mathewhe/aqua_rat huggingface dataset:
Question: One robot builds a robot in 1 hour, another one builds a robot in 2 hours. The 2 robots work together and when a new robot is complete, it joins the others, working at a constant rate of one robot in 2 hours. How much time will it take until there are 7 robots altogether, if the robots build only one robot at a time?
(A) 70 1/7 min
(B) 94 1/7 min
(C) 110 1/7 min
(D) 112 1/7 min
(E) 131 1/7 min
Rationale: First the 2 robots work at the rate of
1 + 1/2 = 3/2
so they complete one robot in 2/3 rd of an hour = 40 minutes - (1)
Now the 3 robots work together at the rate of
1 + 1/2 + 1/2 = 4/2 = 2/1
so they complete one robot in 1/2 an hour,i.e 30 minutes - (2)
Now the 4 robots work together at the rate of
1 + 1/2 + 1/2 + 1/2 = 5/2
so they complete one robot in 2/5th of an hour - (3)
Now the 5 robots work together at the rate of
1 + 1/2 + 1/2 + 1/2+1/2 = 3
so they complete one robot in 1/3th of an hour - (4)
Now the 6 robots work together at the rate of
1 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2=7/2
so they complete one robot in 2/5th of an hour - (5)
And now we have 7 robots
So Total = (1) + (2) + (3)+(4)+(5) = 131 1/7minutes
Answer - E
Answer: (E) 131 1/7 min
Question: Teas worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs 152 per Kg , the price of the third variety per Kg will be?
(A) Rs. 147.50
(B) Rs. 785.50
(C) Rs. 174.50
(D) Rs. 258.50
(E) None of these
Rationale: Explanation :
Since first and second varieties are mixed in equal proportions.
So, their average price =Rs. (126+135)/2.
=>Rs. 130.50.
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1.
We have to find x.
By the rule of alligation, we have:
Cost of 1 kg Cost of 1 kg
of 1st kind of 2nd kind
(Rs. 130.50) (Rs. x)
\ /
Mean Price
(Rs. 152)
/ \
xâˆ’152 22.50
=>xâˆ’(152/22.50)=1.
=>xâˆ’152=22.50.
=>x= 174.50 Rs.
Answer : C
Answer: (C) Rs. 174.50
Question: One side of a triangle has length 5 and a second side has length 4. Which of the following could be the area of the triangle?
I. 15
II. 10
III. 5
(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II and III
Rationale: The triangle will have a maximum area when it is a right angled triangle
The largest triangle will be formed when 5 and 4 are the base and height of triangle .
Area = 1/2 * 5 * 4 = 10
There is no lower limit on the area of any triangle whose only 2 sides are known.
Then 0 < Area <= 10
The answer is D.
Answer: (D) II and III only
Question: One card is drawn from a pack of 52 cards. What is the probability that the card drawn is a ten or a spade?
(A) 3/7
(B) 4/13
(C) 4/15
(D) 7/19
(E) 11/31
Rationale: Out of 52 cards there will be 13 spades including 1 ten and there are 3 more tens. Total 16
probability= 16/52 = 4/13
Answer is B
Answer: (B) 4/13
Question: According to the directions on a packet of smoothie mix, 1 3-ounce packet of smoothie mix is to be combined with 19 ounces of water to make a smoothie. How many 3-ounce packets of smoothie mix are required to prepare 150 12-ounce smoothies?
(A)  120
(B)  150
(C)  180
(D)  240
(E)  600
Rationale: This question wasn't particularly grueling, but I think it's the first where I had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the GMAT. It actually came to me by accident. Basically, if we thought that the 3 packets of powder were included in the 12 ounces of water, that would mean we would need 150 packets of smoothie mix (along with 12(150) ounces of water for a total of 150 packets. However, we know, after a more careful reading of the stimulus, that the 3 ounces are NOT included in the 12 ounces. As such, the answer has to be LESS than 150 packets, since 150 would be too much powder considering you already have 150(12) ounces of water and need less packets than water to make a smoothie. As such, the only answer less than 150 is 120, A. Does this make sense? Or am I way off base?
E
Answer: (E)  600
Question: There are m cities. What is the number of airlines that connected 2 different cities (airline from city A to city B is different with airline from city B to city A)?
(A) n(n-1)
(B) m(m-1)
(C) n(n-1)/2
(D) n(n+1)/2
(E) n2
Rationale: First of all, the possible number of airlines is m. Then, the possible number of airlines departing from one city to another becomes (m-1). Hence, the answer is m(m-1), which makes A an answer choice.
B
Answer: (B) m(m-1)
Question: In how many ways can the integer 800 be expressed as a product of two different positive integers?
(A) 10
(B) 7
(C) 5
(D) 4
(E) 2
Rationale: 800=(2^5)*(5^2)
Since 800 is not a perfect square, no of ways=7
Answer B
Answer: (B) 7
Question: One day, Connie plays a game with a fair 6-sided die. Connie rolls the die until she rolls a 6, at
which point the game ends. If she rolls a 6 on her first turn, Connie wins 6 dollars. For each
subsequent turn, Connie wins 1
6 of the amount she would have won the previous turn. What is
Connie's expected earnings from the game?
(A) 32/31
(B) 33/31
(C) 34/31
(D) 36/31
(E) 0/31
Rationale: Connie has a 1
6 chance of winning 6 dollars her first turn. She has a 5/6
1/6 chance of
winning 1 dollar her second turn. Next, she has a 25
36
1/6 chance of winning 1/6 dollars her third turn.
Generalizing, Connie's expected earnings form a geometric series with initial term 1/6 *6 = 1 and
common ratio 5/6* 1/6 = 5/36 . Hence, Connie's expected earnings are
1/1- 5/36
=
36/31
correct answer D
Answer: (D) 36/31
Question: Visitors to show were charged Rs.15 each on the first day. Rs.7.50 on the second day, Rs.2.50 on the third day and total attendance on the three days were in ratio 2:5:13 respectively. The average charge per person for the whole show is?
(A) Rs.6.00
(B) Rs.5.50
(C) Rs.5.00
(D) Rs.7.00
(E) Rs.8.00
Rationale: Answer: Option C
2: 5: 13
2x 5x 13x
15 7.5 2.5
30x + 37.5x + 32.5x = 100x/20x
average = 5
Answer: (C) Rs.5.00
Question: In the first round of the elections, the only two candidates got exactly the same number of votes. During the second round, 20,000 votes switched from the first candidate to the second one. The total number of votes remained the same in both rounds, and no other votes switched sides. If, in the second round, the winning candidate got five times as many votes as the other candidate, how many people have voted in each round?
(A) 15,000
(B) 30,000
(C) 40,000
(D) 50,000
(E) 60,000
Rationale: Let A be the first candidate and B be the second one.
Given x+20000 = 5(x-20000)
4x = 120000=>x=30000
2x=60000
IMO option E.
Answer: (E) 60,000
Question: The average weight of a group of boys is 30 kg. After a boy of weight 37 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
(A) A)4
(B) B)8
(C) C)6
(D) D)2
(E) E)1
Rationale: Let the number off boys in the group originally be x.
Total weight of the boys = 30x
After the boy weighing 37 kg joins the group, total weight of boys = 30x + 37
So 30x + 37 = 31(x + 1) = > x = 6.
Answer:C
Answer: (C) C)6
Question: 6x – 5y + 3z = 23
4x + 8y – 11z = 7
5x – 6y + 2z = 11
Given the equations above, x + y + z = ?
(A)  11
(B)  12
(C)  13
(D)  14
(E)  15
Rationale: (6x – 5y + 3z) - (5x – 6y + 2z ) = 23-11
or, x+y+z = 12
Option B is the ans
Answer: (B)  12
Question: If (1+z)y=y, which of the following must be true?
(A) z=-1 or y=0
(B) z=0 or y=-1
(C) z=1 or y=1
(D) z=-1 or y=-1
(E) z=0 or y=0
Rationale: We have (1+z)y=y.
If x=0, y=y. True
If y=0, (1+z)*0=0 True
So, E will be the answer.
Answer: (E) z=0 or y=0
Question: Three coins are tossed. Find the probability of at least 2 tails ?
(A) 1/2
(B) 2/3
(C) 1/4
(D) 1/8
(E) 3/8
Rationale: n(s) = 2^3 = 8
let E is the event of getting at least 2 tails
n(E) = TTT, TTH , HTT, THT = 4
P(E) = n(E) / n(s)
= 4/8
= 1/2
Ans- A
Answer: (A) 1/2
Question: The amount of water (in ml) that should be added to reduce 12 ml. Lotion, containing 50% alcohol, to a lotion containing 30% alcohol, is?
(A) 8 ml
(B) 5 ml
(C) 4 ml
(D) 6 ml
(E) 1 ml
Rationale: 6 6
30% 70%
30% ----- 6
70% ------? => 14 - 6 = 8 ml
Answer:A
Answer: (A) 8 ml
Question: Mary and Mike enter into a partnership by investing $550 and $450 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Mary received $1000 more than Mike did, what was the profit made by their business in that year?
(A) $8000
(B) $10000
(C) $15000
(D) $12000
(E) $12500
Rationale: Explanatory Answer
Let the profit made during the year be $3x
Therefore, $x would have been shared equally and the remaining $2x would have been shared in the ratio 5.5 : 4.5
i.e., 55% of 2x would go to Mary and 45% of 2x would go to Mike.
Hence, Mary would get (55 - 45)% of 2x more than Mike
Or10% of 2x = $1000
i.e.,(60/100)*2x = 1000
or 2x = 10000.
Hence, the profit made by the company during the year $3x = $15000.
Answer : C
Answer: (C) $15000
Question: In an election, candidate A got 79% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favour of candidate.
(A) 357003
(B) 357090
(C) 37667
(D) 379888
(E) 287761
Rationale: Total number of invalid votes = 15 % of 560000
= 15/100 × 560000
= 8400000/100
= 84000
Total number of valid votes 560000 – 84000 = 476000
Percentage of votes polled in favour of candidate A = 75 %
Therefore, the number of valid votes polled in favour of candidate A = 75 % of 476000
= 75/100 × 476000
= 35700000/100
= 357090
Answer:B
Answer: (B) 357090
Question: A plane flies 660 km with the wind and 570 km against the wind in the same length of time. If the speed of the wind is 15 km/h, what is the speed of the plane in still air?
(A) 185 km/h
(B) 195 km/h
(C) 205 km/h
(D) 215 km/h
(E) 225 km/h
Rationale: The speed of the plane in still air = x km/h
The speed of the wind is 15 km/h
Speed with the wind = (x + 15) km/h
Speed against the wind = (x â€“ 15) km/h
Time = Distance/ Speed
660 / (x+15) = 570 / (x-15)
660(x-15) = 570(x+15)
66x - 990 = 57x + 855
9x = 1845
x = 205
Therefore, the speed of the plane in still air is 205 km/h.
The answer is C.
Answer: (C) 205 km/h
Question: Quentin's income is 60% less than Rex's income, and Sam's income is 25% less than Quentin's income. If Rex gave 60% of his income to Sam and 40% of his income to Quentin, Quentin's new income would be what fraction of Sam's new income?
(A) 8/9
(B) 11/12
(C) 8/13
(D) 11/13
(E) 12/13
Rationale: We can take some easy numbers and make calculations simpler.
Let R ( Rex's income) = 100
Q (Quentin's income) = 40%R = 40
S (Sam's income) = 75% Q = (3/4)*40 = 30
Now, if Rex gives 40% to Quentin --> Q = 40 + 40 = 80
60% given to Sam --> S = 30+60 = 90
The ratio is : Q/S = 80/90 = 8/9
ANSWER:A
Answer: (A) 8/9
Question: Find 95 ×× 97
(A) 92/198
(B) 92/12
(C) 92/13
(D) 92/10
(E) 92/15
Rationale: Here both numbers are less than 100. So they are deficient of - 5 and - 3 compared with 100. So
Answer:	E
Answer: (E) 92/15
Question: What is the principal sum?
I. The sum amounts to Rs. 660 in 3 years at S.I.
II. The sum amounts to Rs. 700 at S.I.
III. The rate of interest is 6% p.a.
(A) I and III only
(B) II and III only
(C) I and II only
(D) Any two of the three
(E) None of these
Rationale: Explanation:
Clearly, I and III is needed to solve this question where as II is not needed
Answer: A
Answer: (A) I and III only
Question: The side of a rhombus is 26 m and length of one of its diagonals is 20 m. The area of the rhombus is?
(A) 388
(B) 267
(C) 298
(D) 480
(E) 281
Rationale: 262 – 102 = 242
d1 = 20 d2 = 48
1/2 * 20 * 48 = 480.Answer:D
Answer: (D) 480
Question: A shopkeeper wishes to give 5% commission on the marked price of an article but also wants to earn a profit of 10%. If his cost price is Rs. 95, then marked price is:
(A) Rs. 100
(B) Rs.110
(C) Rs. 120
(D) Rs. 130
(E) None
Rationale: Solution: CP = Rs. 95.
Then SP = 95 + 10% of 95 = Rs. 104.5.
Let MP = X. He gives 5% commission on MP.
So,
SP = X - 5% of X
SP = 0.95X.
104.5 = 0.95X.
X = 104.5/0.95 = 110.
Thus, MP = Rs. 110.
Short-cut
95===10%(gain)===>104.5===5%(Commission)===>109.72( = 110)
Answer: Option B
Answer: (B) Rs.110
Question: A and B together can do a work in 9 days. If A alone can do it in 18 days. In how many days can B alone do it?
(A) 10
(B) 99
(C) 18
(D) 55
(E) 21
Rationale: 1/9 – 1/18 = 1/18
=> 18
Answer: C
Answer: (C) 18
Question: There are some pigeons and hares in a zoo. If heads are counted, there are 250. If legs are counted, there are 580. The number of hares in the zoo is?
(A) 40
(B) 50
(C) 60
(D) 70
(E) 80
Rationale: 250*2 = 500
580
-----
80
1----2
?----80 = 40
ANSWER:A
Answer: (A) 40
Question: The average age of 30 students in a class is 14 years. If the age of teacher is also included, the average becomes 15 years, find the age of the teacher.
(A) 43
(B) 44
(C) 45
(D) 47
(E) 48
Rationale: Explanation:
If teacher's age is 14 years, there is no change in the average. But teacher has contributed 1 year to all the students along with maintaining his age at 15.
Age of teacher = Average age of all + Total increase in age
= 15 + (1 x 30 ) = 45 years
Answer:C
Answer: (C) 45
Question: There are 3 red paints and 1 white paint that can be mixed to make new red paint colors. The paints are labeled A for Red78/Red23, B for Red23/Red17, C for Red17/White001. When mixing the paint for the new paint Firehouse Red, the formula calls for 4A:1D. How many of each paint is in Firehouse Red?
(A) none of the below options
(B) one part White001 : four parts Red23
(C) four parts Red78 : one part Red17
(D) four parts Red23 : one part Red17
(E) one part White001 : four parts Red78
Rationale: Solution
A : B = Red78 : Red23, B : C = Red23 : Red17, C : D = Red17 : White1
âˆ´Aâˆ¶Bâˆ¶Câˆ¶D= Red78 : Red23 : Red17 : White001.
Thus, A : D = Red78 : White001
4A:1D = Red78, Red78, Red78, Red 78 : White001
Correct Option E
Answer: (E) one part White001 : four parts Red78
Question: A man can row 7.2 kmph in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of stream.
(A) 2.4 km/hr
(B) 12.5 km/hr
(C) 1 2.6 km/hr
(D) 22.5 km/hr
(E) 22.6 km/hr
Rationale: Given that, time taken to travel upstream = 2 × time taken to travel downstream
When distance is constant, speed is inversely proportional to the time
Hence, 2 × speed upstream = speed downstream
Let speed upstream = x
Then speed downstream = 2x
we have, 1/2(x+2x) = speed in still water
⇒1/2(3x)=7.2
3x = 14.4
x = 4.8
i.e., speed upstream = 4.8 km/hr
Rate of stream = 1/2(2x−x)=x/2=4.8/2=2.4 km/hr
Answer is A
Answer: (A) 2.4 km/hr
Question: Two pipes A and B can fill a cistern in 75/2 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:
(A) 5 min.
(B) 9 min.
(C) 10 min.
(D) 15 min
(E) 18 min
Rationale: If B is closed after x mins, then
30*2/75 + x/45 = 1
x/45 = 1 - 4/5 = 1/5
x= 45/5 = 9 mins
ANSWER:B
Answer: (B) 9 min.
Question: During the months May through October, Teddy the bear sextuples his weight, and during the months November through April, Teddy loses 100 pounds. If at the beginning of November 1973, Teddy's weight was m pounds, what was Teddy's weight in pounds by the end of April 1976?
(A) 36m - 1300
(B) 36m - 1200
(C) 6m - 1300
(D) 6m - 1200
(E) 6m
Rationale: Nov ' 73 = m
April ' 74 = m - 100
Oct ' 74 = 6m - 300
April' 75 = 6m - 400
Oct' 75 = 36m - 1200
April'76 = 36m - 1300
Hence answer will be (A) 36m - 1300
Answer: (A) 36m - 1300
Question: A person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 24m/h. what is the speedof the person while he was going to his office?
(A) 8km/h
(B) 10km/h
(C) 12km/h
(D) 16km/h
(E) 14km/h
Rationale: u = k , v= 3k
\inline \therefore \frac{2uv}{u+v}\: \: \Rightarrow \frac{2\times k\times 3k}{(k+3k)}=24
\inline \Rightarrow 1.5k = 24
\inline \Rightarrow k=16km/h
D
Answer: (D) 16km/h
Question: A car travels uphill at 30 km/hr and downhill at 80 km/hr. It goes 100 km uphill and 50 km downhill. Find the average speed of the car?
(A) 38kmph
(B) 33kmph
(C) 34kmph
(D) 35kmph
(E) 36kmph
Rationale: avg speed=total distance/total time.
total distance traveled=100+50=150km;
time taken for uphill journey=100/30=10/3;
time taken for down hill journey=50/80=5/8;
avg speed=150/(10/3+5/8)=38kmph
ANSWER:A
Answer: (A) 38kmph
Question: The number of arrangements that can be made with the letters of the word WORDS so that the vowels occupy the even places?
(A) 14
(B) 32
(C) 777
(D) 24
(E) 221
Rationale: The word MEADOWS has 7 letters of which 3 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 1 even places in 1! i.e., 1 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.
Hence the total ways are 24 * 1 = 24.
Answer:D
Answer: (D) 24
Question: There are 50 students in a class. If 14% are absent on a particular day, find the number of students present in the class.
(A) 43
(B) 36
(C) 28
(D) 129
(E) 11
Rationale: Number of students absent on a particular day = 14 % of 50
i.e., 14/100 × 50 = 7
Therefore, the number of students present = 50 - 7 = 43 students.
Answer:A
Answer: (A) 43
Question: A train running at the speed of 27 km/hr crosses a post in 20 seconds. What is the length of the train?
(A) 200
(B) 150
(C) 300
(D) 175
(E) 250
Rationale: Speed=(27x5/18)=7.5 m/sec.
Length of the train=(Speed x Time).
Length of the train=7.5 x20	m = 150 m.
Answer: B
Answer: (B) 150
Question: The inverse ratio of 3: 2: 1 is?
(A) 2:3:7
(B) 2:3:9
(C) 2:3:2
(D) 2:3:6
(E) 2:3:1
Rationale: 1/3: 1/2: 1/1 = 2:3:6
Answer:D
Answer: (D) 2:3:6
Question: Luke travelled 12 2/3 miles in 1 hours and 40 minutes. What was his average rate of speed in miles per hour?
(A) 7
(B) 7 3/5
(C) 8 1/5
(D) 9
(E) 9 2/5
Rationale: D = 12(2/3) = 38/3
T = 1(2/3) = 5/3
S = D/T = 7 3/5
Answer = B
Answer: (B) 7 3/5
Question: If x = 7 and y = −2, what is the value of (x − 2y)^y?
(A) −100
(B) 0.001
(C) 0.25
(D) 4
(E) 8
Rationale: Quickly we can spot that answer is neither integer nor negative. Eliminate A, DE
by inversing and squaring 0.001
Answer: B
Answer: (B) 0.001
Question: The sum of 4 hours 45 minutes and 5 hours 55 minutes is approximately what percent of a day?
(A) 32%
(B) 36%
(C) 40%
(D) 44%
(E) 48%
Rationale: Since the question is asking for an approximate percentage
4:45+5:55 ~ 11 hours
% of day = 11*100/24 ~ 11*100/25= 44%
Answer is D.
Answer: (D) 44%
Question: A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is:
(A) 8.5 km/hr
(B) 10 km/hr
(C) 12.5 km/hr
(D) 9 km/hr
(E) None of these
Rationale: Explanation:
Man's speed with the current = 15 km/hr
=> speed of the man + speed of the current = 15 km/hr
speed of the current is 2.5 km/hr
Hence, speed of the man = 15 - 2.5 = 12.5 km/hr
man's speed against the current = speed of the man - speed of the current
= 12.5 - 2.5 = 10 km/hr
ANSWER IS B
Answer: (B) 10 km/hr
Question: 90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 20% of the total school population of x students, what is x?
(A) 125
(B) 150
(C) 212
(D) 250
(E) 500
Rationale: 90=x/100*20/100*x=>x^2 = 9*10000/2 = > x =212
C
Answer: (C) 212
Question: If z + | z | = 0, which of the following must be true?
(A) z > 0
(B) z≥0
(C) z< 0
(D) z≤0
(E) z = 0
Rationale: Manipulate the equations:
z + | z | = 0
|z| = -y
-z > 0 OR -z = 0
This means z could be 0 or z is less than 0.
D. z≤0
E. z=0
Answer: D
Answer: (D) z≤0
Question: If 20% of s = t, then t% of 20 is the same as
(A) 10% of s
(B) 4% of s
(C) 20% of s
(D) None
(E) 30% of s
Rationale: Explanation :
20% of s = t
=> t = 20/100s
Then,
t% of 20 = (t/100)*20=((20/100)*s)*20/100
=(2020s)/(100100) =4s/100 = 4% of s
Answer : B
Answer: (B) 4% of s
Question: What is the minimum value of z for which z^2 + z - 3/6 > 0 is not true?
(A)  -5/2
(B)  -3/2
(C)  -1
(D)  1/4
(E)  1/2
Rationale: I think C -1 is the best ans...
Answer: (C)  -1
Question: One side if a square is doubled. If the parameter is now 12x. What was the length of one of the sides before it was doubled?
(A) 12x/4
(B) 12x/2
(C) 6x/2
(D) 12x/6
(E) 4x/1
Rationale: If the parameter is now 12x, the each side is 12x/4. To get the original each side is divided by 2. One side is represented by 1 since it's a square. 1/2 is 0.5, which when times by 4 is 2. Thus the answer is 12x/2. Answer option B.
Answer: (B) 12x/2
Question: How many of the following numbers are divisible by 22 ?
264, 396, 462, 792, 968, 2178, 5184, 6336
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: By using your calculator you can calculate that the following numbers are divisible by 22 : 264, 396, 462, 792, 968, 2178, 6336.
Required number of number = 7.
E
Answer: (E) 7
Question: A lady builds 10cm length, 13cm width, and 5cm height box using 5cubic cm cubes. What is the minimum number of cubes required to build the box?
(A) 107
(B) 108
(C) 130
(D) 150
(E) 145
Rationale: Number of cubes required = Volume of box/Volume of cube
= 10*13*5/5
=130 cubes
ANSWER:C
Answer: (C) 130
Question: For an integer n greater than 1, n* denotes the product of all the integers from 1 to n inclusive. How many prime numbers are there between 7*+3 and 7*+7, inclusive ?
(A) 4
(B) 1
(C) 2
(D) 3
(E) 0
Rationale: Given that n* denotes the product of all the integers from 1 to n, inclusive so, 7* + 3 = 7! + 2 and 7* + 7 = 7! + 7.
Now, notice that we can factor out 3 our of 7! + 3 so it cannot be a prime number, we can factor out 4 our of 7! + 4 so it cannot be a prime number, ... The same way for all numbers between 7! + 3 and 7! +7, inclusive. Which means that there are no primes in this range.
Answer: E
Answer: (E) 0
Question: Find the smallest number of 6 digits which is exactly divisible by 111?
(A) 12000
(B) 15550
(C) 100011
(D) 158993
(E) 100010
Rationale: Smallest number of 6 digits is 100000.
On dividing 100000 by 111, we get 100 as remainder.
Number to be added = (111 - 100) - 11.
Hence, required number = 100011
Answer B
Answer: (B) 15550
Question: If m is a positive integer and m^2 is divisible by 24, then the largest positive integer that must divide m is?
(A)  3
(B)  6
(C)  8
(D)  12
(E)  16
Rationale: M^2 is divisible by 48 so M^2 must be multiple of 48.
If the value of M is Multiples of 8 then it will satisfy the condition. If we If M is 12 or 24 or 36 then it ans is C but if M = 48 then answer should be 16.
Is the question right? Or am i missing some thing?
C
Answer: (C)  8
Question: A certain college's enrollment at the beginning of 1992 was 20 percent greater than it was at the beginning of 1991, and its enrollment at the beginning of 1993 was 15 percent greater than it was at the beginning of 1992. The college's enrollment at the beginning of 1993 was what percent greater than its enrollment at the beginning of 1991 ?
(A) 17.5%
(B) 24%
(C) 30%
(D) 35%
(E) 38%
Rationale: Suppose enrollment in 1991 was 100
Then enrollment in 1992 will be 120
And enrollment in 1993 will be 120*1.15=138
Increase in 1993 from 1991 = 138-100= 38
Answer : E
Answer: (E) 38%
Question: a person travels from his house to office from 11:10am to 11:50 am and covers a distence of 13.4km. find the average speed of the person.
(A) 20.1km/h
(B) 20.5km/h
(C) 21.1km/h
(D) 22.1km/h
(E) 20.9km/h
Rationale: time=11:50-11:10=40min=2/3hour
distance=13.4km
speed=13.4*3/2=20.1km/h
ANSWER:A
Answer: (A) 20.1km/h
Question: 3/x + 3x = 3(x-9)
(A) -9
(B) -1/6
(C) -1/9
(D) 1/9
(E) 9
Rationale: We can solve - expand the right side, multiply by x on both sides and then subtract away the 3x^2 terms:
(3/X) + 3x = 3(x-9)
(3/x) + 3x = 3x - 18
3 + 3x^2 = 3x^2 - 18x
3 = -18x
-1/6 = x
and to confirm, you can plug that answer back into the original equation to see that it makes the left and right sides equal.
B
Answer: (B) -1/6