mathewhe/aqua_rat huggingface dataset:
Question: This is how Edward’s Lotteries work. First, 9 different numbers are selected. Tickets with exactly 7 of the 9 numbers randomly selected are printed such that no two tickets have the same set of numbers. Finally, the winning ticket is the one containing the 7 numbers drawn from the 9 randomly. There is exactly one winning ticket in the lottery system. How many tickets can the lottery system print?
(A)  9C7
(B)  9P3
(C)  9C9
(D)  9C6
(E)  69
Rationale: since we have to select random 7 numbers from 9 and they all are distinct. i think it should be 9C7 or A
Answer: (A)  9C7
Question: If a Ã— b = 2a - 3b + ab, then 1 Ã— 2 + 2 Ã— 1 is equal to :
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Explanation:
1 Ã— 2 + 2 Ã— 1 = (2 Ã— 1 - 3 Ã— 2 + 1 Ã— 2) + ( 2 Ã— 2 - 3 Ã— 1 + 2 Ã— 1)
= (2 - 6 + 2 + 4 -3 +2) = 1.
Answer: A
Answer: (A) 1
Question: Ratio of present age of P and Q is 7 : 3. After four years their ages are in the ratio of 2 : 1. What is the present age of P ?
(A) 24 years
(B) 28 years
(C) 32 years
(D) Data inadequate
(E) None of these
Rationale: P⁄Q = 7⁄3 ⇒ Q = 3⁄7P.....(i)
also,2Q + 8 = P + 4
or, 2Q – P = – 4...(ii)
Combining equations (i) and (ii), we get
P = 28 years
Answer B
Answer: (B) 28 years
Question: If $x is invested at a constant annually compound interest rate of k percent, what is the ratio of the total amount including interest after 4n years to that after 2n years?
(A) (1+k)^n
(B) (1+k/100)^2n
(C) (1+kn/100)
(D) (1+n/100)^k
(E) (1+kn)
Rationale: Amount after 4n years will be = x ( 1 + k/100)^4n
Amount after 3n years will be = x ( 1 + k/100)^2n
So, required ratio will be -
{ x ( 1 + k/100)^4n } / {x ( 1 + k/100)^2n } = (1+k/100)^2n
Hence answer will be a. (1+k/100)^2n
B
Answer: (B) (1+k/100)^2n
Question: Which of the following inequalities is represented by the following number line?
–7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7
(A) –5 < x < 5
(B) –5 ≤ x < 5
(C) –5 < x ≤ 5
(D) |x| < 5
(E) 5 ≤ |x|
Rationale: The number line includes all values that are both greater than or equal –5, but strictly
less than 5, so the correct answer B)–5 ≤ x < 5
Answer: (B) –5 ≤ x < 5
Question: The largest number in a series of consecutive even integers is w. If the number of integers is n, what is the smallest number in terms of w and n?
(A) w– 2n
(B) w–n + 1
(C) w– 2(n– 1)
(D) n– 6 + w
(E) w – n/2
Rationale: Another method would be to use the concept of Arithmetic Progressions. Consecutive even integers form an AP where the common difference is 2.
In an AP, Last term = First term + (n-1)*common difference
w = First term + (n-1)*2
First term = w - 2(n-1)
ANSWER:C
Answer: (C) w– 2(n– 1)
Question: 8 books are to be arranged in a shelf. Among these, 3 are copies of the same Math book, 3 are copies of the same Physics book and the remaining are copies of the same Chemistry book. How many different arrangements can be created?
(A) 8!/{3!^3}
(B) 8!/{3!3!2!2!}
(C) 8!/{3!^2}
(D) 8!/{(2!)(3!^2)}
(E) 8!/{2!^3}
Rationale: The total number of ways in which a total N items, out of which p are identical of one type, q are identical of another type and rest are different, can be arranged in a line is N!/{p!q!}
In the given problem, we have 8 books out of which 3 are identical Math books, 3 are identical Physics books and the remaining 2 are the same Chemistry books.
Hence the number of words that can be formed is 8!/{3!3!2!}
Ans D
Answer: (D) 8!/{(2!)(3!^2)}
Question: In a certain experiment, the data collected is the number of organisms per sample, and this data follows a normal distribution. If the sample of data has a mean of 80 and a standard deviation of 14, which of the following is exactly 2.60 standard deviations more than the mean?
(A) a) 43.6
(B) b) 60
(C) c) 72
(D) d) 77.5
(E) e) 81
Rationale: Standard Deviation is a relatively rare category in the Quant section, although you're like to be tested on it 1 time on Test Day. You'll never be asked to calculate SD though, so you really just need to learn the basic 'concepts' behind it.
Here, we're told two things about a group of numbers:
1) The average of the group is 80
2) The standard deviation of the group is 14
If you go 1 SDupfrom the average, you hit.....80+14 = 94
If you go 1 SDdownfrom the average, you hit.....80-14 = 66
If you go 2 SDsupfrom the average, you hit.....80+2(14) = 108
If you go 2 SDsdownfrom the average, you hit.....80-2(14) = 52
Etc.
Here, we're asked for the number that is EXACTLY 2.60 SDs above the mean....
2.60 SDsupwould be.....80 + 2.60(14) = 43.6
A
Answer: (A) a) 43.6
Question: If X and Y are sets of integers, X # Y denotes the set of integers that belong to set X or set Y, but not both. If X consists of 12 integers, Y consists of 18 integers, and 6 of the integers are in both X and Y, then X # Y consists of how many integers?
(A) 6
(B) 16
(C) 18
(D) 30
(E) 174
Rationale: The number of integers that belong to set X ONLY is 12-6=6;
The number of integers that belong to set Y ONLY is 18-6=12;
The number of integers that belong to set X or set Y, but not both is 6+12=18.
Answer: C.
Answer: (C) 18
Question: If x is the median of the set {x, 11/3, 28/9, 21/5, 9/2}, x could be
(A) 16/5
(B) 17/5
(C) 30/7
(D) 4
(E) 31/7
Rationale: The median is the middle number once all the numbers are arranged in increasing/decreasing order.
We see that
11/3 = 3.something,
28/9 = 3.something
21/5 = 4.something
9/2 = 4.something
So x should greater than the smallest two numbers and smaller than the greatest two numbers. We can see that x = 4 is possible. (First look at the simplest option or the middle option since options are usually arranged in increasing/decreasing order)
Answer (D)
Answer: (D) 4
Question: If e>0.9, which of the following options can be the value of e?
(A) 0.9^2
(B) √(0.9)
(C) 0.09
(D) 0.9
(E) 0.9^3
Rationale: Lets take a few examples
When .2 is squared it gives .04
when .5 is squared it gives .25
When .9 is squared it gives .81
So raising a fraction to its power of 2 or 3 only reduces the value of the fraction
This is because
.2 = 2/10
.2^2= 4/100
.2^3=8/1000
Since the denominator gets an extra 0 each time u increase the power , it is going to drag the value down
But if you just think about the opposite case :
Then we can see , if squaring a fraction diminish its value, then taking the square root of it will again increase its value
that is √(0.04) will give you back 0.2
so √(0.04) > 0.04
so obviously diminishing the power will appreciate the value
So e √(0.9) > 0.9
Hence Correct Answer is (B)
Answer: (B) √(0.9)
Question: If 25/999=0.002, what is the 81st digit to the right of the decimal point in the decimal equivalent of the fraction?
(A) 6
(B) 5
(C) 4
(D) 3
(E) 2
Rationale: 0.[u]25[/u = 0.002002002002.....
Every 3rd digit is 5 and every multiple of 3 will be the digit 2. Since 81 is multiple of 3, the 81st digit is 2.
Answer E
Answer: (E) 2
Question: A man sells an article at 10% gain. Had be sold at for Rs.60/- more he could have gained 20% what is cost price of article
(A) Rs.500
(B) Rs.600
(C) Rs.650
(D) Rs.760
(E) Rs.800
Rationale: First selling price = 110 % -----> X Rupees
=sold at for Rs.60/- = 120 % -----> X + 60 Rupees
~
----------------------------------------------
10 % --------> 60
100 % ------->Rs.600/-
Option 'B'
Answer: (B) Rs.600
Question: An article is bought for Rs.600 and sold for Rs.550, find the loss percent?
(A) 8 1/3%
(B) 16 1/3%
(C) 19 2/3%
(D) 16 2/3%
(E) 16 8/3%
Rationale: 600 ---- 50
100 ---- ? => 8 1/3%
Answer: A
Answer: (A) 8 1/3%
Question: The product of two numbers is 4107. If the H.C.F of these numbers is 37, then the greater number is?
(A) 377
(B) 126
(C) 111
(D) 727
(E) 121
Rationale: Let the numbers be 37a and 37b.
Then, 37a * 37 b = 4107 => ab = 3
Now, co-primes with product 3 are (1, 3).
So, the required numbers are (37 * 1, 37 * 3) i.e., (1, 111).
Greater number = 111.
Answer:C
Answer: (C) 111
Question: Tom and Jerry are running on the same road towards each other. If Tom is running at a speed of 2.5 meters per second and Jerry is running 36% slower, how much time E will it take them to meet if the initial distance between the two is 50 meters and Tom started running 20 seconds before Jerry did?
(A) 2 minute and 12 seconds.
(B) two minutes.
(C) 44 seconds.
(D) 20 seconds.
(E) 12 seconds.
Rationale: Tom is running alone for 20 seconds.
So he will cover a distance of 20*2.5 = 50 m in 20 seconds=E
Basically, Jerry has not started yet , and Tom has covered the distance alone and met Jerry on the other side
D is the answer
Answer: (D) 20 seconds.
Question: Denise is trying to open a safe whose combination she does not know. IF the safe has 5000 possible combinations,and she can try 50 different possibilities,what is the probability that she does not pick the one correct combination.
(A) 0.08
(B) 159/160
(C) 157/160
(D) 3/160
(E) 0.99
Rationale: If Denise does not pick the correct combination in first 50 try, then the correct combination is one of remaining 4950. So Probability = 4950/5000 = 0.99
answer is E
Answer: (E) 0.99
Question: Venki takes a trip and drives 5 hours from Town X to Town Z at a rate of 80 miles per hour. On her way back, Venki drives 45 miles per hour and stops in Town Y which is midway between Town X and Town Z. How many hours does it take Venki to drive from Town Z to Town Y?
(A) 1.01
(B) 4.44
(C) 11.5
(D) 1.75
(E) 2.14
Rationale: distance from X to Z =5 hr* 80 mph= 400 miles
hence distance from Y to Z= 1/2*400=200
time=200/45=4.44 hrs
IMO: B
Answer: (B) 4.44
Question: A Raz's company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?
(A)  1:2
(B)  4:5
(C)  1:1
(D)  3:2
(E)  5:3
Rationale: A Raz's company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. 1996- x----- y------- x+y
1997- x1---- y1-- x1+y1
x1= a*x .....(P)
y1= 1.07*y...(Q)
x1+y1/x+y = 1.01
solve using P and Q and find x/y
Answer: (A)  1:2
Question: what is the smallest integer that is multiple of 5,7 and 20
(A) 141
(B) 180
(C) 130
(D) 122
(E) 140
Rationale: Correct Answer :E
It is the lcm of 5,7 and 20 which is 140
Answer: (E) 140
Question: The sum of four consecutive numbers is 102. The greatest among these three number is:
(A) 26
(B) 28
(C) 29
(D) 30
(E) 27
Rationale: Let the numbers be x, x + 1 , X+2 and x + 3
Then,
x + (x + 1) + (x + 2)+(X+3) = 102
4x = 96
x = 24
Greatest number, (x + 3) = 27
ANSWER:E
Answer: (E) 27
Question: When positive integer F is divided by positive integer B, the result is 4.35. Which of the following could be the reminder when F is divided by B?
(A)  13
(B)  14
(C)  15
(D)  16
(E)  17
Rationale: the remainder will be obtained from the decimal part when F is divided by B i.e. 0.35
0.35 = 35/100 = 7/20 so possible remainders are 7,14,21,28. Only option B-14 satisfies this
PS: for B-14 F=174 and B=40
Answer: (B)  14
Question: (0.82)(power 3) - (0.1)(power 3)/ (0.82)(power 2) + 0.082 + (0.1)(power 2) is:
(A) 0.86
(B) 0.68
(C) 0.96
(D) 0.69
(E) 0.72
Rationale: Given expression
= (0.82) (power 3) - (0.1)(power 3) / (0.82)(power 2) + (0.82 x 0.1) + (0.1)(power 2)
= a (power 3) - b(power 3) / a(power 2) + ab + b(power 2)
= (a - b)
= (0.82 - 0.1)
= 0.72
Answer is E
Answer: (E) 0.72
Question: How many three digit numbers C greater than 330 can be formed from the digits 1, 2, 3, 4, 5 and 6, if each digit can only be used once?
(A) 72
(B) 48
(C) 120
(D) 96
(E) 76
Rationale: Find the number of 3 digit numbers greater than 300, and then subtract from them the number of three digit numbers between 300 and 330 formed with the given 6 digits.
ABC three digit numbers greater than 300 - total of 4*5*4=80, because a must be greater than 2, so 4 possibilities left; B 5 remaining, and C 4 remaining possibilities to choose from.
Between 300 and 330 there are 1*2*4=8 numbers with the given property: A = 3, 1 possibility; B can be only 1 or 2 (ABC < 330), so two possibilities; C the remaining 4 possibilities after choosing A and B.
Total possible choice 80 - 8 =72=C
Answer: A.
Answer: (A) 72
Question: AB
+BA
___
181
In the addition problem above, A and B represent digits in two different two-digit numbers. What is the sum of A and B?
(A) 6
(B) 8
(C) 9
(D) 11
(E) 14
Rationale: two ways to do it..
1) straight logic..
we can see that ones digit is 1 when units digit B and A are added..
only 14 fits in..
Answer :E
Answer: (E) 14
Question: In a group of donkeys and pigs, the numbers of legs are 16 more than twice the number of heads. The number of donkeys is
(A) 6
(B) 8
(C) 11
(D) 12
(E) 13
Rationale: Let the number of donkeys be x and the number of pigs be y. Then,
4x + 2y = 2(x + y) = 16 or 2x + (2x + 2y) = (2x + 2y) +16
or 2x = 16 or x = 8.
ANSWER:B
Answer: (B) 8
Question: An express A starts at 2.30 pm from nampali station and travels towards vizag station at speed of 80 kmph. Another expressstarts at 4.30 pmfrom nampali station to vizag station at speed of 100 kmph. How far awayfrom station Nampali will the two trains meet??
(A) 600 km
(B) 700 km
(C) 750 km
(D) 800 km
(E) 900 km
Rationale: Let train A take x hours to reach the point of meeting(let it be P)
Then train B will reach the same point in x-2 hours.
Distance covered to reach P by train A in x hours=Distance covered by B to reach P in x-2 hrs.
80*x=100(x-2)
80x=100x-200
x=10 hrs.
Distance from Nampali=x*speed of train A
=10*80
=800 km
ANSWER:D
Answer: (D) 800 km
Question: If the number 517 * 324 is completely divisible by 3, then the smallest whole number in the place of * will be:
(A) 0
(B) 1
(C) 2
(D) 3
(E) None of these
Rationale: (5+1+7+A+3+2+4)=(22+A)MUST BE DIVISIBLE BY 3.
HENCE THE SMALLEST WHOLE No. must be 2
ANSWER:B
Answer: (B) 1
Question: A shopkeeper sells 20% of his stock at 25% profit ans sells the remaining at a loss of 5%. He incurred an overall profit of Rs. 400. Find the total worth of the stock?
(A) 25500
(B) 25000
(C) 40500
(D) 20000
(E) 40000
Rationale: Let the total worth of the stock be Rs. x.
The SP of 20% of the stock = 1/5 * x * 5/4 = 5x/20
The SP of 80% of the stock = 4/5 * x * 0.95 = 152x/200
Total SP = 50x/200 + 152x/200 = 202x/200
Overall profit = 152x/200 - x = 2x/200
x/50 = 400 => x = 40000
Answer:E
Answer: (E) 40000
Question: Letters of the word DIRECTOR are arranged in such a way that all the vowels come together. Find out the total number of ways for making such arrangement.
(A) 4320
(B) 2720
(C) 2160
(D) 1120
(E) None of these
Rationale: Taking all vowels (IEO) as a single letter (since they come together) there are six letters
Hence no. of arrangements = 6!⁄2! × 3! = 2160
[Three vowels can be arranged 3! ways among themselves, hence multiplied with 3!.]
Answer C
Answer: (C) 2160
Question: A can do a piece of work 30 days. B can do work in 45 days. In how many days they will complete the work together?
(A) 15 days
(B) 16 days
(C) 19 days
(D) 17 days
(E) 18 days
Rationale: LCM = 90, Ratio= 30:45=2:3
No of days= 90/(2 + 3) = 90/5 = 18 days
ANSWER:E
Answer: (E) 18 days
Question: What ratio must wheat A at Rs.10.50/kg be mixed with wheat B at Rs.12.30/kg, so that the mixture be worth of Rs.11/kg?
(A) 2:5
(B) 3:7
(C) 5:9
(D) 6:11
(E) 13:5
Rationale: Convert Rs into paise, to make the calculation easy
Ratio =	(B – M)
(M – A)
The required ratio = 130 : 50 = 13 : 5
E
Answer: (E) 13:5
Question: There are 8 books on a shelf, of which 3 are paperbacks and 5 are hardbacks. How many possible selections of 4 books from this shelf include at least one paperback?
(A) a) 40
(B) b) 45
(C) c) 50
(D) d) 55
(E) e) 65
Rationale: approach 1
at-least 1 paper back = total - no paper back
8c4-5c4 = 65
approach 2
at-least 1 paper back = 1 paper back , 3 hard back or 2 paper back 2 hard back
= 3c1*5c3+3c2*5c2+3c3*5c1 = 65
Answer is E
Answer: (E) e) 65
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 150 m and they cross each other in 12 sec, then the speed of each train is?
(A) 30
(B) 35
(C) 45
(D) 37
(E) 38
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (150 + 150)/12 => x = 12.5
Speed of each train = 10 m/sec.
= 12.5 * 18/5 = 45 km/hr.
Answer: Option C
Answer: (C) 45
Question: Amber works 15 days a month at d dollars per day for m months out of the year. Which of the following represents her monthly pay?
(A) 15d
(B) 20dm
(C) 10md/6
(D) 20d/m
(E) 20md
Rationale: ANSWER: A The passage states that she works 15 days a month at d dollars per day, so 15 d is her monthly pay
Answer: (A) 15d
Question: 2 friends A and B running up hill and then to get down length of road-440 yads A on his return journey met B going up at 20 yards from top if A has finished race 5 minute earlier than B then how much time A had taken to complete the race?
(A) 100 minute
(B) 110 minute
(C) 120 minute
(D) 130 minute
(E) 140 minute
Rationale: total journey= 440*2=880
A meet B 20 yards from top in getting down it means he has covered 440+20=460 yards while B is 420 yards.so he is 40 yards ahead of B which is equals to 5 minute.
so 40 yards in 5 min
880 yards will be in 5*880/(40)=110 minute
ANSWER:B
Answer: (B) 110 minute
Question: The banker's discount of a certain sum of money is Rs. 36 and the true discount on the same sum for the same time is Rs. 30. What is the sum due?
(A) Rs. 180
(B) Rs. 120
(C) Rs. 220
(D) Rs. 200
(E) Rs.140
Rationale: F = (BD ×TD)/(BD – TD)=(36×30)/(36–30)=36×30/6=36×5
= Rs. 180
ANSWER:A
Answer: (A) Rs. 180
Question: The simple interest on a sum of money is 4/9 of the principal and the number of years is equal to the rate percent. Find the rate and the time?
(A) 6 2/3%
(B) 6 2/9%
(C) 6 3/3%
(D) 9 2/3%
(E) 7 2/3%
Rationale: 4/9 P = (P*R*R)/100
R = 20/3 = 6 2/3%
Answer: A
Answer: (A) 6 2/3%
Question: A reduction of 20% in the price of salt enables a lady to obtain 2 kgs more for Rs.100, find the original price per kg?
(A) 12.6
(B) 12.1
(C) 12.5
(D) 12.4
(E) 12.7
Rationale: 100*(20/100) = 20 --- 2
? --- 1 => Rs.10
100 --- 80
? --- 10 => Rs.12.5
Answer: C
Answer: (C) 12.5
Question: The value of (0.2×0.2+0.01) (0.1×0.1+0.02)-1 is equal to
(A) 5/3
(B) 9/5
(C) 41/4
(D) 41/12
(E) None
Rationale: Solution
Given expression	(0.2×0.2+0.01)/ (0.1×0.1×+0.02)
= 0.04+0.01/0.01+0.02
= 0.05 / 0.03
= 5 / 3.
Answer A
Answer: (A) 5/3
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions.
(A) 670
(B) 704
(C) 677
(D) 655
(E) 555
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: Option B
Answer: (B) 704
Question: Rs.160 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?
(A) 388
(B) 266
(C) 120
(D) 299
(E) 267
Rationale: 4x 5x 6x
100 50 25
400x + 350x + 150x = 16000
x = 20
6x = 120
Answer: C
Answer: (C) 120
Question: A can do a piece of work in 22 days and B alone can do it in 10 days. B works at it for 5 days and then leaves. A alone can finish the remaining work in
(A) 5days
(B) 6days
(C) 11days
(D) 8.5days
(E) 9days
Rationale: Explanation:
B's 5 days work =
1/10∗5=1/2
Remaining work =1−1/2=1/2
A can finish work =22∗1/2=11 days
Option C
Answer: (C) 11days
Question: If m is an integer such that (-2)^2m=2^(3-m) then m=?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 6
Rationale: (-2)^(2m) = 4^m
and
2^(3-m) = 4^((3-m)/2)
Therefore,
m = (3-m)/2
2m = 3 - m
m = 1
Answer A
Answer: (A) 1
Question: A dishonest milkman wants to make a profit on the selling of milk. He would like to mix water (costing nothing) with milk costing Rs.46 per litre so as to make a profit of 20% on cost when he sells the resulting milk and water mixture for Rs.54 In what ratio should he mix the water and milk?
(A) 1:20
(B) 1:10
(C) 1:8
(D) 1:45
(E) 6:11
Rationale: water = w (liter)
Milk = m (liter)
==> Cost = Price x Quantity = 0.46m
==> Revenue = Price x Quantity = 0.54(m + w)
==> Profit =0.54(m+w) - 0.46m = 0.2*(0.46m)[20% of cost]
==> 0.54m + 0.54w - 0.46m = 0.092m
==> 0.012m = 0.54w
==> m/w = 0.54/0.012 = 45
--OR--
w/m = 1/45
D is correct.
Answer: (D) 1:45
Question: Excluding the stoppages, the speed of a bus is 64 km/hr and including the stoppages the speed of the bus is 48km/hr. For how many minutes does the bus stop per hour?
(A) 15 min
(B) 10 min
(C) 12 min
(D) 20 min
(E) 18 min
Rationale: Speed of the bus without stoppage=64 km/hr
Speed of the bus with stoppage=48km/hr
Difference in speed=16 km/hr
so,the time taken in the stoppages = time taken to cover 16 km=(16/64)hr = 1/4 hr =15 min
ANSWER:A
Answer: (A) 15 min
Question: The lateral surface area of cuboid length 12 m, breadth 8 m and height 6m.
(A) 540
(B) 240
(C) 440
(D) 140
(E) 340
Rationale: Cuboid lateral surface = 2h(l+b)
= 2 × 6 (20) = 240 m(power2)
Answer is B
Answer: (B) 240
Question: What is the probability of flipping a fair coin seven times and the coin landing on heads on at least two flips?
(A) 7/8
(B) 15/16
(C) 31/32
(D) 63/64
(E) 127/128
Rationale: The number of possible outcomes is 2^7=128.
0 heads: There is 1 way to have all tails.
1 head: There are 7 ways to have one head.
P(0 or 1 head)=8/128=1/16
P(at least 2 heads)=1 - 1/16 = 15/16
The answer is B.
Answer: (B) 15/16
Question: Which of the following number is divisible by 24 ?
(A) 35718
(B) 63810
(C) 3125736
(D) 537804
(E) None
Rationale: 24 = 3 x8, where 3 and 8 co-prime.
Clearly, 35718 is not divisible by 8, as 718 is not divisible by 8.
Similarly, 63810 is not divisible by 8 and 537804 is not divisible by 8.
Consider option (C),
Sum of digits = (3 + 1 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 3.
Also, 736 is divisible by 8.
3125736 is divisible by (3 x 8), i.e., 24.
C
Answer: (C) 3125736
Question: The number of the members of a club is more than 10 and less than 40. When 3 people sit at a table, other people exactly divided to 6-people groups (6 people sit at a table) or 5-people groups (5 people sit at a table). If the members are divided to 7-people groups, how many people will be left?
(A) 0.
(B) 1.
(C) 2.
(D) 4.
(E) 5.
Rationale: The number of members is 5k+3 = 6j+3
The only number in this range which satisfies this is 33.
33/7 = 4(7) + 5
The answer is E.
Answer: (E) 5.
Question: On an order of 5 dozen boxes of a consumer product, a retailer receives an extra dozen free. This is equivalent to allowing him a discount of:
(A) 15 2/2
(B) 17 3/2
(C) 18 3/4
(D) 19 2/3
(E) 16 2/3
Rationale: E
16 2/3
Clearly, the retailer gets 1 dozen out of 6 dozens free.
Equivalent discount = 1/6 * 100 = 16 2/3%.
Answer: (E) 16 2/3
Question: B @ K I 9 D Â© 5 2 T $ M 4 E J # U R 1 A Î´ K 5 W 6 % F Q 7 H P 8 Z
How many such numbers are there in the above arrangement each of which is immediately followed by a symbol but not immediately preceded by a consonant?
(A) None
(B) One
(C) Two
(D) Three
(E) More than three
Rationale: Explanation:
Consonant Number Symbol
There is no such combination.
ANSWER IS A
Answer: (A) None
Question: The residents of the town L participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of town L, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week?
(A) - 30
(B) - 20
(C) - 18
(D) - 12
(E) - 6
Rationale: (21-6*2)<number of hours that Pat watched television last week <(21-6*1)
=9<P<15
Only option E (12) satisfies this condition.
Answer: (E) - 6