mathewhe/aqua_rat huggingface dataset:
Question: Every student in a certain classroom was given one colored marble. 1/2 of the students were given a blue marble, 1/3 of the students were given a yellow marble, and all of the other students were given a red marble. After lunch, 1/3 of the students who had blue marbles and 1/4 of the students who had yellow marbles left the classroom; the other students did not leave. What fraction of all students have either a blue or yellow marble now?
(A) 7/9
(B) 6/7
(C) 5/7
(D) 4/7
(E) 4/9
Rationale: Lets pick smart numbers. Total number of students in the classroom: 12
Blue marble (1/2): 6
Yellow marble (1/3): 4
Red marble (1/6): 2
After lunch
Blue marble: 4
Yellow marble: 3
Red marble: 2
New Total number of students in the classroom: 9
Blue and Yellow marbles: 7
Answer 7/9 or A
Answer: (A) 7/9
Question: Joe invested a certain sum of money in a simple interest bond whose value grew to $260 at the end of 3 years and to $360 at the end of another 5 years. What was the rate of interest in which he invested his sum?
(A) 6%
(B) 8%
(C) 10%
(D) 12%
(E) 15%
Rationale: In 5 years, the value grew $100, so the simple interest was $20 per year.
In 3 years, the total interest was 3*$20 = $60
The principal is $260 - $60 = 200.
The interest rate is $20/$200 = 10%
The answer is C.
Answer: (C) 10%
Question: The average salary of 15 people in the shipping department at a certain firm is $21,000. The salary of 5 of the employees is $25,000 each and the salary of 4 of the employees is $16,000 each. What is the average salary of the remaining employees?
(A)  $19,250
(B)  $18,500
(C)  $21,000
(D)  $15,850
(E)  $12,300
Rationale: total salary... 15*21k=315k
5 emp @ 25k =125k
4 emp @ 16k =64k
remaing 6 emp sal = 315k-125k-64k =126k
average=126k/6 = 21000
Ans: C
Answer: (C)  $21,000
Question: How many multiples of 6 are less than 5000, and also multiples of 8?
(A) 104
(B) 208
(C) 625
(D) 832
(E) 833
Rationale: LCM of 6 & 8 = 24
Tried dividing 5000 by 24
Got quotient 208.33'So B is answer
Answer: (B) 208
Question: A train 500 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
(A) 32
(B) 28
(C) 49
(D) 64
(E) 21
Rationale: S = (500 + 300)/45 = 800/45 * 18/5 = 64
Answer: D
Answer: (D) 64
Question: There are different 20 circles. What is the number of the greatest possible points with which the circles intersect?
(A) 380
(B) 200
(C) 110
(D) 180
(E) 200
Rationale: Maximum points of intersection between n different circles = n*(n - 1) = 20*19 = 380
Answer: A
Answer: (A) 380
Question: A gardener grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 193 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year?
(A) 8,208
(B) 9,409
(C) 11,424
(D) 12,586
(E) can not be determined
Rationale: Let the side for growing cabbages this year be X ft. Thus the area is X^2.
Let the side for growing cabbages last year be Y ft. Thus, the area was Y^2.
The area would have increased by 193 sq ft as each cabbage takes 1 sq ft space.
X^2 - Y^2 = 193
(X + Y)(X - Y) = 193
193 is a prime number and thus it will be (97+96)*(97-96).
Thus X = 97 and Y = 96
X^2 = 97^2 = 9409
The answer is B.
Answer: (B) 9,409
Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
(A) 6.25
(B) 6.5
(C) 6.75
(D) 7
(E) 8
Rationale: Solution
Required run rate	= 282 - (3.2 x 10) / 40
= 250 / 40
= 6.25.
Answer A
Answer: (A) 6.25
Question: There are three rooms in a motel: one single, one double and one for four persons. How many ways are there to house seven persons in these rooms ?
(A) 7! / 1! 2! 3!
(B) 7!
(C) 7! / 3
(D) 7! / 3!
(E) 7! / 4
Rationale: Choose 1 person for the single room & from the remaining choose 2 for the double room & from the remaining choose 4 people for the four person room,
Then, 7C1 x 6C2 x 4C4 = 7! / 1! 2! 3!
ANSWER:A
Answer: (A) 7! / 1! 2! 3!
Question: The principal that amounts to Rs. 3913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is?
(A) s. 3096
(B) s. 4076
(C) s. 4085
(D) s. 4096
(E) s. 5096
Rationale: Principal = [4913 / (1 + 25/(4 * 100))3]
= 3913 * 16/17 * 16/17 * 16/17 = Rs. 3096.
ANSWER:A
Answer: (A) s. 3096
Question: During a sale of 20% on everything in a store, a kid is successful in convincing the store manager to give him 20 candies for the discounted price of 14 candies. The store still makes a profit of 18% on this sale. What is the mark up percentage on each candy?
(A)  100%
(B)  80%
(C)  75%
(D)  66+2/3%
(E)  55%
Rationale: Hi Akhil, I can share the way I solved it..
Let's say Marked price = M
So, there's a discount of 20% on M So, new S.P. = 80% of M
Now, the child convinces the owner to sell 20 candies for the price of 14 candies .
Let's say each candy after discount is 1$. So, S.P. of 20 candies = 20$. THe child bought it for 14 $ So, he got a discount of 6/20 *100 = 30%
So, the latest S.P. = 70% of 80% of M = 0.7* 0.8 M
Now, we are given that the shopkeeper still makes a profit of 12%. So we have ,
0.7 * 0.8 * M = 1.12 C.P
So, we get, M= 2 C.P.
i.e. Marked price was kept 100% above C.P.
D
Answer: (D)  66+2/3%
Question: A bat is bought for Rs.440 and sold at a gain of 20% find its selling price
(A) s.430/-
(B) s.480/-
(C) s.400/-
(D) s.528/-
(E) s.600/-
Rationale: 100 % ------> 440
120 % ------> 440*120/100
Selling price = Rs.528/-
D
Answer: (D) s.528/-
Question: A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be:
(A) 22
(B) 23
(C) 24
(D) 26
(E) 28
Rationale: let hens be x and cows be y
now,
feet: x*2+y*4=140
heads: x*1+y*1=48
implies, 2x+4y=140 and x+y=48
solving these two equations, we get x=26 and y=22
Therefore, hens are 26.
ANSWER:D
Answer: (D) 26
Question: One hour after Yolanda started walking from X to Y, a distance of 17 miles, Bob started walking along the same road from Y to X. If Yolanda's walking rate was 3 miles per hour and Bobт's was 4 miles per hour, how many miles had Bob walked when they met?
(A) 24
(B) 23
(C) 22
(D) 21
(E) 8
Rationale: When B started walking Y already has covered 3 miles out of 17, hence the distance at that time between them was 17-3=14 miles.
Combined rate of B and Y was 3+4=7 miles per hour, hence they would meet each other in 14/7=2 hours. In 6 hours B walked 2*4=8 miles.
Answer: E.
Answer: (E) 8
Question: Find the simple interest on Rs. 70,000 at 16 2/3% per year for 9 months.
(A) 7500
(B) 6500
(C) 8750
(D) 9500
(E) None of them
Rationale: P = Rs.70000,R = 50/3% p.a and T = 9/12 years = 3/4years.
Simple Interest = (P*R*T)/100 = Rs.(70,000*(50/3)*(3/4)*(1/100))= Rs.8750
Answer is C.
Answer: (C) 8750
Question: Each of the 26 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 11 students sign up for the poetry club, 17 students for the history club, and 15 students for the writing club. If 5 students sign up for exactly two clubs, how many students sign up for all three clubs?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: The total number in the three clubs is 11+17+15=43.
All 26 students signed up for at least one club.
5 of those students signed up for exactly one more club.
43 - 31 = 12 so 6 students must have signed up for exactly three clubs.
The answer is E.
Answer: (E) 6
Question: 7858,3929,163.70,20.46, ?
(A) 1.25
(B) 2.69
(C) 3.87
(D) 2.04
(E) 4.12
Rationale: Explanation :
Terms are continuously divided by 2,4,6 ,8, and so on
7858
7858Ã· 2= 3929
3929 Ã· 4 =982.25
982.25 Ã· 6 = 163.70
163.70 Ã· 8= 20.46
20.46Ã·10=2.04
Answer : Option D
Answer: (D) 2.04
Question: The sum of the squares of the first 15 positive integers (1^2 + 2^2 + 3^2 + . . . + 15^2) is equal to 1280. What is the sum of the squares of the second 15 positive integers (16^2 + 17^2 + 18^2 + . . . + 30^2) ?
(A)  2480
(B)  3490
(C)  6785
(D)  8255
(E)  9255
Rationale: You'll never need a formula for the sums of squares on the actual GMAT. You don't need to use that formula here, though it's not all that straightforward to solve without one. Two different approaches:
16^2 + 17^2 + 18^2 + ... + 30^2 = (15 + 1)^2 + (15 + 2)^2 + (15 + 3)^2 + ... + (15 + 15)^2
Now we can expand each square; they are all in the (x + y)^2 = x^2 + 2xy + y^2 pattern.
= (15^2 + 2*15 + 1^2) + (15^2 + 4*15 + 2^2) + (15^2 + 6*15 + 3^2) + ... + (15^2 + 30*15 + 15^2)
Now we have fifteen 15^2 terms, so adding these gives 15*15^2 = 15^3 = 3375. We also have the entire sum 1^2 + 2^2 + ... + 15^2, which we know is equal to 1240. Finally adding the middle terms, we have:
2*15 + 4*15 + 6*15 + ... + 30*15 = 15(2 + 4 + 6 + .... + 30) = 15*2*(1 + 2 + 3 + ... + 15) = 15*2*8*15 = 3600
So the sum must be 3375 + 1240 + 3600 = 8215
Alternatively, we can use a different factoring pattern. We want to find the value of 30^2 + 29^2 + ... + 17^2 + 16^2. Well if we subtract 15^2 + 14^2 + .... + 2^2 + 1^2 from this, the answer will be 1240 less than what we want to find. So if we can find the value of
30^2 + 29^2 + ... + 17^2 + 16^2 - (15^2 + 14^2 + .... + 2^2 + 1^2)
then we can add 1240 to get the answer. Now grouping the terms above to get differences of squares, we have
= (30^2 - 15^2) + (29^2 - 14^2) + ... + (16^2 - 1^2)
and factoring each of these using x^2 - y^2 = (x + y)(x - y), we have
= 45*15 + 43*15 + 41*15 + ... + 17*15 = 15(45 + 43 + 41 + ... + 17)
In brackets we have an equally spaced sum with fifteen terms, which we can evaluate using the familiar formula. So the above equals
15*15*62/2 = 6975
and adding back the 1280, we get the answer of 8255.(ANS D)
Answer: (D)  8255
Question: John completes a piece of work in 10 days, Rose completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is?
(A) 6 days
(B) 8 days
(C) 10 days
(D) 12 days
(E) 14 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 10 × 40/50 = 8 days
B)
Answer: (B) 8 days
Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/3 hours to fill the tank. The leak can drain all the water of the tank in?
(A) 17
(B) 19
(C) 18
(D) 14
(E) 11
Rationale: Work done by the tank in 1 hour = (1/2 - 1/3) = 1/14 Leak will empty the tank in 14 hrs. Answer: D
Answer: (D) 14
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 25 hours and 16 hours respectively. The ratio of their speeds is?
(A) 4:5
(B) 4:3
(C) 4:4
(D) 4:9
(E) 4:2
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √16 : √25 = 4:5
Answer:A
Answer: (A) 4:5
Question: How many three-digit integers between 311 and 401, exclusive, are divisible by 3 when the tens digit and the hundered digit are switched?
(A) 30
(B) 19
(C) 22
(D) 3
(E) 90
Rationale: Answer is 30
No of digits between 311 and 401 (exclusive) = 401-311-1 = 89
No Intergers divisble by 3 =~ 89/3 ~ 30
Divsiblivity rule for 3 is Sum of all digits must be divisble by 3. It doesn't matter if hundred digit and tens digits are switched.
e.g 372 is divisble by 3 (becae 3+7+2= 12 (divisble by 3))
switch digits 732 also divisble by 3 (becae 7+3+2= 12 (divisble by 3))
Divsiblivity rule for 3 is Sum of all digits must be divisble by 3. It doesn't matter if hundred digit and tens digits are switched.
You have right. So it is enough to proceed like usual to find the numbers in a given range that are divisible by 3. So 399-312/3 +1 =30.
Answer : A
Answer: (A) 30
Question: Large, medium and small ships are used to bring water. 4 large ships carry as much water as 7 small ships; 3 medium ships carry as much water as 2 large ships and 1 small ship. If 15 large, 7 medium and 14 small ships, each made 36 journeys to bring a certain quantity of water, then in how many journeys will 12 large, 14 medium and 21 small ships bring the same quantity of water?
(A) 29
(B) 30
(C) 20
(D) 50
(E) 55
Rationale: Explanation :
Here, Large, Medium and Small ships are denoted by the symbol L, M and S.
Now, according to the question,
4L = 7S. ------(i)
3M = 2L + S. ------(ii)
Using above equations, the ratios of the capacity of the Large, Medium and Small ships are :-
7: 6 : 4.
Let, the number of journeys required be x. Since, quantity of water remains the same, so :-
=((15×7+7×6+14×4)36) = x (12×7+14×6+21×4).
=>((15×7+7×6+14×4)36) / (12×7+14×6+21×4)= x
=>x=7308/252
=>x=29.
Answer : A
Answer: (A) 29
Question: The sale price sarees listed for Rs.200 after successive discount is 20% and 5% is?
(A) 187
(B) 169
(C) 152
(D) 178
(E) 175
Rationale: 200*(80/100)*(95/100)
= 152
Answer:C
Answer: (C) 152
Question: Bhavan travelled for 20 hours. He covered the first half of the distance at 50 kmph and remaining half of the distance at 40 kmph. Find the distance travelled by Bhavan?
(A) 888.89
(B) 788.89
(C) 899.89
(D) 688.89
(E) 899.99
Rationale: Let the distance travelled be x km.
Total time = (x/2)/50 + (x/2)/40= 20 => x/100 + x/80 = 20 => (4x + 5x)/400 = 20
=> x = 888.89 km
Answer:A
Answer: (A) 888.89
Question: Mary purchased Brand X pens for $2 apiece and brand Y for $1 apiece. If Elena purchased a total of 12 of these pens for $20.00, how many brand X pens did she purchase?
(A) 8
(B) 9
(C) 5
(D) 4
(E) 6
Rationale: 2x+y=20 -only one positive integers solutions x=8 and y=4
Answer is A
Answer: (A) 8
Question: Of the families in City X in 1994, 35 percent owned a personal computer. The number of families in City X owning a computer in 1998 was 20 percent greater than it was in 1994, and the total number of families in City X was 4 percent greater in 1998 than it was in 1994. what percent of the families in City X owned a personal computer in 1998?
(A) 50.12%
(B) 40.52%
(C) 40.56%
(D) 40.38%
(E) 40.14%
Rationale: Say a 100 families existed in 1994 then the number of families owning a computer in 1994 - 40
Number of families owning computer in 1998 = 35 * 120/100 = 42
Number of families in 1998 = 104
The percentage = 42/104 * 100 = 40.38%.
Option: D
Answer: (D) 40.38%
Question: A jar contains only red, yellow, and orange marbles. If there are 3 red, 5 yellow, and 4 orange marbles, and 2 marbles are chosen from the jar at random without replacing any of them, what is the probability that 2 yellow, 1 red, and no orange marbles will be chosen?
(A) 1/60
(B) 1/45
(C) 2/45
(D) 3/22
(E) 6/22
Rationale: I started by finding the 2 probabilities, without calculation, like this:
P(YYR)
P(YRY)
P(RYY)
I calculated the first one and ended in 1/22. I looked at the answer choices at this point and saw answer D: 3/22.
This helped me realise that for the 6 possible orderings the probabbility is the same. So, it should be (1/22)*(6), which indeed is 6/22.
E
Answer: (E) 6/22
Question: A train overtakes two persons who are walking in the same direction to that of the train at 2 kmph and
4 kmph and passes them completely in 9 and 10 seconds respectively. What is the length of the train?
(A) 40 m
(B) 10 m
(C) 20 m
(D) 30 m
(E) 50 m
Rationale: Let speed of the train be v kmph
(v-2) :(v-4) = 10:9
9 v -18=10 v-40
v=22
Length of the train=(22-2) x 5/18 x 9=50 metre
Answer: E
Answer: (E) 50 m
Question: In a room there are 12 people. Each person shook hands with every other person. How many hand shakes were there?
(A) 58
(B) 60
(C) 62
(D) 64
(E) 66
Rationale: 12C2 = 66
The answer is E.
Answer: (E) 66
Question: six years ago, the ratio of the ages of kunal and sagar was 6:5. four years hence, the ratio of their ages will be 11:10. what is sagar's age at present?
(A) 18 years
(B) 16 years
(C) 22 years
(D) 20 years
(E) none of these
Rationale: the age of kunal and sagar 6 years ago 6x and 5x respectively.
((6x+6)+4)/((5x+6)+4)=11/10
10(6x+10)=11(5x+10)
5x=10. x=2, sagar's present age = (5x+6)=16 years
correct answer (B)
Answer: (B) 16 years
Question: A’s speed is 20/14 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?
(A) 1/17
(B) 3/17
(C) 1/10
(D) 6/20
(E) 3/10
Rationale: We have the ratio of A’s speed and B’s speed. This means, we know how much distance A covers compared with B in the same time.
This is what the beginning of the race will look like:
(Start) A_________B______________________________
If A covers 20 meters, B covers 14 meters in that time. So if the race is 20 meters long, when A reaches the finish line, B would be 6 meters behind him. If we want the race to end in a dead heat, we want B to be at the finish line too at the same time. This means B should get a head start of 6 meters so that he doesn’t need to cover that. In that case, the time required by A (to cover 20 meters) would be the same as the time required by B (to cover 14 meters) to reach the finish line.
So B should get a head start of 6/20th of the race.
Answer (D)
Answer: (D) 6/20
Question: A warehouse had a square floor with are 10,000 sq.metres. A rectangular addition was built along
one entire side of the warehouse that increased the floor by one-half as much as the original floor. How many metres did the addition extend beyond the original building?
(A) 10
(B) 20
(C) 50
(D) 200
(E) 500
Rationale: length=100,b=?
area of rectangle=l*b
original floor=10,000 sq.metres
increasing the original floor by half of the original floor=10000+1/2(10000)
=15000
so 15000-10000=5000(area of rectangular portion)
l*b=5000
l=100 so 100*b=5000 ->b=50
so extended part is of 50metres
ANSWER:C
Answer: (C) 50
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:
(A) 14 years
(B) 19 years
(C) 33 years
(D) 38 years
(E) 48 years
Rationale: Let the son's present age be x years. Then, (38 - x) = x
2x = 38.
x = 19.
Son's age 5 years back (19 - 5) = 14 years. Answer: Option A
Answer: (A) 14 years
Question: anup manages to draw 7 circles of equal radii with their centres on the diagonal of a square such that two extreme circles touch two sides of the square and each middle circle touches two circles on either side. find the ratio of radius of the circles to the side of the square.
(A) 1:(2+6^(1/2))
(B) 1:(4+7^(1/3))
(C) (2+7^(1/2)):1
(D) (2+7^(1/2)):2
(E) None of these
Rationale: diagonal of square=(2*r)*7+(2^(1/2)*r-r)*2
diagonal has 7 squares diameters length +little distance between extreme squares to the end point [form a square of side r from center of extreme circle to the extreme end to find distance]
distance=2^(1/2)*r-r
D=a*2^(1/2)
a=2^(1/2)*[6*r + 2^(1/2)*r]
r/a =1:[2+6*2^(1/2)]
answer is none of the above
ANSWER:E
Answer: (E) None of these
Question: There are 3 numbers A, B and C. If A:B = 3/4, B:C = 4/5, C:D = 5/6, then C:D will be?
(A) 1 : 2
(B) 3 : 5
(C) 5 : 7
(D) 5:6
(E) 5 : 3
Rationale: Sol. A : B = 3 : 4, B : C = 4 : 5, C : D = 5 : 6
∴A∶B∶C∶D= 3 : 4 : 5 : 6.
Thus, C: D = 5 : 6
D
Answer: (D) 5:6
Question: In the xy plane line m has the equation 4x + y = e. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r?
(A) -4/3
(B) 1/4
(C) -4
(D) 3/4
(E) 4/3
Rationale: The equation of line m is y=-4x+e. Now, since line n is perpendicular to line m, then its slope is negative reciprocal of the slope of line m, so the slope of n is 1/4. Next, as line n passes through the origin (0, 0) and has the slope of 1/4 then its equation is y=1/4*x.
Point (r, r+1) lies on line n means that (r+1)=1/4*r --> r=-4/3.
Answer: A.
Answer: (A) -4/3
Question: What is the sum of all 3 digit positive integers that can be formed using the digits 1, 5, and 8, if the digits are allowed to repeat within a number Y?
(A) 126
(B) 1386
(C) 3108
(D) 308
(E) 13986
Rationale: As we are using digits 1,5, 8 and digits are allowed to repeat. Each of the unit, tenth and hundredth digit can be used by each of three digits.
So,Total possible numbers with these digits=3 X 3 X 3 =27.
First, As we have 27 three digit number, Sum will be for sure more than 2700..Eliminate options A,B,D
Second, If you imagine numbers Y with the given digits 1,5,8. We have numbers like 888,885,855,858,851. Sum is for sure more than 4000.Eliminate option C.
You are left withanswer E.
Answer: (E) 13986
Question: A train crosses a 120-metre and a 70-metre long plat form in 17 seconds and 12 seconds respectively. What is the speed of the train ?
(A) 10 ms-1
(B) 16 ms-1
(C) 20 ms-1
(D) 24 ms-1
(E) 45 ms-1
Rationale: Explanation :
let the length of the train be x
∴ 120+x/17 = 70+x/12
1440 + 12x = 1190 + 17x
∴ x = 250/5 = 50m
∴ Speed = 120+50/17 = 170/17 = 10 ms-1
Answer : Option A
Answer: (A) 10 ms-1
Question: What is the dividend. divisor 17, the quotient is 9 and the remainder is 5?
(A) 150
(B) 54
(C) 158
(D) 160
(E) 180
Rationale: D = d * Q + R
D = 17 * 9 + 5
D = 153 + 5
D = 158
C)
Answer: (C) 158
Question: The cost of a car was $3,000 in 1960. In 2010, the price had increased to $5,000. What was the percent increase in the cost of the car?
(A) 33.3%
(B) 45%
(C) 60%
(D) 66.6%
(E) 55.8%
Rationale: Increase = 5000-3000 = 2000
% increase = 2000*100/3000 = 66.6%
Answer: option D
Answer: (D) 66.6%
Question: A patient was given a bottle of tablets by the doctor and he was asked to take five tablets in a gap of 30 minutes.
In how much time will he be able to take all the five tablets?
(A) 1 Hour.
(B) 2 Hour.
(C) 3 Hour.
(D) None
(E) Cannot be determined
Rationale: Suppose he takes the first tablet at 8:00 pm. Then the second will be consumed by him at 8:30, third at 9:00, fourth at 9:30 and fifth at 10:00.
Time = 2 hour
Answer B
Answer: (B) 2 Hour.
Question: If n is a positive integer and n^2 is divisible by 150, then what is the largest positive integer that must divide n?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: 150 = 2 * 3 * 5^2
If 150 divides n^2, then n must be divisible by 2 * 3 * 5 = 30
The answer is C.
Answer: (C) 30
Question: A can do a piece of work in 10 days and B can do the same work in 12 days. A and B worked together for 3 days. How many more days are required to complete the remaining work if they work together?
(A) 3 (5/18)
(B) 3 (5/16)
(C) 2 (5/11)
(D) 3 (5/13)
(E) 3 (5/21)
Rationale: A can do 1/10 of the work in a day.
B can do 1/12 of the work in a 1 day.
Both of them together can do (1/10 + 1/12) part of work in 1 day = (6 + 5)/60 = 11/60
They take 60/11 days to complete the work together.
Given that they already worked for 3 days.
The number of days required to complete remaining work => 60/11 - 3 = 27/11 = 2 (5/11) days.
Answer:C
Answer: (C) 2 (5/11)
Question: A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 6 more days. How many days would it have taken the second carpenter to do the complete job working alone?
(A) 4 2/3
(B) 7
(C) 9
(D) 24
(E) 21
Rationale: A carpenter worked only 1 day on something that takes him 6 MORE days.
Means;
Carpenter finishes his work in 7 days.
Let his buddy finish the same task in x days.
Respective rates per day:
1/7 AND 1/x
To complete 1 work:
First guy worked for 5 days @ rate=1/7 per day.
Second one worked for 6 days @ rate=1/x per day
Expression:
Days*Rate=Work
5*1/7+6*1/x=1
5x+42=7x
2x=42
x=21 days.
Ans:E
Answer: (E) 21
Question: How many factors of 240 are also multiples of 3 ?
(A) 5
(B) 8
(C) 9
(D) 10
(E) 20
Rationale: take factors of 240
240= 2^4*3^1*5^1
Total factors of 240= (4+1)*(1+1)*(1+1)
=5*2*2
=20
out of total factors of 20, half will have 0 as power of 3 and half will have 1 as power of 3. It is because we have considered only 0 and 1 as power of 3 to compute total factors of 240.
Therefore factors that are multiple of 3= 20/2= 10
Ans - D
Answer: (D) 10