mathewhe/aqua_rat huggingface dataset:
Question: Two trains run in opposite directions on a circular track. Train A travels at a rate of 4π miles per hour and Train B runs at a rate of 6π miles per hour. If the track has a radius of 6 miles and the trains both start from Point T at the same time, how long, in hours, after the trains depart will they again meet at Point T?
(A) 3
(B) 6
(C) 9
(D) 18
(E) 22
Rationale: I don't agree with your solutions, first. And second the answer choices don't seem to contain the right answer.
My solution is as follows, and I ask anyone to correct me if I am wrong.
Solution 1
Let the distance covered by train A be X, thus that covered by the train B will be 12*3.14-X
dA = X dB = 12*3.14 - X
Times taken by A and B are
tA= X/4*3.14 , tB = (12*3.14 - X)/6*3.14 (ii)
Since they have been traveling for the same period of time, then
X/4*3.14 = (12*3.14 - X)/6*3.14
X/2 =(12*3.14 -X)/3
3X = 2(12*3.14 -X)
5X = 24*3.14
X = 24*3.14/5
Plugging that in either equation of (ii) yields t = 6/5
Solution 2
We add the speed of A and B: totalSpeed T= 4*3.14 + 6*3.14 = 10*3.14
Total distance covered = 12*3.14
t ime = distance / speed = 12*3.14/10*3.14 = 6/5.
tA =( X/4*3.14) =(24*3.14/5)/4*3.14 = 6/5=B
Answer: (B) 6
Question: Yesterday's closing prices of 1,760 different stocks listed on a certain stock exchange were all different from today's closing prices. The number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price. How many of the stocks closed at a higher price today than yesterday?
(A)  960
(B)  726
(C)  1,100
(D)  1,320
(E)  1,694
Rationale: Lets consider the below -
The number of stocks that closed at a higher price = H
The number of stocks that closed at a lower price = L
We understand from first statement -> H+L = 1760 ----(1)
We understand from second statement -> H = (120/100)L => H = 1.2L ----(2)
Solve eq (1)(2) to get H = 960.
A is my answer.
Answer: (A)  960
Question: If s,u, and v are positive integers and 2s=2u+2v, which of the following must be true?
i. s=u
ii. u is not equal to v
iii. s > v
(A) None
(B) I only
(C) II only
(D) III only
(E) II and III
Rationale: Given: 2s=2u+2v --> s=u+v. Now, since s, u, and v are positive integers then s is more than either u or v, so I is never true and III is always true. As for II: it's not necessarily true, for example 4=2+2. So, we have that only option III must be true.
Answer: D
Answer: (D) III only
Question: For all real numbers v, an operation is defined by the equation v* = v - v/3. If (v*)* = 4, then v=
(A) 6
(B) 9
(C) 12
(D) 15
(E) 18
Rationale: (v*)* = (v - v/3) - (v - v/3) / 3
4 = 2v/3 - 2v/9 = 4v/9
v = 9
The answer is B.
Answer: (B) 9
Question: Five 6 faced dice are thrown together. The probability that all the three show the same number on them is?
(A) 1/32
(B) 1/1296
(C) 1/33
(D) 1/38
(E) 1/34
Rationale: The three dice can fall in 6 * 6 * 6 * 6 * 6 = 7776 ways.
Hence the probability is 6/7776
= 1/1296
Answer: B
Answer: (B) 1/1296
Question: Which is greatest in 16 ( 2/3) %, 2/5 and 0.17 ?
(A) 16 (2/3)
(B) 0.17
(C) 2/5
(D) all are equal
(E) none
Rationale: 16 (2/3)% =[ (50/3)* )1/100)]
= 1/6 = 0.166,
2/15 = 0.133.
Clearly,
0.17 is the greatest.
Answer is B.
Answer: (B) 0.17
Question: An article is bought for Rs.675 and sold for Rs.800, find the gain percent?
(A) 38%
(B) 28%
(C) 18%
(D) 22%
(E) 13%
Rationale: 675 ---- 125
100 ---- ? =>
=18%
Answer:C
Answer: (C) 18%
Question: The product A of the first 10 prime numbers is closest to which of the following?
(A) 6.5 x 10^7
(B) 6.5 x 10^8
(C) 6.5 x 10^9
(D) 6.5 x 10^10
(E) 6.5 x 10^11
Rationale: The first 10 primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
So, we need to find approximate value of 2*3*5*7*11*13*17*19*23*29.
# of different approximations are possible. For example:
2*5=10
3*17=~50 (actually more than 50);
7*13=~100 (actually less than 100);
11*19=~200 (actually more than 200)
23*29=667=A
2*3*5*7*11*13*17*19=~10*50*100*200*667=10^7*667=6.67*10^9.
Answer: C.
Answer: (C) 6.5 x 10^9
Question: If x and y are perfect squares, then which five of the following is not necessarily a perfect square?
(A) x^2
(B) xy
(C) 4x
(D) x+y
(E) x^5
Rationale: If x=y=1^2=1, then each option but A is a perfect square, therefore A is NOT necessarily a perfect square.
Answer: A.
Answer: (A) x^2
Question: There are 7 non-collinear points. How many triangles can be drawn by joining these points?
(A) 12
(B) 27
(C) 35
(D) 28
(E) 11
Rationale: A triangle is formed by joining any three non-collinear points in pairs.
There are 7 non-collinear points
The number of triangles formed = 7C3
= 35
Answer: C
Answer: (C) 35
Question: A train is 435 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length
(A) 20 seconds
(B) 30 seconds
(C) 46 seconds
(D) 50 seconds
(E) None of these
Rationale: Explanation:
Speed = 45 Km/hr = 45*(5/18) m/sec
= 25/2 m/sec
Total distance = 435+140 = 575 meter
Time = Distance/speed
=575∗2/25=46seconds
Option C
Answer: (C) 46 seconds
Question: The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:
(A) 0º
(B) 10º
(C) 5º
(D) 20º
(E) 30º
Rationale: Angle traced by hour hand in 13/3 hrs =(360/12 x 13/3)º = 130º. Angle traced by min. hand in 20 min. = (360/60	x 20)º = 120º. Required angle = (130 - 120)º = 10ºAnswer : B
Answer: (B) 10º
Question: Speed of a boat in standing water is 8 kmph and the speed of the stream is 2 kmph. A man rows to place at a distance of 210 km and comes back to the starting point. The total time taken by him is:
(A) 48 hours
(B) 51 hours
(C) 36 hours
(D) 56 hours
(E) None
Rationale: Sol.
Speed upstream = 6 kmph; Speed downstream = 10 kmph.
∴ total time taken = [210/6 + 210/10] hours = 56 hours.
Answer D
Answer: (D) 56 hours
Question: Jill invests $10000 in an account that pays an annual rate of 3.96%, compounding semi-annually. Approximately how much does she have in her account after two years?
(A) $10079.44
(B) $10815.83
(C) $12652.61
(D) $14232.14
(E) $20598.11
Rationale: Solution: first of all, notice the magic word “approximately” — the test-writer is letting us know estimation is perfectly fine. Furthermore, the answer choices are nicely spread out, which will facilitate estimating.
OK, get ready for some fast & furious estimation. The interest rate 3.96% is an ugly number, so I’m going to approximate that as 4%. It compounds semiannually, so that means that there’s 2% every six months, and that happens four times in two years. Well, 2% of $10000 is $200. If you get $200, or a little more, on four occasions, that’s a little more than $800 in interest. We expect an answer slightly higher than $10800, so of course (B) is just right.
Notice, I estimated so that everything up until the last sum was single-digit math. Single-digit calculations are a good standard for which to strive when you are practicing estimation.
By the way, if you find the bank that will do answer (E), double your money in only two years, that’s terrific, but it probably is something wildly illegal, a Ponzi scheme or worse! In the real world, that just doesn’t happen. On word problems, especially in financial situations, you should always have your antenna up for what’s realistic or unrealistic.
answer (B)
Answer: (B) $10815.83
Question: If n is an integer, which of the following CANNOT be a factor of 3n+4?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 3n+4=3(n+1)+1 cannot be a multiple of 3, it's 1 more than multiple of 3: ... 4, 7, 10, 13, 16, ... Hence it cannot be a multiple of 2*3=6 as well.
Answer: C.
Answer: (C) 6
Question: The parameter of a square is equal to the perimeter of a rectangle of length 22 cm and breadth 16 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)
(A) 77.14 cm
(B) 47.14 cm
(C) 84.92 cm
(D) 29.85 cm
(E) 23.57 cm
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(22 + 16) = 76 cm Parameter of the square = 76 cm
i.e. 4a = 76
A = 19
Diameter of the semicircle = 19 cm
Circimference of the semicircle
= 1/2(∏)(19)
= 1/2(22/7)(19) = 418/14 = 29.85 cm to two decimal places
ANSWER:D
Answer: (D) 29.85 cm
Question: n a contest, a bowl contains 10 keys, one of which will open a treasure chest and nine of which will not. If a contestant selects the key that opens the treasure chest, she wins the contents of that chest. If Anna is allowed to draw two keys, simultaneously and at random, from the bowl as the first contestant, what is the probability that she wins the prize?
(A) 1/10
(B) . 1/9
(C) 1/5
(D) 19/90
(E) 2/9
Rationale: The total possibilities existing while withdrawing two keys are: 10C2 = 45
For Anna to win, 9 combinations exist assuming Key 1 to unlock the treasure E.g(1,2), (1,3)....(1,9)
P = 9/45 = 1/5
Option C
Answer: (C) 1/5
Question: Special codes are designated by either a 3-letter or a 4-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different codes that can be designated with this system?
(A) 2(26)^4
(B) 26(26)^3
(C) 27(26)^3
(D) 26(26)^4
(E) 27(26)^4
Rationale: 26^3+26^4 = 26^3(1+26)=27*26^3
The answer is C.
Answer: (C) 27(26)^3
Question: The manager of a produce market purchased a quantity of tomatoes for $0.80 per pound. Due to improper handling, 10 percent of the tomatoes, by weight, were ruined and discarded. At what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 12 percent of the cost of the tomatoes.
(A) $0.94
(B) $0.96
(C) $0.99
(D) $1.00
(E) $1.20
Rationale: Assume the manager bought 100 tomatoes.
Cost Price = 80
Given: 10% are damaged --> Available tomatoes to sell = 90
90 * x - 80 = 0.12 * 80
90x - 80 = 9.6
90x = 89.6
x = 89.6/90 = 0.995
x is slightly under 0.9955 = 0.99
Answer: C
Answer: (C) $0.99
Question: A bag contains $510 in the form of 50 p, 25 p and 20 p coins in the ratio 2 : 3 : 4. Find the number of coins of each type.
(A) 200, 400, 500
(B) 300, 200, 600
(C) 800, 400, 600
(D) 400, 600, 800
(E) 600, 700, 900
Rationale: Let the number of 50 p, 25 p and 20 p coins be 2x, 3x and 4x.
Then 2x × 50/100 + 3x × 25/100 + 4x × 20/100 = 510
x/1 + 3x/4 + 4x/5 = 510
(20x + 15x + 16x)/20 = 510
⇒ 51x/20 = 510
x = (510 × 20)/51
x = 200
2x = 2 × 200 = 400
3x = 3 × 200 = 600
4x = 4 × 200 = 800.
Therefore, number of 50 p coins, 25 p coins and 20 p coins are 400, 600, 800 respectively.
Answer is D
Answer: (D) 400, 600, 800
Question: For all numbers a and b, the operationis defined by ab = (a + 2)(b – 3).
If 3x = –75, then x =
(A)  –15
(B)  –13
(C)  -14
(D)  -12
(E)  15
Rationale: (3+2)(x-3)=-75..
x-3=-15..
x=-12
D
Answer: (D)  -12
Question: Find the value of 1/(3+1/(3+1/(3-1/3)))
(A) 21/89
(B) 89/27
(C) 27/89
(D) 1/14
(E) 1/56
Rationale: 1/[3 + (1/(3+1/(3 - 1/3)))]
=> 1/[3 + 1/(3 + 1/(8/3))]
=> 1/[3 + 1/(3 + 3/8)]
=> 1/[3 + 8/27]
=> 1/(89/27)
=> 27/89
C
Answer: (C) 27/89
Question: If x, y, and z are consecutive odd integers, with x < y < z, then which of the following must be true?
I. y-x is even
II. (z-x)/y is an integer
III. xz is even
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III
Rationale: consecutive odds are:
2x+1, 2x+3, 2x+5
I. (2x+3)-(2x+1) = 2, so divisible by 2 and even - TRUE
II. ((2x+5)-(2x+1))/(2x+3)=4/(2x+3)=4/(odd number)= Not an integer - NOT TRUE
III. (2x+1)*(2x+5)=4x^2+10x+2x+5=4x^2+12x+5=(2x(x+6)+5)/2 is not integer, so NOT TRUE
ANSWER: A
Answer: (A) I only
Question: A man can swim in still water at 3 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
(A) 1.7
(B) 1.0
(C) 1.2
(D) 1.5
(E) 1.16
Rationale: M = 3
S = x
DS = 3 + x
US = 3 + x
3 + x = (3 - x)2
3 + x = 6 -2x
3x = 3
x = 1.0
Answer: B
Answer: (B) 1.0
Question: John buys 100 shares of par value Rs. 20 each, of a company, which pays an annual dividend of 12% at such a price that he gets 10% on his investment. Find the market value of a share.
(A) 2
(B) 24
(C) 5
(D) 6
(E) 8
Rationale: Face value of each share = Rs.20
Total dividend received by John = 100Ã—20Ã—12/100 = Rs.240
Let market value of 100 shares = Rs.x
xÃ—10/100=240
x = 2400
ie, Market value of 100 shares = Rs.2400
Hence, Market value of each share = Rs.24
Answer is B
Answer: (B) 24
Question: From theinteger n, if n*n*n is odd, then what is true from below options?
(A) n is odd and n*n is even
(B) n is odd
(C) n*n is even
(D) n is even
(E) n*n is odd
Rationale: n is odd and n*n is even
Option A
Answer: (A) n is odd and n*n is even
Question: What is the sum of the different positive prime factors of 660?
(A) 5
(B) 10
(C) 15
(D) 17
(E) 21
Rationale: Prime factorization of 660
=66 * 10
=6*11 * 10
=2*3 * 2*5 * 11
=2^2 * 3 * 5 * 11
Sum of the different positive prime factors of 660 = 2+3+5+11
=21
Answer E
Answer: (E) 21
Question: For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT
(A) 32
(B) 38
(C) 44
(D) 52
(E) 63
Rationale: For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT
A. 32
B. 38
C. 44
D. 52
E. 63
Important property:remainder cannot be greater than the divisor.
Therefore, since the remainder when q is divided by r is 7, then r>7;
Similarly, since the remainder when s is divided by t is 3, then t>3.
Now, all answers, except 38 can be represented as the product of two multiples one of which is greater than 7 and another is greater than 3:
32=8*4
44=11*4
52=13*4
63=9*7
However, 38=1*38 or 19*2, thus rt cannot equal to 38.
Answer: B.
Answer: (B) 38
Question: Of the 65 cars on a car lot, 45 have air-bag, 30 have power windows, and 12 have both air-bag and power windows. How many of the cars on the lot have neither air-bag nor power windows?
(A)  8
(B)  2
(C)  10
(D)  15
(E)  18
Rationale: Total -Neither = All Air bag + All Power Windows - Both
or 65 - Neither = 45 + 30 -12 = 63.
=> Neither = 2, hence B.
Answer : B
Answer: (B)  2
Question: The G.C.D of 1.08, 0.36 and 0.6 is
(A) 0.19
(B) 0.1
(C) 0.18
(D) 0.11
(E) 0.12
Rationale: Explanation:
Given numbers are 1.08 , 0.36 and 0.60
H.C.F of 108, 36 and 60 is 12 [because G.C.D is nothing but H.C.F]
therefore H.C.F of given numbers = 0.12
Answer: E
Answer: (E) 0.12
Question: A person has 100$ in 10$ and 5$ bill.If the 5$ bill quantity is twice that of 10$ bill.What is quantity of 10$.
(A) 2
(B) 6
(C) 7
(D) 8
(E) 5
Rationale: Let amount of 10$ be x.Then amount of 5$ be 2x. Now 5*2x+10*x=100.Thus x=5.Answer:E
Answer: (E) 5
Question: A room contains 160 people, 15 percent of whom are women. A group of people, 20 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?
(A) 10
(B) 20
(C) 40
(D) 60
(E) 80
Rationale: Say group of x people left the room.
# of women in the room was 0.15*160=24;
# of women in the group that left 0.2x;
# of women in the room after the group left it is 0.1(160-x);
So, 24-0.2x= 0.1(160-x) --> x=80.
Answer: E.
Answer: (E) 80
Question: In how many ways Chief Minister and Minister be elected from a team of 12 members?
(A) 124
(B) 129
(C) 132
(D) 154
(E) 165
Rationale: To do this, if captain is elected first, then we have 12 ways of doing this.
For election of vice-captain, we have only 11 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 12*11 = 132 ways.
C
Answer: (C) 132
Question: In how many ways can a Chief Minister and a Vice Minister be elected from a team of 8 members?
(A) 32
(B) 40
(C) 48
(D) 56
(E) 64
Rationale: There are 8 choices for the Chief Minister.
Then there are 7 choices for the Vice Minister.
The total number of ways is 8*7 = 56.
The answer is D.
Answer: (D) 56
Question: If a boat goes 7 km upstream in 42 minutes and the speed of the stream is 5 kmph, then the speed of the boat in still water is :
(A) 3.5 km/hr
(B) 4.2 km/hr
(C) 5 km/hr
(D) 10.5 km/hr
(E) None of these
Rationale: Solution
Speed of stream = 1/2 (15-8) km/hr= 3.5kmph . Answer A
Answer: (A) 3.5 km/hr
Question: In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 140800, how many purple chips were selected?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 140800 = 1*5^2*8^3*11
The factors of 8 must come from the purple point value, so there are 3 purple chips.
The answer is C.
Answer: (C) 3
Question: Two numbers are less than a third number by 30% and 37%. How much percent is the second number is less than the first?
(A) 10%
(B) 15%
(C) 20%
(D) 25%
(E) 30%
Rationale: Let the third number be x
first number = 70% of x = 7x/10; second number = 63% of x = 63x/100;
Difference = 7x/10 - 63x/100 = 7x/100; Required percentage = 7x/100 * 10/7x * 100 = 10%
Answer is A
Answer: (A) 10%
Question: A candidate appearing for an examination has to secure 40% marks to pass paper I. But he secured only 40 marks and failed by 20 marks. What is the maximum mark for paper I?
(A) 110
(B) 120
(C) 130
(D) 140
(E) 150
Rationale: he secured 40 marks nd fail by 20 marks so
total marks for pass the examinatn=60
let toal marks x
x*40/100=60
x=150
ANSWER:E
Answer: (E) 150
Question: Find the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs.15of money?
(A) 1500
(B) 2999
(C) 2772
(D) 2987
(E) 2661
Rationale: P = 15(100/10)2 => P = 1500.Answer:A
Answer: (A) 1500
Question: A single discount equivalent to the discount series of 20%, 10% and 8% is?
(A) 31.5
(B) 33.8
(C) 31.6
(D) 31.3
(E) 31.1
Rationale: 100*(80/100)*(90/100)*(92/100)
= 66.2
100 - 66.2 = 33.8
Answer:B
Answer: (B) 33.8
Question: B completes a work in 6 days. A alone can do it in 10 days. If both work together, the work can be completed in how many days?
(A) 3.33 days
(B) 4.33 days
(C) 5.33 days
(D) 6.33 days
(E) 7.33 days
Rationale: 1/5 + 1/10 = 3/10
10/3 = 3.33 days
ANSWER:A
Answer: (A) 3.33 days
Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
(A) 276
(B) 299
(C) 322
(D) 345
(E) 365
Rationale: Clearly, the numbers are (23 x 13) and (23 x 14).
Larger number = (23 x 14) = 322. Answer: Option C
Answer: (C) 322
Question: Which of the following reaches the largest value over the range -1 <= R <= 1?
(A) (R+3)^100
(B) (R+3)/(R^100)
(C) (R+1000)
(D) 97^97
(E) (R/2R)
Rationale: (R+3)/(R^100) can be equal any arbitrarily large number. Some of the other options are large, but they all have a definite maximum. (R+3)/(R^100) does not, so the correct answer is B.
Answer: (B) (R+3)/(R^100)
Question: Two circles, one with radius 10 inches and the other with radius 4 inches, are tangent at point A. Two insects start crawling at the same time from point A: one along the larger circle at 3π inches per minute, the other along the smaller circle at 2.5π inches per minute. How much time has elapsed when the two insects meet again at point A?
(A)  15 minutes
(B)  30 minutes
(C)  40 minutes
(D)  1 hour
(E)  1 hour, 20 minutes
Rationale: First we figure out the circumference of the circles so we can determine how long it takes to complete one revolution from point A to point A .
C (large) = 20pi
C (small) = 8pi
R (large) = 3pi
R (small) = 5/2pi
It takes 20/3 minutes to make one revolution around the larger circle
It takes 8/(5/2) = 16/5 minutes to make one revolution around the smaller circle
The time it takes them to intersect can be determined by finding the LCM of both times. Get the denominators of both numbers equal one another.
20/3 = 100/15
16/5 = 48/15
LCM of 48 and 100:
48 = 2*2*2*2*3
100 = 2*2*5*5
LCM = 2*2*2*2*3*5*5 = 1200
1200/15 = 80 minutes.
(E) 1 hour, 20 minutes
Answer: (E)  1 hour, 20 minutes
Question: In how many ways can 3 postcards can be posted in 5 postboxes?
(A) 125
(B) 286
(C) 296
(D) 199
(E) 167
Rationale: Ans: First card can go into any of the five boxes, Second can go into any of the five boxes, Third can go into any of the five boxes = 5×5×5=1255×5×5=125
Answer:A
Answer: (A) 125
Question: Which of the following integers is a divisor of(15!+11)?
(A) 15
(B) 14
(C) 11
(D) 7
(E) 2
Rationale: When we say 15!, it just means 1*2*3*4*5*...*13*14*15
So you need to find the integer which is a divisor of
(1*2*3*4*5*...*13*14*15 + 11) = 11 (1*2*3*4*5*...10*12*13*14*15 + 1) We obtain this by taking 11 common.
Hence 11 is definitely a divisor of (15! + 11).
C
Answer: (C) 11
Question: Pipes A and B can fill a tank in 6 and 4 hours. Pipe C can empty it in 12 hours. If all pipes are opened together, then the tank will be filled in?
(A) 3hr
(B) 2hr
(C) 1hr
(D) 9/7hr
(E) 5/3hr
Rationale: Net part filled in 1 hour = 1/6 + 1/4 - 1/12 = 1/3
The tank will be full in 3 hr
Answer is A
Answer: (A) 3hr
Question: A number with an interesting property:
When I divide it by 2, the remainder is 1.
When I divide it by 3, the remainder is 2.
When I divide it by 4, the remainder is 3.
When I divide it by 5, the remainder is 4.
When I divide it by 6, the remainder is 5.
When I divide it by 7, the remainder is 6.
When I divide it by 8, the remainder is 7.
When I divide it by 9, the remainder is 8.
When I divide it by 10, the remainder is 9.
It's not a small number, but it's not really big, either.
When I looked for a smaller number with this property I couldn't find one.
Can you find it?
(A) 2588
(B) 2474
(C) 2254
(D) 2519
(E) 8725
Rationale: D
2519
The number has to end in 9.
Looked brute force for small numbers.
59 and 119 were promising, but no cigar.
Then looked for agreement among
39 + multiples of 40,
69 + multiples of 70 and
89 + multiples of 90
Smallest one was 2519.
Answer: (D) 2519
Question: In a certain warehouse, 90 percent of the packages weigh less than 75 pounds, and a total of 48 packages weigh less than 25 pounds. If 80 percent of the packages weigh at least 25 pounds, how many of the packages weigh at least 25 pounds but less than 75 pounds?
(A) 8
(B) 64
(C) 168
(D) 102
(E) 144
Rationale: If 80% of the packages weigh at least 25 pounds
This means that 20% of the packages weigh LESS THAN 25 pounds
Let T = TOTAL number of packages
So, 20% of T = # of packages that weigh LESS THAN 25 pounds
48 packages weigh LESS THAN 25 pounds
GREAT. So, 20% of T = 48
Rewrite to get: 0.2T = 48
Solve:T = 240
90% of the packages weigh less than 75 pounds
So, 90% ofT= number of packages that weigh less than 75 pounds
90% of240=216, so216packages weigh less than 75 pounds
OF THOSE216packages that weigh less than 75 pounds,48packages weigh less than 25 pounds.
So, the number of packages that weight BETWEEN 25 and 75 pounds =216-48= 168 = C
Answer: (C) 168
Question: Paul and Jack are 2 mechanics who work 8 hours per day changing oil in cars at The Oil Spot. If Paul can change oil in 2 cars per hour, and Jack can change oil in 3 cars per hour. What is the least number of cars per work day the 2 men can finish?
(A) 50
(B) 40
(C) 35
(D) 10
(E) 90
Rationale: The proportion equation can be used. Let x = number cars and C = least number of cars per day the 2 men can finish (C = x/(8 hours), P = cars per hour Paul can change, and J = cars per hour Jack can change. Note: 8 hours = a work day
P + J = C
(2 cars/hour) + (3 cars/hour) = x/(8 hours)
Proportion: 2/1 + 3/1/ = x/300
x = 8(2 + 3) = 40. At least 40 cars per work day.
Answer is B
Answer: (B) 40
Question: If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the
average marks of all the students is
(A) 54.48
(B) 54.68
(C) 54.6
(D) 54.58
(E) None of these
Rationale: Explanation:
(55×50)+(60×55)+(45×60)55+60+45
8750160=54.68
Answer: Option B
Answer: (B) 54.68
Question: The total of 324 of 20 paise and 25 paise make a sum of Rs. 70. The no of 20 paise coins is
(A) 238
(B) 277
(C) 220
(D) 200
(E) 288
Rationale: Explanation:
Let the number of 20 paise coins be x. Then the no of 25 paise coins = (324 - x).
0.20 * (x) + 0.25 (324 - x) = 70 => x = 220..
Answer: C) 220
Answer: (C) 220