = 120:135:150
= 24:27:30
= 8:9:10
Share of P= 56700*8/27 = 2100*8 = 16800
Share of Q = 56700*9/27 = 2100*9 = 18900
Share of R = 56700*10/27 = 2100*10 = 21000. Answer : Option A
Answer: (A) 16800 , 18900 , 21000
Question: The arithmetic mean and standard deviation of a certain normal distribution are 15.5 and 1.5, respectively. What value is exactly 2 standard deviations less than the mean?
(A) 10.5
(B) 11
(C) 11.5
(D) 12
(E) 12.5
Rationale: The value which isexactlytwo SD less than the mean is:mean-2*SD=15.5-2*1.5=12.5.
Answer: E.
Answer: (E) 12.5
Question: A bookseller has two display windows. She plans to display 5 new fiction books in the left window, and 3 new non-fiction books in the right window. Assuming she can put the three fiction books in any order, and separately, the three non-fiction books in any order, how many total configurations will there be for the two display windows?
(A) 240
(B) 720
(C) 144
(D) 336
(E) 420
Rationale: Two displays books could be arranged n! # of total arrangements are combinations multiplied together,
5!*3! =120*6=720
Answer is B
Answer: (B) 720
Question: A student multiplied a number by 3/5 instead of 5/3, What is the percentage error in the calculation ?
(A) 22
(B) 64
(C) 365
(D) 29
(E) 36
Rationale: Let the number be x.
Then, ideally he should have multiplied by x by 5/3. Hence Correct result was .
By mistake he multiplied x by 3/5 . Hence the result with error =
Then, error =
Error % = = 64 %
Answer: B
Answer: (B) 64
Question: Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 4 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?
(A) 5 : 1
(B) 10 : 5
(C) 15 : 2
(D) 20 : 2
(E) 25 : 2
Rationale: U/I = 4/2
I/B = 5/1
Since I is multiple of both 2 (as per first ratio) and 5 (as per second ratio) so let's assume that I = 10
i.e. Multiplying teh first ratio by 5 and second ration by 2 in each numerator and denominator
then, U : I : B = 20 : 10 : 2
i.e. U : B = 20 : 2
Answer: Option D
Answer: (D) 20 : 2
Question: If A speaks the truth 20% of the times, B speaks the truth 80% of the times. What is the probability that at least one will tell the truth
(A) 0.82
(B) 0.84
(C) 1.5
(D) 1.2
(E) 1.4
Rationale: probability of A speaks truth p(A)=2/10;false=8/10
probability of B speaks truth p(B)=8/10;false=2/10.For given qtn
Ans=1-(neither of them tell truth).Because A & B are independent events
=1-[(8/10)*(2/10)]=1-16/100=1-0.16=0.84
ANSWER:B
Answer: (B) 0.84
Question: A man saved $2.50 in buying some lumber on sale. If he spent $25 for the lumber, which of
the following is closest to the percentage he saved?
(A) 8%
(B) 9%
(C) 10%
(D) 11%
(E) 12%
Rationale: 2.5/27.5 = 1/11 = 9/99 which is close to 9%.
correct answer B
Answer: (B) 9%
Question: If a student loses 6 kilograms, he will weigh twice as much as his sister. Together they now weigh 126 kilograms. What is the student's present weight in kilograms?
(A) 82
(B) 84
(C) 86
(D) 88
(E) 90
Rationale: Let x be the weight of the sister.
Then the student's weight is 2x+6.
x + (2x+6) = 126
3x = 120
x = 40 kg
Then the student's weight is 86 kg.
The answer is C.
Answer: (C) 86
Question: If (x + 1) times (2x + 1) is an odd integer, then x must be
(A) an odd integer
(B) an even integer
(C) a prime number
(D) a composite number
(E) a negative integer
Rationale: (x + 1) times (2x + 1) means (x + 1) * (2x + 1)..
(x + 1)*(2x + 1)= 2x^2+3x+1...
for 2x^2+3x+1 to be odd, 3x+1 should be odd..
hence 3x should be even, which further leads to x as even..
so x is even integer..
ANSWER:B
Answer: (B) an even integer
Question: A certain sum of money doubles itself in 15 years in how much many years will it trible itself at the same rate?
(A) 20 years
(B) 30 years
(C) 88 years
(D) 44 years
(E) 11 years
Rationale: 100 ---- 100 --- 15
100 --- 15
--------------------
300 ---- 30 years
Answer: B
Answer: (B) 30 years
Question: If a·b·c·d=330, where a, b, c and d are positive integers, and a<b<c<d, which of the following could be the value of d−a?
(A) 9
(B) 10
(C) 11
(D) 13
(E) 15
Rationale: prime factorize : 330 = 2*3*5*11
Hence a = 2 and d = 11 .
Hence answer is 11 - 2 = 9
Answer A
Answer: (A) 9
Question: Evaluate: 983 x 207 - 983 x 107
(A) 98300
(B) 98500
(C) 98600
(D) 98900
(E) 98100
Rationale: 983 x 207 - 983 x 107 = 983 x (207 - 107) = 983 x 100 = 98300.
Answer is A.
Answer: (A) 98300
Question: Caleb and Kyle built completed the construction of a shed in 10 and half days. If they were to work separately, how long will it take each for each of them to build the shed, if it will take Caleb 2 day earlier than Kyle?
(A) 10 and 12
(B) 9 and 11
(C) 20 and 22
(D) 8 and 10
(E) 19 and 21
Rationale: Work = (A)(B)/(A+B) where A and B are the individual times of each entity.
Here, we're told that (working together) the two workers would complete a job in 12 days. This means that (individually) each of them would take MORE than 10 days to do the job.
Answers E, A and C are illogical, since the individual times must both be greater than 10 days.
so we can TEST the values for Answers B and D.
Using the values for Answers B and D...
Answer B: (20)(22)/(20+22) = 440/42 = 10.5 This is a match
Final Answer:
C
Answer: (C) 20 and 22
Question: A & B started a partnership business. A's investment was thrice the investment of B and the period of his investment was two times the period of investments of B. If B received Rs 6000 as profit , what is their total profit?
(A) 28000
(B) 30000
(C) 42000
(D) 34000
(E) None of these
Rationale: Explanation :
Suppose B's investment = x. Then A's investment= 3x
Suppose Bs period of investment = y, then A's period of investment = 2y
A : B = 3x * 2y : xy
= 6 : 1
Total profit * 1/7 = 6000
=> Total profit = 6000*7 = 42000. Answer : Option C
Answer: (C) 42000
Question: In one hour, a boat goes 9 km along the stream and 5 km against the stream. The speed of the boat in still water (in km/hr) is:
(A) 2
(B) 4
(C) 7
(D) 12
(E) 15
Rationale: Sol.
Speed in still water = 1/2 (9+5) kmph = 7 kmph.
Answer C
Answer: (C) 7
Question: Mahesh marks an article 15% above the cost price of Rs. 540. What must be his discount percentage if he sells it at Rs. 496.80?
(A) 18%
(B) 21%
(C) 20%
(D) 19%
(E) None of these
Rationale: CP = Rs. 540, MP = 540 + 15% of 540 = Rs. 621
SP = Rs. 496.80, Discount = 621 - 496.80 = 124.20
Discount % = 124.2/621 * 100 = 20%
ANSWER:C
Answer: (C) 20%
Question: In the last set of tests, a student scored marks in each of 5 subjects in the ratio 4:5:6:7:8 and got an overall score of 72%. If a mark of 50% in a subject is a pass and the maximum marks of each subject is the same, how many subjects did the student pass?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: The tests scores are 4k, 5k, 6k, 7k, and 8k.
The sum of the test scores is 30k.
The average test score is 30k/5 = 72. Then k = 12.
The test scores are 48, 60, 72, 84, and 96.
The student passed 4 subjects.
The answer is D.
Answer: (D) 4
Question: 7^6n -1^ 6n When n is an integer > 0 is divisible by
(A) 119
(B) 127
(C) 141
(D) 154
(E) 165
Rationale: 127
B
Answer: (B) 127
Question: What annual installment will discharge a debt of Rs. 1428 due in 3 years at 12% simple interest?
(A) 315
(B) 345
(C) 425
(D) 335
(E) None of them
Rationale: Let each Installment be Rs. x
Then, ( x+ ((x*12*1)/100)) + (x+ ((x*12*2)/100) ) + x = 1428
=((28x/25) + (31x/25) + x) = 1428 ïƒ› (28x+31x+25x)=(1428*25)
x= (1428*25)/84 = Rs.425.
Therefore,	Each installment = Rs. 425.
Answer is C.
Answer: (C) 425
Question: A sells a Cricket Bat to B at a profit of 20%. B sells it to C at a profit of 25%. If C pays $228 for it, the cost price of the Cricket Bat for A is:
(A) 152
(B) 120
(C) 130
(D) 160
(E) 210
Rationale: A
152
125% of 120% of A = 228
125/100 * 120/100 * A = 228
A = 228 * 2/3 = 152.
Answer: (A) 152
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 14%?
(A) 20%
(B) 28%
(C) 29%
(D) 40%
(E) 70%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 86
2/3 SP1 = 86
SP1 = 129
100 --- 29 => 29%
Answer:C
Answer: (C) 29%
Question: An investment E gained an interest payment of $250 each month when the annual interest rate was 8%, how much more should we invest annually if we want to gain 12% more per month with a new annual interest rate of 7.5% ?
(A) $9,360
(B) $9,100
(C) $8,250
(D) $7,300
(E) $7,150
Rationale: Answer is D : 7,300
An investment E gained an interest payment of $250 each month when the annual interest rate was 8%,Interest per annum with 8% interest rate is = 250* 12 = Principal * Interest Rate(8/100)
This gives Principal as 37,500$
For an revised interest of 12% more and new interest rate of 7.5% , ie. 250* 12 * 1.12 = Principal * Interest Rate (7.5/100)
This gives the new Principal as 44,800.
The question is how much more should we invest, so 44,800 - 37,500 = 7,300.D
Answer: (D) $7,300
Question: A is a working partner and B is a sleeping partner in a business. A puts in 50,000 and B 60,000. A gets 12.5% of the profit for managing the business, and the rest is divided in proportion to their capitals. Find the share of A in profit of 8800.
(A) 3500
(B) 4600
(C) 5400
(D) 4800
(E) None of these
Rationale: The amount A gets for managing
= 12.5% of Rs. 8800 = 1100
Remaining profit = 8800 – 1100 = 7700
This is to be divided in the ratio 5 : 6.
Share of A = 5/11 of 7700 = 3500
⇒ Total share of A = 3500 + 1100 = 4600.
Answer B
Answer: (B) 4600
Question: The average weight of 8 persons increases by 4.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person ?
(A) 75 kg
(B) 65 kg
(C) 55 kg
(D) 85 kg
(E) 101 kg
Rationale: Total weight increased = (8 x 4.5) kg = 36 kg.
Weight of new person = (65 + 36) kg = 101 kg.
Answer: E
Answer: (E) 101 kg
Question: If it takes 12 identical printing presses exactly 5 hours to print 12,000 newspapers, how long would it take 6 of these presses to print 8,000 newspapers?
(A) 6 hrs 40 mins
(B) 6 hrs 50 mins
(C) 6 hrs 30 mins
(D) 5 hrs 40 mins
(E) 6 hrs 50 mins
Rationale: 12 presses - 12,000 newspapers - 5 hours ;
6 presses - 6,000 newspapers - 5 hours ; (300 mins)
6 presses - 8,000 newspapers - 300/6000*8000 = 400 mins = 6 hrs 40 mins
Answer : A
Answer: (A) 6 hrs 40 mins
Question: The volumes of two cones are in the ratio 1 : 20 and the radii of the cones are in the ratio of 1 : 2. What is the ratio of their heights?
(A) A)2:5
(B) B)2:7
(C) C)1:5
(D) D)2:1
(E) E)2:9
Rationale: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/20 = (1)2h1/(2)2h2
=> h1/h2 = 1/5
i.e. h1 : h2 = 1 : 5
Answer: C
Answer: (C) C)1:5
Question: A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
(A) 7
(B) 8
(C) 9
(D) 4
(E) 3
Rationale: 30 --- 3 DS = 10
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (10 + 6)/2
= 8
Answer: B
Answer: (B) 8
Question: A certain junior class has 100 students and a certain senior class has 80 students. Among these students, there are 6 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 will be a sibling pair?
(A) 3/40000
(B) 1/3600
(C) 9/2000
(D) 3/4000
(E) 1/15
Rationale: Let's see
Pick 6/100 first
Then we can only pick 1 other pair from the 800
So total will be 6 / 80 *100
Simplify and you get 3/4000
Answer is D
Answer: (D) 3/4000
Question: A train sets off at 2 p.m. at the speed of 50 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 75 kmph. At what time the trains will meet?
(A) 6.37 p.m
(B) 6.20 p.m
(C) 6.30 p.m
(D) 6.38 p.m
(E) 6.10 p.m
Rationale: D = 50 * 1 Â½ = 75 km
RS = 75 â€“ 50 = 25
T = 75/25 = 3 h
3.30 + 3 h = 6.30 p.m.
Answer: C
Answer: (C) 6.30 p.m
Question: In a recent election, Geoff received 0.5 percent of the 6,000 votes cast. To win the election, a candidate needed to receive more than x% of the vote. If Geoff needed exactly 3,000 more votes to win the election, what is the value of x ?
(A)  50
(B)  50.5
(C)  56
(D)  60
(E)  63
Rationale: Word problems are tricky in somehow more than other problem because you have the additional step to translate.
Breaking the problem: Geoff how many votes he receives ?? 30 votes
he needs 3571 more votes so : 30+3000= 3030
Now what's the problem wants ?? a x %........3030 is what % of total votes 6000........translating: 3030= x/100 * 6000 ---
x= 50.5 %..........B
Answer: (B)  50.5
Question: 1/(5-2√6)=?
(A) 9+4√5
(B) 9-4√5
(C) 9+2√5
(D) 9-2√5
(E) 5+2√6
Rationale: This question requires us to rationalize (fix) the denominator.
For more on this technique, seehttps://www.gmatprepnow.com/module/gmat ... video/1044
Given: 1/(5-2√6)
Multiply top and bottom by the CONJUGATE of 5-2√6, which is 5+2√6
E
Answer: (E) 5+2√6
Question: In a class of 32 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?
(A) 3
(B) 5
(C) 8
(D) 11
(E) 15
Rationale: Total # of students = 32
Avg # of books per student = 2
Total # of books = 32*2 = 64
# of student borrowed at least 3 books = 32-2-12-10 = 8
# of books borrowed by above 8 students = 60-(12*1)+(10*2) = 32
Considering that 7 out of above 8 students borrowed only 3 books, # of books borrowed = 7*3 = 21
So maximum # of books borrowed by any single student = 32 -21 =11
option D
Answer: (D) 11
Question: A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Rs. 855, the total profit is:
(A) Rs. 1425
(B) Rs. 1500
(C) Rs. 1537.50
(D) Rs. 1576
(E) Rs. 1600
Rationale: Explanation:
Let the total profit be Rs. 100.
After paying to charity, A's share = Rs.(95 X 3/5)=Rs. 57
If A's share is Rs. 57, total profit = Rs. 100.
If A's share Rs. 855, total profit =(100/57 X 855)=1500.
ANSWER IS B
Answer: (B) Rs. 1500
Question: A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track at the average speed of 2 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?
(A) 0.5< t < 0.75
(B) 1.75< t < 2.0
(C) 2.0 < t < 2.5
(D) 2.5 < t < 3.0
(E) 3 < t < 3.5
Rationale: D=2, and R=1
circumference thus is 2pi miles
we know that she walked 2mph
knowing the formula rt=D, we can deduce that t= D/r
D is 2pi miles and r is 2mph
t = 2pi/2
pi can be rewritten as 22/7
2*22/7 = 44/7 and multiply this by 1/2 = 44/14. This is greater than 3, but less than 3.5, therefore, 3<t<3.5. Answer choice E.
Answer: (E) 3 < t < 3.5
Question: From the numbers given below select the √11?
(A) 1.5
(B) 2.9
(C) 4.0
(D) 3.1
(E) 3.3
Rationale: 3.3 is the correct answer
Let us simply square all the numbers
3.3*3.3=10.89
3.1*3.1=9.61
Difference
11 - 10.89=0.11
11 - 9.61=1.39
Since 0.11 is lesser of the both, 3.3 is closer
Answer is E
Answer: (E) 3.3
Question: When tossed, a certain six-sided die has an equal probability of landing on any of the six sides. If the die is tossed 2 times, what is the probability that it will land on the same side each time?
(A) 1/2
(B) 1/6
(C) 1/12
(D) 1/36
(E) 1/60
Rationale: On the first toss, the die will land on one of the sides.
On the second toss, the probability of landing on the same side is 1/6.
P(same side both times)=1/6.
The answer is B.
Answer: (B) 1/6
Question: Eight years ago, Rhea was half of Rick in age. If the ratio of their present ages is 3:4, what is the total of their present ages?
(A) 25 years
(B) 28 years
(C) 32 years
(D) 26 years
(E) 28 years
Rationale: let rhea age be x
rick age be y
given
x-8=1/2(y-8)......a
also given
x/y=(3/4)
=>x=3/4(y).......b
by solving a and b
we get y=16
x=12
then x+y=12+16=28
ANSWER:B
Answer: (B) 28 years
Question: You are standing in one of the biggest palaces in the world "Hofburg Palace, Vienna". In palace five commando are staying. Each commando has allotted five big rooms and each room contains five huge Tigers.
Each huge tiger has five small tigers.
We all know a tiger has 4 legs.
So how many legs are there in the palace ?
(A) 3012
(B) 3011
(C) 3010
(D) 3013
(E) 3015
Rationale: Solution:
3012
Explanation:
A)
Five Commando alloted 5 room each, Number of rooms = 5 * 5 = 25
Number of huge Tiger = 25 * 5 = 125
Number of small Tigers = 125 * 5 = 625
Total tigers = 625 + 125 = 750
Number of legs of tigers = 750 * 4 = 3000 ..............................(1)
B)
There are 5 soldiers =>
Number of legs of soldiers = 5*2 = 10 .......................(2)
C)
Your leg = 2 ............(3)
Summing all , 3000 + 10 + 2 = 3012
Answer A
Answer: (A) 3012
Question: John's age is 86 years. If he is 4 more than twice the age of his son, find the age of his son.
(A) 20 years
(B) 22 years
(C) 40 years
(D) 50 years
(E) 60 years
Rationale: Let Mike's son age be x.
4 + 2 x = 84
x = 40
Hence Mike's son age is 40 years
Answer : C
Answer: (C) 40 years
Question: The L.C.M of two numbers is 48. The numbers are in the ratio 2:3. The sum of numbers is:
(A) 28
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: Let the numbers be 2x and 3x.
Then, their L.C.M = 6x. So, 6x = 48 or x = 8.
The numbers are 16 and 24.
Hence, required sum = (16 + 24) = 40.
ANSWER:C
Answer: (C) 40
Question: Veena ranks 73rd from the top in a class of 182. What is her rank from the bottom if 22 students have failed the examination?
(A) 88
(B) 108
(C) 110
(D) 90
(E) 93
Rationale: total student=182
failed=22
paasd student=182-22=160
from bottom her rank is=160-73+1=88
ANSWER:A
Answer: (A) 88
Question: How many 3-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
(A) 690
(B) 720
(C) 740
(D) 760
(E) 780
Rationale: The word 'LOGARITHMS' has 10 different letters.
Hence, the number of 3-letter words(with or without meaning) formed by using these letters
= 10P3
=
10
×
9
×
8
=
720
Option B
Answer: (B) 720
Question: If a man lost 4% by selling oranges at the rate of 16 a rupee at how many a rupee must he sell them to gain 28%?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 10
Rationale: 96% ---- 16
128% ---- ?
96/128 * 16 = 12
Answer: A
Answer: (A) 12
Question: Stock / Number of shares
V ------------ 68
W ---------- 112
X ------------ 56
Y ------------ 94
Z ------------ 45
The table shows the number of shares of each of the 5 stocks owned by Mr Sami. If Mr. Sami was to sell 20 shares of Stock X and buy 22 shares of stock Y, what would be the increase in the range of the numbers of shares of the 5 stocks owned by Mr. Sami?
(A) 4
(B) 6
(C) 9
(D) 13
(E) 20
Rationale: Based on the original number of shares, the range would be: 112 - 45 = 67
However, the prompt tells us that two of the values in the table are going to change. After the changes, the values will be:
V 68
W 112
X 36
Y 116
Z 45
Now the range is 116 - 36 = 80
The INCREASE in the range requires us to compare thenewrange to theoldrange: 80 - 67 = 13
D
Answer: (D) 13
Question: A boy is travelling from his home to school at 3 km/hr and reached 7 min late. Next day he traveled at 12 km/hr and reached 8 min early. Distance between home and school?
(A) 1km
(B) 3km
(C) 4km
(D) 5km
(E) 6km
Rationale: Let the distance be x
T1 = x/3 hr
T2 = x/12hr
Difference in time = 7+8 = 15 =1/4hr
x/3-x/12 = 1/4
x/4 = 1/4
x = 1 km
Answer is A
Answer: (A) 1km
Question: The average of five results is 46 and that of the first four is 45. The fifth result is?
(A) 18
(B) 50
(C) 27
(D) 23
(E) 12
Rationale: 5 * 46 – 4 * 45
= 50
Answer:B
Answer: (B) 50
Question: For covering 88km a wheel revolve 1000 times.what is the radius of wheel?
(A) 14 m
(B) 24 m
(C) 28 m
(D) 40 m
(E) none of the above
Rationale: distance travel in 1 round=88000/1000m=88 m
perimeter=88 m,2πr=88,2R=[88*7/22]=28 m
hence, diameter=28 m
answer C
Answer: (C) 28 m
Question: A chair is bought for Rs.600/- and sold at a loss of 10% find its selling price
(A) Rs.540/-
(B) Rs.550/-
(C) Rs.560/-
(D) Rs.590/-
(E) Rs.580/-
Rationale: 100 % ------> 600 (100 * 6 = 600)
90 % ------> 540 (90 * 6 = 540)
Selling price = Rs.540/-
A)
Answer: (A) Rs.540/-
Question: A florist has 2 azaleas, 4 buttercups, and 5 petunias. The florist puts two flowers together at random in a bouquet. However, the customer calls and says that she does not want two of the same flower. What is the probability that the florist does not have to change the bouquet?
(A) 43/55
(B) 38/55
(C) 17/55
(D) 8/11
(E) 7/11
Rationale: The probability that two of the same flowers were chosen:
P(AA) = 2/11 * 1/10 = 2/110
P(BB) = 4/11 * 3/10 = 12/110
P(PP) = 5/11 * 4/10 = 20/110
The sum of these probabilities is 17/55
P(two flowers are different) = 1 - 17/55 = 38/55
The answer is B.
Answer: (B) 38/55
Question: The H.C.F. of two numbers is 38 and the other two factors of their L.C.M. are 12 and 10. The larger of the two numbers is:
(A) 678
(B) 456
(C) 234
(D) 476
(E) 432
Rationale: :	Explanation:
Clearly, the numbers are (38 x 12) and (38 x 10).
{\color{Blue} \therefore } Larger number = (38 x 12) = 456.
Answer: B)456
Answer: (B) 456
Question: In one alloy there is 12% chromium while in another alloy it is 8%. 10 kg of the first alloy was melted together with 30 kg of the second one to form a third alloy. Find the percentage of chromium in the new alloy.
(A) 9.4%
(B) 9.6%
(C) 9%
(D) 9.8%
(E) 10%
Rationale: The amount of chromium in the new 10+30=40 kg alloy is 0.12*10+0.08*30=3.6 kg, so the percentage is 3.6/40*100=9%.
Answer: C
Answer: (C) 9%
Question: The length of a side of a hexagon is 7 inches. What is the perimeter?
(A) 48
(B) 42
(C) 44
(D) 45
(E) 40
Rationale: Hexagon. It means 6 equal sides.
p = 6(7) = 42 inches
Answer B
Answer: (B) 42
Question: How much is 80% of 40 is greater than 4/5 of 25?
(A) 17
(B) 19
(C) 11
(D) 12
(E) 10
Rationale: (80/100) * 40 – (4/5) * 25
32 - 20 = 12
Answer: D
Answer: (D) 12