mathewhe/aqua_rat huggingface dataset:
Question: The speeds of three asteroids were compared. Asteroids X-13 and Y-14 were observed for identical durations, while asteroid Z-15 was observed for 2 seconds longer. During its period of observation, asteroid Y-14 traveled three times the distance X-13 traveled, and therefore Y-14 was found to be faster than X-13 by 6000 kilometers per second. Asteroid Z-15 had an identical speed as that of X-13, but because Z-15 was observed for a longer period, it traveled five times the distance X-13 traveled during X-13's inspection. Asteroid X-13 traveled how many kilometers during its observation?
(A) 500
(B) 1,600/3
(C) 1,000
(D) 1,500
(E) 2,500
Rationale: X13: (t, d, s)
Y14: (t, 3d, s+6000mi/hour)
Z15: (t+2 seconds, s, 5d)
d=?
Distance = Speed*Time
x13: d = s*t
x14: 3d = (s+6000)*t ===> 3d = ts+6000t
z15: 5d = s*(t+2t) ===> 5d = st+2st ===> 5d - 2st = st
3d = 5d - 2st + 6000t
-2d = -2st + 6000t
2d = 2st - 6000t
d = st - 3000t
x13: d = s*t
st - 3000t = s*t
s - 3000 = s
-1500 = s
I got to this point and couldn't go any further. This seems like a problem where I can set up individual d=r*t formulas and solve but it appears that's not the case. For future reference how would I know not to waste my time setting up this problem in the aforementioned way? Thanks!!!
The distance of Z15 is equal to five times the distance of X13 (we established that x13 is the baseline and thus, it's measurements are d, s, t)
S(T+2) = 5(S*T)What clues would I have to know to set up the equation in this fashion? Is it because I am better off setting two identical distances together?
ST+2S = 5ST
T+2 = 5T
2=4T
t= 1/2
We are looking for distance (d=s*t) so we need to solve for speed now that we have time.
Speed y14 - speed x13
Speed = d/t
3d/t - d/t = 6000 (remember, t is the same because both asteroids were observed for the same amount of time)
2d = 6000
2 = 3000
d=s*t
d=3000*(1/2)
d=1500
ANSWER:D
Answer: (D) 1,500
Question: A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.400, find the original price per kg?
(A) s.7
(B) s.9
(C) s.10
(D) s.11
(E) s.19
Rationale: 100*(20/100) = 20 --- 10
? --- 1 => Rs.2
400 --- 80
? --- 2 => Rs.10
Answer:C
Answer: (C) s.10
Question: The true discount on a bill of Rs. 2560 is Rs. 360. What is the banker's discount?
(A) Rs. 432
(B) Rs. 422
(C) Rs. 419
(D) Rs. 442
(E) None of these
Rationale: Explanation :
F = Rs. 2560
TD = Rs. 360
PW = F - TD = 2560 - 360 = Rs. 2200
True Discount is the Simple Interest on the present value for unexpired time
=>Simple Interest on Rs. 2200 for unexpired time = Rs. 360
Banker's Discount is the Simple Interest on the face value of the bill for unexpired time
= Simple Interest on Rs. 2160 for unexpired time
=360/2200 × 2560 = 0.16 × 2560 = Rs. 419 Answer : Option C
Answer: (C) Rs. 419
Question: Statements: Population increase coupled with depleting resources is going to be the scenario of many developing countries in days to come. Conclusions: 1) The population of developing countries will not continue to increase in future. 2) It will be very difficult for the governments of developing countries to provide its people decent quality of life.
(A) Only conclusion I follows
(B) Only conclusion II follows
(C) Either I or II follows
(D) Neither I nor II follows
(E) Both I and II follow
Rationale: The fact given in I is quite contrary to the given statement. So, I does not follow. II mentions the direct implications of the state discussed in the statement. Thus, II follows.
B
Answer: (B) Only conclusion II follows
Question: Which number need to add to 172835 to get a number exactly divisible by 136?
(A) 27
(B) 25
(C) 26
(D) 21
(E) 24
Rationale: 172835 / 136 = 1270 and reminder = 115.
136-115 = 21
So, the next number divisible by 115 is 21 places in front of 172835
Which means 21 + 172835 =172856
21 should be added to 172835
D
Answer: (D) 21
Question: The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
(A) 17 kmph
(B) 40 kmph
(C) 16 kmph
(D) 18 kmph
(E) 20 kmph
Rationale: Speed downstream
= 60 + 20 = 80 kmph
Speed upstream
= 60 - 20
= 40 kmph
Answer:B
Answer: (B) 40 kmph
Question: The market value of a certain machine decreased by 30 percent of its purchase price each year. If the machine was purchased in 1982 for its market value of $10,000, what was its market value two years later?
(A)  $8,000
(B)  $4,000
(C)  $3,200
(D)  $2,400
(E)  $800
Rationale: B.
Market value in 1982= $ 10000
Market value in 1983 = $ 10000- ($ 10000 x 30/100) = 10000-3000= $ 7000
Market value in 1984 = Market value in 1983 - (30 % of $10000)= 7000-3000 = $4000
Answer: (B)  $4,000
Question: Ayesha's father was 40 years of age when she was born while her mother was 32 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
(A) 12 years
(B) 14 years
(C) 16 years
(D) 7 years
(E) 6 years
Rationale: Explanation:
Mother's age when Ayesha's brother was born = 32 years.
Father's age when Ayesha's brother was born = (40 + 4) = 44 years.
Required difference = (44 - 32) = 12 years.
Answer: Option A
Answer: (A) 12 years
Question: 12 men take 18 days to complete a job whereas 12 women in 18 days can complete 5/6 of the same job. How many days will 10 men and 8 women together take to complete the same job?
(A) 6
(B) 13 1â„2
(C) 13
(D) Data inadequate
(E) None of these
Rationale: 12 M Ã— 18 = 12 W Ã— 18 Ã— 6/5
\ w = 5/6 M
10M + 8W = 10M + 8 Ã— 5/6M = 16 2/3 M
\16 2/3men can complete the same work
in 12Ã—18/16 2/3=13 days
Answer C
Answer: (C) 13
Question: Rectangular tile each of size 25cm by 65cm must be laid horizontally on a rectangular floor of size 150cm by 390cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is:
(A) 50
(B) 40
(C) 25
(D) 36
(E) 45
Rationale: Area of tile = 25*65 = 1625
Area of floor = 150*390 = 58500
No of tiles = 58500/1625 = 36
So, the no of tile = 36
ANSWER:D
Answer: (D) 36
Question: Simplify (5^y + 5^y + 5^y + 5^y + 5^y) (4^y + 4^y + 4^y + 4^y)
(A)  4^4y * 3^3y
(B)  20^y+1
(C)  16^y + 9^y
(D)  12^y
(E)  4^y * 12^y
Rationale: ans B
(5^y + 5^y + 5^y + 5^y + 5^y) (4^y + 4^y + 4^y + 4^y)
(5*5^y)(4*4^y)
20*20^y=20^(y+1)..
Answer: (B)  20^y+1
Question: A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:
(A) 250
(B) 276
(C) 280
(D) 285
(E) None
Rationale: Since the month begins with sunday,to there will be five sundays in the month
Average required = (510x5 + 240x25 /30) = 8550/30 =285
Answer: Option D
Answer: (D) 285
Question: Find a sum for 1st 6 prime number's?
(A) 41
(B) 28
(C) 30
(D) 34
(E) 36
Rationale: Required sum = (2 + 3 + 5 + 7 + 11 + 13) = 41
Note: 1 is not a prime number
Option A
Answer: (A) 41
Question: The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8500. If his salary for the month of May is Rs.6500, find his salary for the month of January?
(A) 4500
(B) 5000
(C) 6000
(D) 6500
(E) 7000
Rationale: Sum of the salaries of the person for the months of January, February, March and April = 4 * 8000 = 32000 ----(1)
Sum of the salaries of the person for the months of February, March, April and May = 4 * 8500 = 34000 ----(2)
(2)-(1) i.e. May - Jan = 2000
Salary of May is Rs.6500
Salary of January = Rs.4500
ANSWER A
Answer: (A) 4500
Question: The mean of 50 observations is 200. But later he found that there is decrements of 15 from each observations. what is the the updated mean is ?
(A) 170
(B) 185
(C) 190
(D) 196
(E) 200
Rationale: 185
Answer is B
Answer: (B) 185
Question: Set S consists of integers {6, 7, 10, 12, 15}. If integer n is included in the set, the average (arithmetic mean) of set S will increase by 40%. What is the value of integer n?
(A) 26
(B) 30
(C) 34
(D) 38
(E) 42
Rationale: The average of the numbers in set S is 10.
If we increase the mean by 40%, the new mean is 14.
Thus, on average, 5 numbers increase by 4.
Therefore n = 14+20 = 34
The answer is C.
Answer: (C) 34
Question: A local bank that has 9 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 9 codes?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Pick any two integer.
Integers: 12
Code: 11, 12, 21, 22 = 4 Codes
Add one more integer: 3
13, 31, 33, 23, 32 = 5 Codes
Total = 9 Codes. Enough. Answer: A
Answer: (A) 3
Question: The area of square ABCD above is 12. The shaded region is the intersection of the square and a circular region centered at C. What is the area of the shaded region?
(A) 18−9∗π
(B) 12−3∗π
(C) 9+9/4∗π
(D) 9+9/2∗π
(E) 9/2−9/4∗π
Rationale: =Square - Quarter circle
=12- pi*12/4
=12- pi*3
ANSWER:B
Answer: (B) 12−3∗π
Question: The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 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) 23.57
(B) 23.54
(C) 23.50
(D) 23.55
(E) 23.51
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm
i.e. 4a = 60
A = 15
Diameter of the semicircle = 15 cm
Circimference of the semicircle
= 1/2(∏)(15)
= 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places
Answer: A
Answer: (A) 23.57
Question: find the odd man out:1,3,10,21,64,129,356,777
(A) 3
(B) 10
(C) 21
(D) 64
(E) 356
Rationale: 1=1
3=3
10=1+0=1
21=2+1=3
64=6+4=10=1+0=1
129=1+2+9=12=1+2=3
356=3+5+6=14=1+4=5( wrong one.. it should be 1)
777=7+7+7=21=2+1=3
Alternative 1 and 3 series..
ANSWER:D
Answer: (D) 64
Question: A certain boxer has agreed to pay his opponent a fee of 2.5% of his total purse for every pound over the specified weight limit he weighs in. If the boxer pays his opponent a fee of $225,000 after weighing in eight pounds over the specified limit, what was the boxer's purse?
(A) $65,625
(B) $105,000
(C) $150,000
(D) $183,750
(E) $1,125,000
Rationale: .025*8 = .2
225000/.2 = $1,125,000
Answer: E
Answer: (E) $1,125,000
Question: In a party attended by 12 persons, each clinch their glass with every other. How many glass clinches?
(A) 51
(B) 52
(C) 53
(D) 66
(E) 55
Rationale: Total no. of person = 12
Total no. of glass clinches = n(n-1)/2
=12*11/2
= 66
ANSWER:D
Answer: (D) 66
Question: In an exam, Amar scored 64 percent, Bhavan scored 36 percent and Chetan 44 percent. The maximum score awarded in the exam is 800. Find the average mark scored by all the three boys?
(A) 384
(B) 826
(C) 207
(D) 269
(E) 208
Rationale: Average mark scored by all the three boys =
[64/100 (800) + 36/100 (800) + 44/100 (800)] / 3
= 384
Answer: A
Answer: (A) 384
Question: A group of 55 adults and 70 children go for trekking. If there is meal for either 70 adults or 90 children and if 28 adults have their meal, find the total number of children that can be catered with the remaining food.
(A) 42
(B) 54
(C) 90
(D) 70
(E) 80
Rationale: Explanation:
As there is meal for 70 adults and 28 have their meal, the meal left can be catered to 42 adults.
Now, 70 adults = 90 children
7 adults = 9 children
Therefore, 42 adults = 54 children
Hence, the meal can be catered to 54 children
ANSWER B
Answer: (B) 54
Question: Life expectancy is defined by the formula 2SB/G, where S = shoe size, B = average monthly electric bill in dollars, and G = GMAT score. If Melvin's GMAT score is twice his monthly electric bill, and his life expectancy is 70, what is his shoe size?
(A) 75
(B) 70
(C) 65
(D) 40
(E) 50
Rationale: Solution -
Given that, G = 2B and Life expectancy(L) = 70
L=2SB/G -> 70 = 2SB/2B --> S=70.
ANS B
Answer: (B) 70
Question: The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4?
(A) 56
(B) 86
(C) 25
(D) 76
(E) 63
Rationale: Average after 11 innings = 36
Required number of runs
= (36 * 11) - (32 * 10)
= 396 - 320
= 76.
Answer:D
Answer: (D) 76
Question: For all integers a and b, a%b = (a + b)(a - b). If 8%x = 15, then which of the following could be a value of x?
(A) -7
(B) -6
(C) 2
(D) 3
(E) 6
Rationale: 8%x = (8+x)(8-x)
64-x^2 = 15
x^2 = 49
x=-7,7
Ans: A
Answer: (A) -7
Question: John makes $50 a week from his job. He earns a raise and now makes $60 a week. What is the % increase?
(A) 16%
(B) 16.66%
(C) 17.9%
(D) 18.12%
(E) 20%
Rationale: Increase = (10/50)*100 = (1/5)*100 = 20%.
E
Answer: (E) 20%
Question: 1+2+2^2+2^3+2^4+2^5+2^6+2^7=？
(A) (2^4-1)(2^4+1)
(B) 2^6+1
(C) 2^5-1
(D) 2^5+1
(E) 2^5-2
Rationale: From 1+2+2^2+2^3+2^4+2^5+2^6+2^7=1(2^8-1)/(2-1)=2^8-1=(2^4-1)(2^4+1), the correct answer is A.
Answer: (A) (2^4-1)(2^4+1)
Question: One card is drawn from a pack of 52 cards. What is the probability that the card drawn is a face card?
(A) 4/13
(B) 5/16
(C) 9/17
(D) 2/5
(E) 3/9
Rationale: Out of 52 cards there will be 16 face cards are there.
probability of getting a face card = 16/52 = 4/13
Answer is A
Answer: (A) 4/13
Question: The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 18000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is
(A) 20
(B) 42
(C) 22
(D) 23
(E) NONE
Rationale: Sol.
Let the total number of workers be x. Then,
8000x = (18000 × 7) + 6000 ( x – 7)
‹=› 2000x = 84000
‹=› x = 42.
Answer B
Answer: (B) 42
Question: Find the number of selections that can be made taking 4 letters from the word "ENTRANCE".
(A) 70
(B) 36
(C) 35
(D) 72
(E) 32
Rationale: We have 8 letters from which 6 are unique.
Possible scenarios for 4 letter selection are:
A. All letters are different;
B. 2 N-s and other letters are different;
C. 2 E-s and other letters are different;
D. 2 N-s, 2 E-s.
Let's count them separately:
A. All letters are different, means that basically we are choosing 4 letters form 6 distinct letters: 6C4=15;
B. 2 N-s and other letters are different: 2C2(2 N-s out of 2)*5C2(other 2 letters from distinct 5 letters left)=10;
C. 2 E-s and other letters are different: 2C2(2 E-s out of 2)*5C2(other 2 letters from distinct 5 letters left)=10;;
D. 2 N-s, 2 E-s: 2C2*2C2=1.
15+10+10+1=36
Answer: B.
Answer: (B) 36
Question: The average of 30 numbers is 25. If each number is multiplied by 5, find the new average?
(A) 115
(B) 125
(C) 135
(D) 145
(E) 155
Rationale: Sum of the 30 numbers = 30 * 25 = 750
If each number is multiplied by 5, the sum also gets multiplied by 5 and the average also gets multiplied by 5.
Thus, the new average = 25 * 5 = 125.
ANSWER:B
Answer: (B) 125
Question: During a clearance sale, a retailer discounted the original price of its TVs by 25% for the first two weeks of the month, then for the remainder of the month further reduced the price by taking 20% off the sale price. For those who purchased TVs during the last week of the month, what percent of the original price did they have to pay?
(A) 40%
(B) 45%
(C) 55%
(D) 60%
(E) 62.5%
Rationale: As it's a percentage problem, start with $100.
The first discount is 25% of $100, so the sales prices is 75% of $100 = $75.
The second discount is 20% of $75. Move the decimal once to the left and double it = $7.5*2 = $15.
The final sales price is $75-$15 = $60, which is 60% of $100.
The correct answer is D
Answer: (D) 60%
Question: Find the greatest number which is such that when794, 858 and 1351 are divided by it, the remainders are all same.
(A) 1
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Given, the remainders are same i.e. differences of that numbers are exactly divisible. Hence, you have to find HCF (x–y, y–z, z–x). 858–794 = 64; 1351–794 = 557; 1351–858 = 493. HCF of (64, 557, 493) = 1.
Answer:A
Answer: (A) 1
Question: Find the annual income derived by investing $ 6800 in 50% stock at 136.
(A) 550
(B) 2500
(C) 250
(D) 3000
(E) 400
Rationale: By investing $ 136, income obtained = $ 50.
By investing $ 6800, income obtained = $ [(50/136)*6800] = $ 2500.
Answer B.
Answer: (B) 2500
Question: A train with 120 wagons crosses John who is going in the same direction, in 36 seconds. It travels for half an hour from the time it starts overtaking the John (he is riding on the horse) before it starts overtaking the Mike(who is also riding on his horse) coming from the opposite direction in 24 seconds. In how much time (in secs) after the train has crossed the Mike do the John meets to Mike?
(A) 3576 s
(B) 3589 s
(C) 3596 s
(D) 3598 s
(E) 3576 s
Rationale: Let the length of the train be L metres and speeds of the train Arun and Sriram be R, A and S respectively, then
---------- (i)
and ---------(ii)
From eq.(i) and (ii)
3(R - A ) = 2 (R + K)
R = 3A + 2K
In 30 minutes (i.e 1800 seconds), the train covers 1800R (distance) but the Arun also covers 1800 A (distance) in the same time. Therefore distance between Arun and Sriram, when the train has just crossed Sriram
= 1800 ( R - A) - 24 ( A + K)
Time required =
= (3600 - 24) = 3576 s
E
Answer: (E) 3576 s
Question: How many even multiples of 15 are there between 149 and 301?
(A) 5
(B) 6
(C) 9
(D) 10
(E) 11
Rationale: 150 = 10*15
300 = 20*15
The even multiples are 15 multiplied by 10, 12, 14, 16, 18, and 20 for a total of 6.
The answer is B.
Answer: (B) 6
Question: A team P of 20 engineers can complete work or task in 32 days. Another team Q of 16 engineers can complete same task in 30 days.Then the ratio of working capacity of 1 member of P to the 1 member of Q is
a. 3 : 2
(A) 22
(B) 34
(C) 77
(D) 29
(E) 21
Rationale: Explanation:
Let the capacity of an engineer in P = x units, and in Q = y units.
Working capacity of P = x × 32 × 20
Working capacity of Q = y × 16 × 30
As the total work is same, we equate the above equations.
⇒ x × 32 × 20 = y × 16 × 30
⇒ xy=16×3032×20=34
Answer: B
Answer: (B) 34
Question: 8 gentlemen and 3 gentlewomen are candidates for 2vacancies. A voter has to vote for 2 candidates. In how many ways can one cast his vote?
(A) 51
(B) 52
(C) 55
(D) 56
(E) 57
Rationale: There are 11 candidates and a voter has to vote for any two of them.
So, the required number of ways is,
= 11C2 = 55.
C
Answer: (C) 55
Question: A can do a half of certain work in 70 days and B one third of the same in 35 days. They together will do the whole work in.
(A) 88 days
(B) 27 days
(C) 78 days
(D) 60 days
(E) 17 days
Rationale: A = 140 days
B = 105 days
1/140 + 1/105 = 7/420 = 1/60
=>60 days
Answer: D
Answer: (D) 60 days
Question: What is the least common multiple of 8,12,32,14
(A) 672
(B) 682
(C) 328
(D) 964
(E) 285
Rationale: The given numbers are 8,12,32,14
thus the l.c.m is 2*2*2*1*3*4*7=672
the answer is A
Answer: (A) 672
Question: Look at this series: 70, 71, 76, __, 81, 86, 70, 91, ... What number should fill the blank?
(A) 60
(B) 70
(C) 82
(D) 77
(E) 52
Rationale: B
70
In this series, 5 is added to the previous number; the number 70 is inserted as every third number.
Answer: (B) 70
Question: The credit card and a global payment processing companies have been suffering losses for some time now. A well known company recently announced its quarterly results. According to the results, the revenue fell to $42.0 billion from $69.0 billion, a year ago. By what percent did the revenue fall?
(A) 20.8
(B) 30.4
(C) 31.8
(D) 39.1
(E) 33.8
Rationale: $69-$42=27$
(27/69)*100=39.13%
ANSWER:D
Answer: (D) 39.1
Question: The difference between the value of a number increased by 12.5% and the value of the original number decreased by 25% is 30. What is the original number Q?
(A) 60
(B) 80
(C) 40
(D) 120
(E) 160
Rationale: (1 + 1/8)x - (1 - 1/4)x = 30
(9/8)x - (3/4)x = 30
x = 80=Q
Answer: B
Answer: (B) 80
Question: A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half ?
(A) 15 min
(B) 20 min
(C) 27.5 min
(D) 30 min
(E) 35 min
Rationale: et total time consumed in filling the tank is n.
(A+B)'s 1 minute work is 1/60 + 1/40 and (A+B) will take half of total time ie
(n/2)(1/60 + 1/40)----------(1)
and rest half will be filled by B only in half of total time means (n/2)(1/40)--(2)
(1)+(2)
(n/2)(1/60 + 1/40) + (n/2)(1/40)=1
n=30
ANSWER:D
Answer: (D) 30 min
Question: What annual payment dischargea debit of Rs.12900, due in 4yrs.At 5% rate?
(A) 2000
(B) 1300
(C) 3000
(D) 4300
(E) 4500
Rationale: A.P.=(200X12900)/[4(200+5X3)]=3000 Ans
Alternative
100+105+110+115=12900
430=12900
100=12900/(430)X100=3000
C
Answer: (C) 3000
Question: Bullock likes to keep a spare tyre in his car every time. On a certain day, he travels 1, 00,000 km and just to make the most of all the tyres, he changes the tyres between his journey such that each tyre runs the same distance.
What is the distance traveled by each tyre?
(A) 50,000 km.
(B) 60,000 km.
(C) 70,000 km.
(D) 80,000 km.
(E) 90,000 km.
Rationale: Solution:
80,000.
Explanation:
The distance traveled by each tyre:
4/5 * 1, 00, 000km = 80,000 km.
Answer D
Answer: (D) 80,000 km.
Question: One-third of 1206 is what percent of 400 ?
(A) 3
(B) 30
(C) 300
(D) 100.5
(E) 201.2
Rationale: Answer
Let one-third of 1206 is N% of 400.
∵ 1206/3 = (N x 400)/100
∴ N = (402 x 100) / 400 = 100.5
Correct Option: D
Answer: (D) 100.5
Question: When 24 is divided by the positive integer i, the remainder is 4. Which of the following statements about i must be true?
I. i is even
II. i is a multiple of 5
III. i is a factor of 20
(A) III only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III
Rationale: 24= m*i + 4
m*i=20
put values of m
m=1 i=20
m=2 i=10
m=4 i=5
I. not true
II. true
III. true
D. correct
Answer: (D) II and III only
Question: In ten years, David will be four times as old as Aaron. Twenty years ago, David was twice as old as Ellen. If David is nine years older than Ellen, how old is Aaron?
(A) 1.5–5
(B) 6–10
(C) 11–15
(D) 16–20
(E) 21–25
Rationale: Let David's present age be 'd', Aaron's present age be 'a' and Ellen's present age be 'e'
In ten years, David will be four times as old as Aaron --> d+10 = 4(a+10)
Twenty years ago, David was twice as old as Ellen --> d-20 = 2(e-20)
David is seven years older than Ellen --> d = e + 9
e+9-20 = 2e-40
e-11 = 2e-40
e = 29
d = 36
46 = 4a + 40
a = 1.5
Answer: A
Answer: (A) 1.5–5
Question: A certain industrial machine requires 15 quarts (480 ounces) of oil every day, and it is given a mixture of oil A and oil B. Oil A consists of 5% special additives while oil B consists of 8% special additives. If the machine needs exactly 40 ounces of the special additives to ensure smooth operation, then how much of oil A, in ounces, should be in the mixture?
(A) a.	A – 53.33
(B) b.	B – 280
(C) c. C – 290
(D) d.	D – 300
(E) e.	E – 320
Rationale: 5%*x + 8% *(480-x)=40
1.6 = 3 %*x
x=53.33
A
Answer: (A) a.	A – 53.33
Question: How many positive integers y less than 30 have no common prime factor with 30?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: y=30=2*3*5. So, the number must be less than 30 and not have primes 2, 3, or 5.
This means that the number could be: 1, 7, 11, 13, 17, 19, 23, or 29. Total of 8 numbers.
Answer: D.
Answer: (D) 8
Question: Pipe A runs 30 liters of water per minute out of a pool that has a total volume of 3,600 liters. Pipe B empties a third of the pool in 6 hours.
Working together how long will it take both pipes to empty the pool?
(A) 2 hours and 36 minutes
(B) 1.5 hours
(C) 9 hours and 12 minutes
(D) 15 hours
(E) 1 hour and 48 minutes.
Rationale: Pipe A has a rate of 30 liters per minute which equals a rate of 1800 liters per hour.
Pipe B has a rate of 200 liters per hour.
200 + 1800 (A+B) = Together they have a rate of 2000 liters per hour.
3600 (The pool) / 2000 = 9/5 = 108 / 60 = 1 Hour and 48 minutes
Answer -E
Answer: (E) 1 hour and 48 minutes.