mathewhe/aqua_rat huggingface dataset:
Question: A box contains 15 items. Six of the items are Pen, five are pencil, and five are eraser. If two items are randomly selected from the box, one after the other, what is the probability that both will be pen?
(A) 1/11
(B) 1/9
(C) 1/3
(D) 1/7
(E) 8/9
Rationale: Probability of getting the first pen - 6/15
Probability of getting the second pen - 5/14
total probability = 6/15*5/14 = 1/7
correct option D
Answer: (D) 1/7
Question: When positive integer x is divided by 11, the quotient is y and the remainder is 4. When 2x is divided by 8, the quotient is 3y and the remainder is 3. What is the value of 13y – x ?
(A) 1
(B) 0
(C) -1
(D) -2
(E) -4
Rationale: (1) x = 11y + 4
(2) 2x = 24y + 3
Let's subtract equation (1) from equation (2).
13y - 1 = x
13y - x = 1
The answer is A.
Answer: (A) 1
Question: The radius of a semi circle is 6.3 cm then its perimeter is?
(A) 32.9
(B) 32.4
(C) 32.2
(D) 32.1
(E) 32.7
Rationale: 36/7
r = 6.3 = 32.4
Answer:B
Answer: (B) 32.4
Question: Which of the following fractions is greater than 23/50?
(A) 2/5
(B) 11/34
(C) 43/99
(D) 16/34
(E) 9/20
Rationale: Answer D
23/50=0.46
16/34=0.470 which is 0.01 greater than 0.46
Answer: (D) 16/34
Question: A, B and C started a partnership business by investing Rs.30000, Rs.45000, Rs.50000 respectively. At the end of the year , the profit were distributed among them. If C's share of profit is 36000, What is the total profit?
(A) 70000
(B) 60000
(C) 80000
(D) 90000
(E) 50000
Rationale: A:B:C =30000:45000:50000
=6:9:10
Let total profit =p
Then pÃ—10/25=36000
p=(36000Ã—25)/10=90000
Answer is D.
Answer: (D) 90000
Question: What is the value of √16% ?
(A) 20%
(B) 30%
(C) 40%
(D) 50%
(E) 60%
Rationale: Explanation: br>√16%
=√14/√100
=4/10
=40/100=40%
correct answer is C)40%
Answer: (C) 40%
Question: If 'a' is a positive integer exactly divisible by 3 or 5 but not divisible by 6.What could possibly be the value of 'a' ?
(A) 60
(B) 30
(C) 18
(D) 27
(E) 15
Rationale: 60 and 30 are both divisible by 3 and 5 but also by 6. so they are not the right answer.
18 and 27 are both clearly not divisible by 5(not correct)
15 is both divisible by 3 and 5 but not by 6.
answer : (E) 15
Answer: (E) 15
Question: A sum of money lent out at S.I. amounts to a total of $600 after 2 years and to $850 after a further period of 5 years. What was the initial sum of money that was invested?
(A) $500
(B) $520
(C) $540
(D) $560
(E) $580
Rationale: S.I for 5 years = $850 - $600 = $250
The S.I. is $50/year
S.I. for 2 years = $100
Principal = $600 - $100 = $500
The answer is A.
Answer: (A) $500
Question: A bike covers a certain distance at the speed of 68km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel?
(A) 85 km/h
(B) 85.34 km/h
(C) 87.67 km/h
(D) 90.66 km/h
(E) 90.64 km/h
Rationale: Ans.(D)
Sol. Total distance = 68 × 8 = 544 km
Now speed = 544/6 = 90.66 km/h
Answer: (D) 90.66 km/h
Question: A company that ships boxes to a total of 12 sales centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (assume that the order of the colors in a pair does not matter)
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Back-solving is the best way to solve this problem.
You basically need 12 combinations (including single colors)
If we start from option 1->
1=> 4C2 + 4 = 10 (Not enough)
2=> 5C2 + 5 = 15 (Enough)
Since the minimum number is asked. It should be 5.
Answer - A
Answer: (A) 5
Question: Ratio and proportion
215:474::537:?
(A) 26
(B) 27
(C) 25
(D) 22
(E) 23
Rationale: 2+1+5+4+7+4 =23
5+3+7+x=23
=> x=8
combination that match 8 is 26 since 2+6=8
ANSWER:A
Answer: (A) 26
Question: If 75 percent of a class answered the first question on a certain test correctly, 65 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?
(A) 10%
(B) (8) 20%
(C) 30%
(D) 60%
(E) 65%
Rationale: I didn't understand how to connect 20 percent with the whole equation.
Why 20 is out of the percentile diagram (circles) but inside of 100?
20% appeared in the exam; however did not answer Question AQuestion B correctly
So they are out of the two circles, however as they have appeared in the exam, they have to be taken into consideration for calculation purpose
I am doing it this way:
Suppose the total class size is 100, then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both.
Now,
100 - [(75 - x) + x + (65 - x)] = 20 .......... values are in percent
x = 20 - 100 + 140
x = 60
Ans: D
Answer: (D) 60%
Question: Two friends phil and andrew started running simultaneously from a point P in the same direction along a straight running track. The ratio of speeds of phil and andrew was 2:5. Two hours later, andrew turned back and started running running backwards at one-fifth of his original speed. He met phil at a distance of 10 km from the point P. what was phil's running speed ?
(A) 1.25 km/hr
(B) 2.25 km/hr
(C) 2.5 km/hr
(D) 3.75 km/hr
(E) 6.25 km/hr
Rationale: let speed of Phil was 2x and that of Andrew was 5x.
They move in same direction. relative speed = 3x.
In two hours distance between two = 3x * 2 = 6x.
Now Andrew turns back. His speed is now x.
Now both runners will have a relative speed : 2x+x = 3x.
The two runners will meet, when the distance between them = 6x is exhausted.
this will be done in 2 hours.
Now in initial 2 hours + these 2 hours Phil ran:
2x * 4 hours = 8x distance
8x = 10
x = 10/8 = 1.25.
Phil's speed = 2x = 2.5.
C is the answer.
Answer: (C) 2.5 km/hr
Question: Ana is a girl and has the same number of brothers as sisters. Andrew is a boy and has twice as many sisters as brothers. Ana and Andrew are the children of Emma. How many children does Emma have?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 8
Rationale: no of girls X
no of boys Y
x-1 = y
y-1 = 2x
multiple first with 2
2x-2= 2y
y-1 -2 = 2y => y=3 ignore sign
put in 1 x= 4
total 7
ANSWER:D
Answer: (D) 7
Question: The G.C.D of 1.08, 0.36 and 1.2 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 1.2
H.C.F of 108, 36 and 120 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, B and C have a few coins with them. 7 times the number of coins that A has is equal to 5 times the number of coins B has while 6 times the number of coins B has is equal to 11 times the number of coins C has. What is the minimum number of coins with A, B and C put together?
(A) 110
(B) 127
(C) 154
(D) 165
(E) 145
Rationale: DETAILED SOLUTION
Given, 7A = 5B
42A = 30B
Also given 6B = 11C
30B = 55C
Therefore 42A = 30B = 55C
Let 42A = 30B = 55C = k
Rewriting, A/55 = B/30 = C/42
The least possible integral values for A, B, C will be A = 42; B = 30 and C = 55
Total = 42 + 30 + 55 = 127
Correct Answer: B
Answer: (B) 127
Question: If a certain toy store's revenue in November was 4/5 of its revenue in December and its revenue in January was 3/4 of its revenue in November, then the store's revenue in December was how many times the average (arithmetic mean) of its revenues in November and January?
(A)  1/4
(B)  1/2
(C)  2/3
(D)  2
(E)  4
Rationale: Let Dec rev =100
Then Nov rev is 4/5 (100) => 80
Therefore Jan rev = 3/4(Nov rev) = 3/4(80) => 60
Hence Dec rev = x*( Nov rev+Jan rev)/2
100 = x* (80+60)/2
x = 100/70 => 1.42=2
Ans) D
Answer: (D)  2
Question: In a 4 person race, medals are awarded to the fastest 3 runners. The first-place runner receives a gold medal, the second-place runner receives a silver medal, and the third-place runner receives a bronze medal. In the event of a tie, the tied runners receive the same color medal. (For example, if there is a two-way tie for first-place, the top two runners receive gold medals, the next-fastest runner receives a silver medal, and no bronze medal is awarded). Assuming that exactly three medals are awarded, and that the three medal winners stand together with their medals to form a victory circle, how many X different victory circles are possible?
(A) 24
(B) 52
(C) 96
(D) 144
(E) 648
Rationale: Possible scenarios are:
1. Gold/Silver/Bronze/No medal (no ties) - 4!=24;
2. Gold/Gold/Silver/No medal - 4!/2!=12;
3. Gold/Silver/Silver/No medal - 4!/2!=12;
4. Gold/Gold/Gold/No medal - 4!/3!=4.
Total X: 24+12+12+4=52
Answer: B.
Answer: (B) 52
Question: For the positive integers x, x + 2, x + 4, x + 7, and x + 32, the mean is how much greater than the median?
(A) 0
(B) 1
(C) 2
(D) 4
(E) 5
Rationale: Mean = (x + x+2 + x+4 + x+7 + x+32)/5
=(5x+45)/5
=x+9
Median = x+4
Thus Mean - Median = x+9 - (x+4)
=5
Answer = E
Answer: (E) 5
Question: In right triangle ABC, AC is the hypotenuse. If AC is 10 and AB + BC = 20, what is the area of the triangle ABC?
(A) 225
(B) 450
(C) 75
(D) 200
(E) 200√2
Rationale: Square AB + BC = 20:
(AB)^2 + 2*AB*BC + (BC)^2 = 400. Since (AC)^2 = (AB)^2 + (BC)^2 = 10^2 = 100, then (AB)^2 + 2*AB*BC + (BC)^2 = 100 + 2*AB*BC = 400.
100 + 2*AB*BC = 400.
AB*BC = 150.
The area = 1/2*AB*BC = 75.
Answer: C.
Answer: (C) 75
Question: Car A runs at the speed of 50 km/hr and reaches its destination in 8 hours. Car B runs at the speed of 60 km/h and reaches its destination in 4 hours. What is the ratio of distances covered by Car A and Car B?
(A) 3 : 7
(B) 4 : 9
(C) 13 : 7
(D) 5 : 3
(E) 6 : 11
Rationale: Car A travels 50 × 8 = 400 km
Car B travels 60 × 4 = 240 km
The ratio is 400 : 240 = 40 : 24 = 5 : 3
The answer is D.
Answer: (D) 5 : 3
Question: If ‘DELHI’ is coded as ‘15’, ‘RAJASTHAN’ is coded as ’45’, then ‘MUMBAI’ is coded as ?
(A) 24
(B) 21
(C) 18
(D) 19
(E) None
Rationale: delhi=38->38-8/2=15
rajasthan=92->92-2/2=45
mumbai=59->59-9/2=25
so none
ANSWER:E
Answer: (E) None
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 68 years now, the son's age five years back was?
(A) 16 years
(B) 14 years
(C) 18 years
(D) 19 years
(E) 29 years
Rationale: Let the son's present age be x years.
Then, (68 - x) = x
2x = 68 => x = 34
Son's age 5 years back = (34 - 5)
= 29 years.
Answer: E
Answer: (E) 29 years
Question: If 36 men can do a piece of work in 25 hours, in how many hours will 15 men
do it ?
(A) 60 hours
(B) 50hours
(C) 65 hours
(D) 45 hours
(E) 30 hours
Rationale: Let the required number of hours be x. Then,
Less men, More hours	(Indirect Proportion)
15 : 36 : : 25 : x<=>(15 x x) =(36 x 25)<=>(36 x 25)/15 = 60
Hence, 15 men can do it in 60 hours
Answer is A.
Answer: (A) 60 hours
Question: At what time between 2 and 3 o'clock will the hands of a clock be together?
(A) (10 + 10/11) min past 9
(B) (10 + 10/11) min past 2
(C) (10 + 10/11) min past 3
(D) (10 + 10/11) min past 7
(E) (10 + 10/11) min past 1
Rationale: Explanation:
At 2 o'clock, the hour hand is at 2 and the minute hand is at 12, i.e. they are 10 min spaces apart.
To be together, the minute hand must gain 10 minutes over the hour hand.
Now, 55 minutes are gained by it in 60 min.
10 minutes will be gained in min. = min.
The hands will coincide at min. past 2.
Answer: B) (10 + 10/11) min past 2
Answer: (B) (10 + 10/11) min past 2
Question: X completes a work in 12 days and Y complete the same work in 24 days. If both of them work together, then the number of days required to complete the work will be?
(A) 6 days
(B) 8 days
(C) 10 days
(D) 12 days
(E) 14 days
Rationale: If X can complete a work in x days and Y can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 12 × 24/ 36 = 8 days.
B)
Answer: (B) 8 days
Question: The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's?
(A) 2.3
(B) 2.6
(C) 3.6
(D) 4.5
(E) 4.6
Rationale: Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)]
= 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20.
Required average = (9.2 / 2) = 4.6.
E
Answer: (E) 4.6
Question: A necklace is made by stringing N individual beads together in the repeating pattern blue bead, green bead, white bead, brown bead, and orange bead. If the necklace design begins with a blue bead and ends with a white bead, then N could equal
(A) 79
(B) 76
(C) 68
(D) 64
(E) 72
Rationale: Recognize that we are going to have to look for an answer thats a multiple of 5, plus 3.
Mutliple of 5 because there are 5 beads in the pattern, and plus 3 because the bead ends on white, which is 3 into the pattern.
I just went through all the answer choices, and only E fits. 5x13 = 65, and 65+3=68
Answer : C
Answer: (C) 68
Question: An = 2An-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If A5 = Q4 and A7 = 316, what is the first value of n for which Qn is an integer?
(A)  1
(B)  2
(C)  3
(D)  4
(E)  5
Rationale: Assuming I have understood the symbols used correctly answer is C- 3
A7 = 2S6 +4 = 316
A6 = 312/2 = 156 = 2A5 + 4
A5 = 152/2 = 76 = Q4
Q4 = 4Q3 + 8 = 76
Q3 = 68/4 = 17
Q3 = 4Q2 + 8 = 17
Q2 = 9/4 = 2.25
Q2 = 4Q1 + 8
Q1 will not be integer=C
Answer: (C)  3
Question: The number of singles that a baseball player hit increased 12 percent from her first season to her second season, and the number of doubles that she hit in the same time period decreased by 2 percent. If the total number of singles and doubles that she hit increased 2 percent from her first season to her second season, what is the ratio of the number of singles she hit in her first season to the number of doubles she hit in her first season?
(A) 1:2
(B) 2:5
(C) 1:3
(D) 2:3
(E) 3:5
Rationale: Soln:-
1.12S + 0.98D = 1.02[S + d]
0.10S = 0.04D
S/D = 2/5
ANSWER:B
Answer: (B) 2:5
Question: If x/y = 3 and (2a - x)/(3b - y) = 3, then the value of a/b is?
(A)  –3
(B)  9/2
(C)  1
(D)  2
(E)  3
Rationale: x = 3y
2a - 3y = 3(3b - y)
2a - 3y = 9b - 3y
2a = 9b
a/b = 9/2
Answer: B
Answer: (B)  9/2
Question: If Greg buys 3 shirts, 6 trousers and 4 ties, the total cost is $80. If Greg buys 7 shirts, 2 trousers and 4 ties, the total cost is $80. How much will it cost him to buy 5 trousers, 4 shirts and 4 ties?
(A) $60
(B) $64
(C) $80
(D) $96
(E) Cannot be determined
Rationale: Solution: 3x+6y+4z=80 7x+2y+4z=80
adding both the equations= 10x+8y+8z=160
5x+4y+4z=80
ans C
Answer: (C) $80
Question: A tradesman by means of his false balance defrauds to the extent of 22%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
(A) 47
(B) 46.8
(C) 48.8
(D) 49
(E) 27
Rationale: Explanation:
g% = 22 + 22+ (22*22)/100
= 48.8%
Answer: C
Answer: (C) 48.8
Question: Jack got paid today for his part-time job as a juggler, and noticed that 20% of his paycheck went to taxes. Jack wants to spend 80% of what's left on a new bike, and put the rest into savings. If Jack puts $20 into savings, how much was his original paycheck before taxes?
(A) $125
(B) $135
(C) $145
(D) $155
(E) $165
Rationale: Let P be Jack's original paycheck value. The value after taxes T is given byT = P - 20%PLet S be the amount put into savings, given byS = T - 80%Tfor S = $20, solve for P$20 = (P - 20%P) - 80%(P - 20%P)P = $125Correct answer A
Answer: (A) $125
Question: In the number 11,0AB, A and B represent the tens and units digits, respectively. If 11,0AB is divisible by 45, what is the greatest possible value of B × A?
(A) 0
(B) 5
(C) 10
(D) 15
(E) 25
Rationale: You should notice that 55*2=110 so 11,000 is divisible by 55: 55*200=11,000 (or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55) --> B*A=0*0=0. Next number divisible by 55 is 11,000+55=11,055: B*A=5*3=15 (next number won't have 110 as the first 3 digits so we have only two options 0 and 25).
Answer: D.
!
Please post PS questions in the PS subforum:gmat-problem-solving-ps-140/
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D
Answer: (D) 15
Question: The average of first ten prime numbers which are odd is?
(A) 15.6
(B) 15.1
(C) 15.9
(D) 15.8
(E) 15.3
Rationale: Sum of first 10 prime no. which are odd
= 158
Average = 158/10
= 15.8
Answer:D
Answer: (D) 15.8
Question: The duplicate ratio of 3:4 is?
(A) 1:2
(B) 1:4
(C) 1:8
(D) 9:16
(E) 1:13
Rationale: 3^2: 4^2 = 9:16
ANSWER:D
Answer: (D) 9:16
Question: Find the value of 3 + 2 â€¢ (5 â€“ 3)
(A) 25
(B) 13
(C) 7
(D) 24
(E) 15
Rationale: 3 + 2 â€¢ (5 â€“ 3)
= 3 + 2 (2)
= 3 + 2 *2
= 3 + 4
= 7
correct answer C
Answer: (C) 7
Question: The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R and 20 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G ?
(A) 15%
(B) 20%
(C) 40%
(D) 50%
(E) 6%
Rationale: Let rate in R = 100x
then P = 75x
G = 100y
P = 80y
Thus
75 x=80y
or x = 1.06 y
Ans R = 106y
so increase = 6%
Answer: E
Answer: (E) 6%
Question: If you are rolling 2 dice, what is the probability of rolling a 11?
(A) 1/2
(B) 4/15
(C) 5/18
(D) 2/3
(E) 1/6
Rationale: The answer would be 5/18, as there are 10/36 ways to get 11. Answer: C
Answer: (C) 5/18
Question: An electric motor makes 3,000 revolutions per minutes. How many degrees does it rotate in one second?
(A) 18.000 d/sec
(B) 28.000 d/sec
(C) 38.000 d/sec
(D) 26.000 d/sec
(E) 35.000 d/sec
Rationale: 3000 revolutions / minute
= 3000*360 degrees / 60 seconds
= 18,000 degrees / second
Answer: (A) 18.000 d/sec
Question: If $5,000,000 is the initial amount placed in an account that collects 7% annual interest, which of the following compounding rates would produce the largest total amount after two years?
(A) compounding annually
(B) compounding quarterly
(C) compounding monthly
(D) compounding daily
(E) All four of these would produce the same total
Rationale: This will produce the maximum yield as the interest accrued each day will be added the very next day to the Principal amount for further computation of interest.
This process will be repeated every day till the amount matures
Compounding annually will give least returns
Compounding daily :Answer: D
Answer: (D) compounding daily
Question: If the speed of X meters per second is equivalent to the speed of Y meters per hour, what is Y in terms of X? (1 kilometer=1000 meters)
(A) 15x/18
(B) 6x/5
(C) 18x/5
(D) 60x
(E) 3600x
Rationale: If the speed of X meters per second is equivalent to the speed of Y kilometers per hour, what is Y in terms of X? (1 kilometer=1000 meters)
We need to find an equation with x in the answer...
convert all measurements so they are alike (i.e. convert km to m, seconds to hours, etc)
Speed = x/t
x meters/second
(3600) x meters/hour
Speed = y/t
y M/hour
Speed = y/hour
y/hour = (3600) x meters/hour
y/1hour = x(3600) / 1 hour
y= x(3600)
y = 3600x
Answer: E.
Answer: (E) 3600x
Question: if 11 oranges bought 10 r and 10 oranges sold 11 r .what is the profit
(A) 11 %
(B) 20 %
(C) 22 %
(D) 21 %
(E) 23 %
Rationale: suppose he bought 110 apples.
cp= Rs 100
SP=Rs 121
% profit = 100*(121-100)/100 = 21 %
ANSWER:D
Answer: (D) 21 %
Question: What is the maximum number of slices can you obtain by cutting a cake with only 4 cuts?
(A) 9
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: step 1: cut the cake from middle in two equal pieces. this is the first cut and we get two pieces.
step 2: put one piece on the other piece vertically and cut them from top to bottom. this is the 2nd cut and we have 4 piece.
step 3: again put the 4 pieces on each other vertically and cut from top to bottom. this is 3rd cut and we have 8 piece.
step[ 4: again put all the 8 pieces on each other vertically and cut from top to bottom. this is the 4th cut and we have 16 equal piece.
ANSWER:D
Answer: (D) 16
Question: Raman covers 1 km in 8 min while suman covers the same distance in 10 min. By what distance does Raman beat Suman ?
(A) 150 m
(B) 65 m
(C) 190 m
(D) 200 m
(E) 220 m
Rationale: Raman covers 1 km in 8 min
and suman cover 1 km in 10 min.
If they starts together, then distance covered by suman in 8 min
= (1000/10) x 8 = 800 m
∴ Raman will beat suman by (1000 - 800 ) m = 200 m
ANSWER :D
Answer: (D) 200 m
Question: How much 60% of 50 is greater than 40% of 30?
(A) 18
(B) 28
(C) 26
(D) 27
(E) 23
Rationale: (60/100) * 50 – (40/100) * 30
30 - 12 = 18
Answer:A
Answer: (A) 18
Question: If 16 machine can finish a job in 45 days, then how many more machines would be needed to finish the job in one -third less time?
(A) a. 3
(B) b. 8
(C) c. 10
(D) d. 12
(E) e. 16
Rationale: You might think of this in a management context - we can use the principle of 'person-hours' to solve any problem where we have identical workers. So, using simpler numbers, suppose you know that 6 identical employees, working simultaneously, would finish a job in 5 hours. Then that job requires 6*5 = 30 total hours of person-work. If instead you wanted the job done in 3 hours, you'd assign 30/3 = 10 employees to do the job, because you want to get a total of 30 hours of work from the employees.
We can solve this problem identically. If 16 machines (identical ones, I assume) work simultaneously for 45 days, they will do a total of 16*45 machine-days of work. So the job requires 16*45 days of machine work in total. We instead want the job done in 1/3 less time, so in 30 days. So we'll need 16*36/30 = 19.2 ~=19 machines, or 3 additional machines.
A
Answer: (A) a. 3
Question: A cubical rectangular bar has the dimensions with the ratio 5 : 4 : 3. Its volume is 7500. What
is the surface area of the bar?
(A) 1350
(B) 2350
(C) 4350
(D) 5640
(E) 8456
Rationale: volume of cubiod is lbh:5x*4x*3x=7500;
x=5
now,area is 2(lb+bh+lh):2(25*20+20*15+25*15)=2350.
therefore,area=2350
ANSWER:A
Answer: (A) 1350
Question: In a certain company, the ratio of the number of managers to the number of non-managers in any department must always be greater than 7 : 32. In the company, what is the maximum number of non-managers in a department that has 8 managers?
(A) 35
(B) 36
(C) 37
(D) 38
(E) 39
Rationale: 8/7 * 32 = 36.6
The answer is B.
Answer: (B) 36
Question: 1/2 + [(2/3 * 3/8)*4] - 9/16 =
(A)  29/16
(B)  19/16
(C)  15/16
(D)  9/13
(E)  0
Rationale: We need to simplify the expression using PEMDAS.
Parentheses
Exponents
Multiplication andDivision
Addition andSubtraction
The calculation of an equation or expression must be carried out in the following order:
1) Operations within parentheses (or absolute value bars or radicals)
2) Exponents
3) Multiplication and division from left to right
4) Addition and subtraction from left to right
The answer is C.
Answer: (C)  15/16
Question: If a positive odd integer N has p positive factors, how many positive factors will 2N have ?
(A) p
(B) 2p
(C) P+1
(D) 2p+1
(E) Cannot be determined
Rationale: no of factor of a=b^m * c^n * d^o * e^q.... = (m+1)*(n+1)*(o+1)*(q+1)...
Given that N is an odd integer. So N can be b^m * c^n * d^o * e^q, where b,c,d,e are odd numbers.
The number of factors of N = (m+1)*(n+1)*(o+1)*(q+1) = p
For a number 2N = 2^1 * b^m * c^n * d^o * e^p, number of factors will be (1+1)*(m+1)*(n+1)*(o+1)*(q+1) = 2*p
So, number of factors of 2N = 2*p
Hence, answer will be B.
Answer: (B) 2p
Question: What is the remainder when 1234 * 6789 * 1111 is divided by 19
(A) 15
(B) 23
(C) 7
(D) 10
(E) 43
Rationale: 12345/19==> Remainder=14
678910/19==> Remainder=2
111111/19==> Remainder=18
=14*2*18=504/19==> Remainder=10
Answer: D
Answer: (D) 10
Question: Aaron will jog from home at 3 miles per hour and then walk back home by the same route at 6 miles per hour. How many miles from home can Aaron jog so that he spends a total of 3 hours jogging and walking?
(A) 3
(B) 6
(C) 2
(D) 5
(E) 8
Rationale: xyt/(x+y)
x= 3, y=6, t= 3
3*6*3/3+6 = 54/9 = 6
Answer : B
Answer: (B) 6
Question: Integer x is equal to the product of all even numbers from 2 to 60, inclusive. If C is the smallest prime number that is also a factor of x-1, then which of the following expressions must be true?
(A)  0<y<4
(B)  4<y<10
(C)  10<y<20
(D)  20<y<30
(E)  y>30
Rationale: C Smallest prime factor is greater than 29. So answer is E
Answer: (E)  y>30