mathewhe/aqua_rat huggingface dataset:
Question: A train 270 m long passed a pole in 27 sec. How long will it take to pass a platform 650 m long?
(A) 92 sec
(B) 89 sec
(C) 54 sec
(D) 27 sec
(E) 22 sec
Rationale: Speed = 270/27 = 10 m/sec.
Required time = (270 + 650)/10
= 92 sec.
Answer: A
Answer: (A) 92 sec
Question: The measurement of a rectangular box with lid is 50cmx30cmx38cm. Find the volume of the largest sphere that can be inscribed in the box (in terms of πcm3). (Hint: The lowest measure of rectangular box represents the diameter of the largest sphere)
(A) 288
(B) 4500
(C) 7200
(D) 864
(E) 9640
Rationale: d=30, r=15;
Volume of the largest sphere= 4/3πr3
= 4/3 *π*15*15*15= 4500πcm3 ANSWER:B
Answer: (B) 4500
Question: 70% of the employees of a company are men. 50% of the men in the company speak French and 40% of the employees of the company speak French. What is % of the women in the company who do not speak French?
(A) 4%
(B) 10%
(C) 83.33%
(D) 90.33%
(E) 20%
Rationale: No of employees=100(say)
Men=70
Women=30
Men speaking french=0.5*70=35
Employees speaking french=0.4*100=40
Therefore women speaking French=40-35=5
And women not speaking French=30-5=25
% of women not speaking French=25/30*100=83.33%
Answer C
Answer: (C) 83.33%
Question: Which of the following statements must be true?
I)The product of first 100 prime numbers is even
II)The sum of first 100 prime numbers is odd.
III)The sum of first five non-negative even numbers is divisible by both 4 and 5
(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II and III
Rationale: First look at some Odd & Even Rules:-
Multiplication
E x E = E
O x O = O
E x O = E = O x O
Addition
E + E = E
E + O = O = O + E
O + O = E
Now coming to the statements:-
I. The product of first 100 prime numbers is even
First 100 prime nos. includes 2 which is the ONLY even no. Hence, any no. multiplied by even no will give an Even No.
II. The sum of first 100 prime numbers is odd
We can figure this out through Cyclicity Rule. Ignore the First TWO Prime Nos. and let us start with 5, which is Odd.
O + O = E (Sum of two primes)
E + O = O (Even is carried over and added to 3rd prime)
O + O = E (Carry over and 4th prime)
E + O = O (5th prime)
O + O = E (6th prime)
Through Cyclicity, we can find out that the sum of any Even No of ODDS will always be EVEN. Since 98th no is Even, the answer will also be EVEN. Now, include the first two prime nos. i.e. 2 & 3.
E + 2(E) + 3(O) = O
Hence, the statement is TRUE.
III. The sum of first five non-negative even numbers is divisible by both 4 and 5
First five non negative even nos. = 0, 2, 4, 6 and 8
Sum = 20. Divisible by both 4 AND 5
Answer : E
Answer: (E) I, II and III
Question: What amount does Kiran get if he invests Rs. 18000 at 15% p.a. simple interest for three years?
(A) 29893
(B) 27773
(C) 29989
(D) 26100
(E) 29883
Rationale: Simple interest = (18000 * 3 * 15)/100 = Rs. 8100
Amount = P + I = 18000 + 8100 = Rs. 26100
Answer: D
Answer: (D) 26100
Question: If P is a prime number greater than 3, find the remainder when P^2 + 13 is divided by 12.
(A) 6
(B) 1
(C) 0
(D) 2
(E) 7
Rationale: Every prime number greater than 3 can be written 6N+1 or 6N-1.
If P = 6N+1, then P^2 + 13 = 36N^2 + 12N + 1 + 13 = 36N^2 + 12N + 12 + 2
If P = 6N-1, then P^2 + 13 = 36N^2 - 12N + 1 + 13 = 36N^2 - 12N + 12 + 2
When divided by 12, it must leave a remainder of 2.
The answer is D.
Answer: (D) 2
Question: Ashok opened a shop investing Rs.60,000 and Madhuri joined him after 2 months investing Rs.90,000. They get a profit of Rs. 1,08,000 after one year. The share of Madhuri is
(A) Rs.35,000
(B) Rs.30,000
(C) Rs.60,000
(D) Rs.45,000
(E) None of the above
Rationale: 60000*12:90000*10=4:5
5/9(108000)=60000
ANSWER:C
Answer: (C) Rs.60,000
Question: If 945*s is a perfect square then s can be which of the following numbers?
(A) 21
(B) 35
(C) 54
(D) 105
(E) 150
Rationale: For a number to be a perfect square all the prime factors must be in pairs. So,
Prime factors of 945 are 3 *3 *3 *5 * 7
1) 21 = 3 * 7
2) 35 = 5 * 7
3) 54 = 2 * 3 * 3 * 3
4) 105 = 3 * 5 * 7
5) 150 = 2 * 3 * 5 * 5
So only answer choice D completes the pairing of 3, 5 and 7. It adds a "3", a "5", and a "7" to the prime factors of 945 (3*3*3*5*7) and makes it a perfect square.
Answer: (D) 105
Question: A swimmer can swim in still water at 4 km/h. If the speed of the water current is 1 km/h, how many hours will the swimmer take to swim against the current for 6 km?
(A) 1.2
(B) 1.4
(C) 1.6
(D) 1.8
(E) 2
Rationale: The swimmer can swim against the current at a speed of 4-1 = 3 km/h.
The time it will take is 6/3 = 2 hours.
The answer is E.
Answer: (E) 2
Question: P = {22, 24, 26, 28, 30, 32}
Q = {2, 24, 25, 26, 27, 28}
R = {4, 7, 10, 13, 16, 19}
If p is the standard deviation of set P, q is the standard deviation of set Q, and r is the standard deviation of set R, which of the following must be true?
(A) p<q<r
(B) p<r<q
(C) q<r<p
(D) q<p<r
(E) r<q<p
Rationale: P has difference by 2.
Q has difference of 22 between 2 and 24 and for other numbers we have difference by 1.
R has difference 3.
We need to take the SD as per the difference.
So Q > R > P. Option B has this set
ANSWER:B
Answer: (B) p<r<q
Question: A cistern is filled by a tap in 3 1/2 hours. Due to leak in the bottom of the cistern, it takes half an hour longer to fill the cistern. If the cistern is full how long will it take the leak to empty it?
(A) 24
(B) 46
(C) 67
(D) 28
(E) 29
Rationale: 2/7 - 1/x = 1/4
x = 28
Answer: D
Answer: (D) 28
Question: Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn
randomly. If it is known that the number on the drawn card is more than 3, what is the probability
that it is an even number?
(A) 3/7
(B) 4/7
(C) 5/7
(D) 5/11
(E) 6/11
Rationale: Let A be the event ‘the number on the card drawn is even’ and B be the
event ‘the number on the card drawn is greater than 3’. We have to find P(A|B).
Now, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Then A = {2, 4, 6, 8, 10}, B = {4, 5, 6, 7, 8, 9, 10}
and A n B = {4, 6, 8, 10}
Also P(A) = 5/2, P(B) = 7/10 and P(A n B) = 4/10
Then P(A|B) = P(A n B)/P(B) = (4/10)/(7/10) = 4/7
B)
Answer: (B) 4/7
Question: A 14 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
(A) 12
(B) 20
(C) 88
(D) 77
(E) 4
Rationale: 1: 2/5 = 5: 2
2/7 * 14 = 4
Answer: E
Answer: (E) 4
Question: 30 men can do a work in 40 days. When should 20 men leave the work so that the entire work is completed in 40 days after they leave the work?
(A) 12 days
(B) 11 days
(C) 10 days
(D) 16 days
(E) 13 days
Rationale: C
10 days
Total work to be done = 30 * 40 = 1200
Let 20 men leave the work after 'P' days, so that the remaining work is completed in 40 days after they leave the work.
40P + (20 * 40) = 1200
40P = 400 => P = 10 days
Answer: (C) 10 days
Question: What is the probability of flipping a fair coin four times and the coin landing on heads on at least two flips?
(A) 1/16
(B) 15/16
(C) 9/16
(D) 11/16
(E) 7/16
Rationale: There are totally 16 outcomes
Chances of all being heads is 1/16
Chances of 3 heads is = 4c34c3 ways = 4/16
Chances of 2 heads is 4c24c2 ways = 6/16
hence 1/16+4/16+6/16=11/161/16+4/16+6/16=11/16
Ans: "D"
Answer: (D) 11/16
Question: There are total 15 people. 7 speaks French and 8 speaks Spanish 3 do not speak any language. Which part of total people speaks both languages.
(A) 3/4
(B) 1/5
(C) 1/6
(D) 3/8
(E) 1/3
Rationale: If x no of people speak both languages then
15 = 8+7-x+3
x=3
so part of total people speaks both languages = 3/15 =1/5
ANSWER:B
Answer: (B) 1/5
Question: The ages of two persons differ by 16 years. If 6 years ago , the elder one be 3 times as old as the younger one, find their present ages .
(A) 10 years and 18 years
(B) 18 years and 26 years
(C) 20 years and 28 years
(D) 14 years and 30 years
(E) 16 years and 25 years
Rationale: Explanation :
Sol. Let the age of the younger person be xx years
Then , age of the elder person = (x+16)(x+16) years
âˆ´âˆ´ 3(xâˆ’6)=(x+16âˆ’6)3(x-6)=(x+16-6)
â‡” 3x âˆ’18=x+10â‡” 3x -18=x+10
â‡” 2x=28â‡” 2x=28
â‡” x=14â‡” x=14
Hence, their present age are 14 years and 30 years .
ANSWER IS D
Answer: (D) 14 years and 30 years
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?
(A) 20%
(B) 30%
(C) 32%
(D) 73%
(E) 84%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 ---20 => 20%
Answer:A
Answer: (A) 20%
Question: Incomes of two companies A and B are in the ratio of 5 : 8. Had the income of company A been more by 40 lakh, the ratio of their incomes would have been 5 : 4. What is the income of company B?
(A) 80 lakh
(B) 50 lakh
(C) 40 lakh
(D) 64 lakh
(E) None of these
Rationale: Let the incomes of two companies A and B be 5x and 8x respectively.
From the question,
5x+40/8x=5/4 ⇒ 20x + 160 = 40x
∴ x = 8
∴ Income of company B = 8x = 64 lakh
Answer D
Answer: (D) 64 lakh
Question: The dimensions of a rectangular solid are 4 inches, 5 inches, and 10 inches. If a cube, a side of which is equal to one of the dimensions of the rectangular solid, is placed entirely within thespherejust large enough to hold the cube, what the ratio of the volume of the cube to the volume within thespherethat is not occupied by the cube?
(A)  10:17
(B)  2:5
(C)  10:19
(D)  25:7
(E)  32:25
Rationale: Answer: C.
Answer: (C)  10:19
Question: Dimitri weighs 2x-x pounds more than Allen weighs. Together, Allen and Dimitri weigh a total of y pounds. Which of the following represents Allen’s weight?
(A) y - x/2
(B) 2x - y/2
(C) (y - x)/2
(D) y - 2x
(E) 2x - y
Rationale: These type of multi-variable story problems are usually perfect for TESTing VALUES.
Here, we're told that Dimitri weighs 2X-X or X pounds more than Allen weighs and that they weight a combined TOTAL of Y pounds.
IF....
Dimitri = 30
Allen = 20
X = 10
Y = 50
We're asked for Allen's weight, so we're looking for an answer that equals 20 when X = 10 and Y = 50.
Answer A: 50 - (10/2) = 45 NOT a match
Answer B: 20 - (50/2) = -5 NOT a match
Answer C: (50-10)/2 = 20 This IS a match
Answer D: 50 - 20 = 30 NOT a match
Answer E: 20 - 50 = -30 NOT a match
Final Answer:
C
Answer: (C) (y - x)/2
Question: In how many ways can the letters of the word MECHANIC be arranged?
(A) 2580
(B) 2500
(C) 20160
(D) 2520
(E) 3420
Rationale: MECHANIC has 8 words, but C is repeated two times. Thus ways = 8! / 2! = 20160 ways
C
Answer: (C) 20160
Question: If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/2, then what is the value of abc/def ?
(A)  27/4
(B)  27/8
(C)  3/4
(D)  3/8
(E)  1/4
Rationale: Say a = 3. Then:
a/b = 1/3 --> b = 9;
b/c = 2 --> c = 9/2;
c/d = 1/2 --> d = 9;
d/e = 3 --> e = 3;
e/f = 1/2 --> f = 6.
abc/def = (3*9*9/2)/(9*3*6) = 3/4.
Answer: C.
Answer: (C)  3/4
Question: A and B can together complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work ?
(A) 4 days
(B) 5 days
(C) 6 days
(D) 7 days
(E) 8 days
Rationale: Explanation:
(A+B)'s 1 day work = 1/4
A's 1 day work = 1/12
B's 1 day work =
(1/4−1/12)=3−1/12=1/6
So B alone can complete the work in 6 days
Option C
Answer: (C) 6 days
Question: How many seconds will a 100 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 11 sec
(B) 6 sec
(C) 77 sec
(D) 14 sec
(E) 12
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 100 * 3/50
= 6 sec.
Answer: B
Answer: (B) 6 sec
Question: A person has his own coach & whenever he goes to railway station he takes his coach. One day he was supposed to reach the railway station at 5 O'clock. But he finished his work early and reached at 3 O'clock. Then he rung up his residence and asked to send the coach immediately. He came to know that the coach has left just now to the railway station. He thought that he should not waste his time and started moving towards his residence at the speed of 3miles/hr. On the way, he gets the coach and reaches home at 6 o'clock. How far is his residence from railway station.
(A) 17 miles
(B) 18 miles
(C) 19 miles
(D) 16 miles
(E) 15 miles
Rationale: He walked for 1.5 hrs and coach travelled in one side for 1.5 hrs instead of 2 hrs to save 0.5 hrs one side journey of coach.
So Coach speed is 3 times speed of man i.e. 9 mph.
Total distance of stn from Home = 1.5( 3+9) = 1.5*12= 18 miles
ANSWER:B
Answer: (B) 18 miles
Question: The jogging track in a sports complex is 726 m in circumference. Deepak and his wife start from the same point and walk in opposite directions at 4.5 km/hr and 3.75 km/hr respectively. They will meet for the first time in?
(A) 2.98 min
(B) 5.28 min
(C) 1.97 min
(D) 2.88 min
(E) 2.77 min
Rationale: Clearly, the two will meet when they are 726 m apart.
To be (4.5 + 3.75) = 8.25 km apart, they take 1 hour.
To be 726 m apart, they take (100/825 * 726/1000) hrs
= (242/2750 * 60) min
= 5.28 min.
Answer: B
Answer: (B) 5.28 min
Question: What should come in place of the question mark (‘?) in the following equation?
18 2⁄5 of 150.8 + ? = 8697.32 – 3058.16
(A) 2764.44
(B) 2864.34
(C) 1864.44
(D) 2684.44
(E) None of these
Rationale: ? = 8697.32 – 3058.16 – 92⁄5 × 150.8
= 5639.16 – 2774.72 = 2864.44
Answer E
Answer: (E) None of these
Question: A train 200 m long passes a man, running at 6 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
(A) 36
(B) 50
(C) 78
(D) 66
(E) 22
Rationale: Speed of the train relative to man
= (200/10) m/sec = 20 m/sec. [20 * (18/5)] km/hr
= 72 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 6) km/hr. x - 6
= 72 ==> x
= 78 km/hr.
Answer:C
Answer: (C) 78
Question: M and N started a business by investing Rs.4000/- and Rs.5000/- respectively. Find the M’s share out of a total profit of Rs.1800:
(A) Rs.500/-
(B) Rs.550/-
(C) Rs.600/-
(D) Rs.650/-
(E) Rs.800/-
Rationale: M = Rs.4000/-
N = Rs.5000/-
M share 4 parts & N share 5 parts
Total 9 parts -----> Rs.1800/-
----> 1 part -------> Rs.200/-
M share = 4 parts -----> Rs.800/-
E
Answer: (E) Rs.800/-
Question: What is the distance covered by a car if it travels with a speed of 160 kmh for 5 hours?
(A) 350 km
(B) 400 km
(C) 800 km
(D) 600 km
(E) 650 km
Rationale: Distance= Time x Speed
5 x 160 = 800
Answer: C
Answer: (C) 800 km
Question: A certain music store stocks 800 cellos and 600 violas. Of these instruments, there are 100 cello-viola pairs, such that a cello and a viola were both made with wood from the same tree (each tree can make at most one viola and one cello, so there are no pairs other than these 90). If one viola and one cello are chosen at random, what is the probability that the two instruments are made with wood from the same tree?
(A) 3/16,000
(B) 1/4,800
(C) 3/1,600
(D) 1/90
(E) 2/45
Rationale: Solution provided by stanford2012 is correct: 100/800 choosing one of the cellos which has a pair viola, 1/600 choosing the viola which is the pair of chosen cello --> P=100/800*1/600=1/4,800.
Answer: B.
Answer: (B) 1/4,800
Question: A boy sitting in a train which is travelling at 30 kmph observes that a goods train travelling in a opposite direction, takes 18 seconds to pass him. If the goods train is 350 m long, find its speed.
(A) 25
(B) 30
(C) 35
(D) 40
(E) 45
Rationale: Relative speed = (350/18)m/s = (350/18)*(18/5) = 70 kmph
speed of goods train = 70-30 = 40 kmph
Answer is D
Answer: (D) 40
Question: There are three secretaries who work for four departments. If each of the four departments have one report to be typed out, and the reports are randomly assigned to a secretary, what is the probability that all three secretary are assigned at least one report?
(A) 8/9
(B) 64/81
(C) 12/27
(D) 16/81
(E) 5/9
Rationale: "We havé total possibilities N =3^4"
What are these total possibilities? They are the ways in which the 4 reports can be distributed among 3 secretaries so that all reports may go to one secretary, the reports may be distributed among 2 secretaries or they may be distributed among all 3. So such cases are included (4, 0, 0), (0, 4, 0), (2, 2, 0), (1, 3, 0), (1, 1, 2), etc
In how many ways can you give 4 reports to only 1 secretary? You choose the secretary who will get the reports in 3C1 = 3 ways
In how many ways can you give 4 reports to only 2 secretaries? Choose the 2 secretaries in 3C2 ways. Each secretary must get at least one report so you can distribute them in 2 ways:
'1 and 3' - Choose one report in 4C1 ways and give it to one secretary in 2C1 ways. The other secretary gets the other 3 reports.
or
'2 and 2' - Choose 2 reports in 4C2 ways and give to the first secretary. The other secretary gets the other two reports.
Total number of ways is 3C2 * (4C1*2C1 + 4C2) = 42 ways
Note that in your method 2^4 is incorrect. It includes the ways in which all 4 reports go to one secretary.
So this means that in 3 + 42 = 45 ways, at least one secretary gets no report. In the rest of 81 - 45 = 36 ways, each secretary gets at least one report.
Required Probability = 36/81 = 12/27
ANS:C
Answer: (C) 12/27
Question: John and Jane went out for a dinner and they ordered the same dish. Both used a 10% discount coupon. John paid a 15% tip over the original price of the dish, while Jane paid the tip over the discounted price for the coupon. If John paid $0.60 more than Jane, what was the original price of the dish?
(A)  24
(B)  34.8
(C)  37.8
(D)  40
(E)  84
Rationale: The difference between the amounts John paid and Jane paid is the deference between 15% of p and 15% of 0.9p:
0.15p - 0.15*0.9p = 0.60 --> 15p - 13.5p = 60 --> p = 40.
Answer: D.
Answer: (D)  40
Question: A welder received an order to make a 1 million liter cube-shaped tank. If he has only 2x4 meter sheets of metal that can be cut, how many metal sheets will be required for this order? (1 cubic meter = 1,000 liters)
(A) 92
(B) 90
(C) 82
(D) 75
(E) 78
Rationale: The question say:A welder received an order to make a 1 million liter cube-shaped tank. (1 cubic meter = 1,000 liters)
In other words, the tank is going to have a volume of 1000 cubic meters. That would equal 1 million liters.
A cube with a volume of 1000 cubic meters must be (10 meters) x (10 meters) x (10 meters).
The question doesn't specify whether this tank should have a closed top or an open top. (The real GMAT is good about specifying things like that.) Here, we are going to assume a closed top, only because if the top is open, we don't use enough metal --- we get an answer smaller than any of the answer choices. A closed-top cube, a full cube, has 6 sides, each of which is (10 meters) x (10 meters). That's a total surface area of 600 sq m.
The question tells us:he has only 2x4 meter sheets of metal that can be cut.
Each sheet has an area of 8 sq m. How many of these need to fill up 600 sq m? 600/8 = 75. He needs 75 sheets.
Answer =D
Answer: (D) 75
Question: John and David can finish a job together in 6 hours. If John can do the job by himself in 8 hours, what percent of the job does David do?
(A) 35%
(B) 45%
(C) 25%
(D) 30%
(E) 20%
Rationale: You can also plug in numbers. For example, Bob and Alice work at a donut factory and make 24 donuts which is the job ( I picked this as a SMART number).
John on his own works 24/8 = 3 donuts per hour.
John and David work 24/6 = 4 donuts per hour so David works 1 donuts/hour
To find out the percentage, David works 1 donuts/hr x 6 hours = 6 donuts per hour.
Therefore 6 donuts/24donuts = 1/4 = 25%
Answer : C
Answer: (C) 25%
Question: 8 noun, 3 verbs and 2 adjectives are written on blackboard.we can form sentence by choosing 1 from each available set without caring it makes sense or not.what is the number of ways of doing this??
(A) 128
(B) 188
(C) 218
(D) 248
(E) 288
Rationale: we have to choose one from each set. 1 from 8 nouns and 1 from 3 verbs and 1 from 2 adjectives.
then we have to arrange 3 different sets in 3! ways.
so,
8c1*3c1*2c1*3!=288
ANSWER:E
Answer: (E) 288
Question: In a class of 30 students, 5 students did not borrow any books from the library, 12 students each borrowed 1 book, 8 students each borrowed 2 books, and the rest of the students each borrowed at least 3 books. If the average (arithmetic mean) number of books borrowed per student was 2, what is the maximum number of books that any single student could have borrowed ?
(A) 5
(B) 8
(C) 15
(D) 18
(E) 20
Rationale: The average number of books per student was 2means that total of 2*30=60 books were borrowed;
5+12+8=25 students borrowed total of 5*0+12*1+8*2=28 books;
So 60-28=32 books are left to distribute among 30-25=5 students, these 5 arethe rest who borrowed at least 3 books;
Tomaximizethe number of books one student from above 5 could have borrowed we shouldminimizethe number of books other 4 students from 5 could have borrowed. Minimum these 4 students could have borrowed is 3 books per student, so total number of books they could have borrowed is 4*3=12 books. So the 5th student could have borrowed is 32-12=20 books.
Answer: E.
Answer: (E) 20
Question: In an examination, a pupil’s average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: Let the number of papers be x. Then, 63x + 20 + 2 = 65x
or 2x = 22 or x = 11.
Answer D
Answer: (D) 11
Question: Fill in the missing number:
18 14 12 11 ? 10.25
(A) 10.1
(B) 10.4
(C) 10.2
(D) 10.5
(E) 10.3
Rationale: D
10.5
Divide each number by 2 and then add 5 to it.
Answer: (D) 10.5
Question: A diner is having lunch at a salad bar. There are four types of lettuce to choose from, as well as four types of tomatoes, and five types of olives. If the diner picks one type of lettuce, one type of tomato, and one type of olive for the salad, how many total options does the diner have for the salad?
(A) 20
(B) 40
(C) 60
(D) 80
(E) 100
Rationale: 4*4*5 = 80
The answer is D.
Answer: (D) 80
Question: The distance between Delhi and Mathura is 200 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?
(A) 10.50 a.m.
(B) 12.00 a.m.
(C) 10.30 a.m.
(D) 11.40 a.m.
(E) 1.40 a.m.
Rationale: D = 200 â€“ 20 = 180
RS = 20 + 25 = 45
T = 180/45 = 4 hours
8 a.m. + 4 hrs 00 min = 12.00 a.m.
ANSWER:B
Answer: (B) 12.00 a.m.
Question: In what time will a car 10 m long moving at the rate of 36 kmph pass a telegraph post on its way?
(A) 8 sec
(B) 1 sec
(C) 9 sec
(D) 6 sec
(E) 2 sec
Rationale: T = 10/36 * 18/5
= 1 sec
Answer:B
Answer: (B) 1 sec
Question: If 2^(2w) = 8^(w−3), what is the value of w?
(A) 3
(B) 6
(C) 9
(D) 12
(E) 15
Rationale: 2^(2w) = 8^(w−3)
2^(2w) = 2^(3*(w−3))
2^(2w) = 2^(3w-9)
Let's equate the exponents as the bases are equal.
2w = 3w-9
w = 9
The answer is C.
Answer: (C) 9
Question: Pipe A can fill the tank in 30 minutes and pipe b can empty the tank in 90 minutes. How long it will take to fill the tank if both pipes are operating together?
(A) 30
(B) 35
(C) 40
(D) 45
(E) 50
Rationale: Pipe A fills 1/30th of the tank in a minute and pipe B empties 1/90th of the tank
(1/30)-(1/90)=(1/x)
2/90=1/x => x=45
Answer: D
Answer: (D) 45
Question: An MBA admissions committee is to be formed randomly from 6 second year MBAs for the 3 positions. If Albert and Jane are applicants, what is the probability that Albert will be selected but Jane will not?
(A) 10%
(B) 17%
(C) 25%
(D) 30%
(E) 44%
Rationale: Probability of selecting Albert but not Jane =
Prob(A,J',J')
= 3* 1/6 * 4/5 * 3/4 (J' is Jane is not selected and we multiply by 3 because A , J' and J' can occur in 3 distinct ways)
= 3/10
=30%
Answer D
Answer: (D) 30%
Question: The average age of students in section A of 125 students is 23 years and the average age of students in section B of 162 students is 25 years. Find the average age of students in both sections taken together?
(A) 26 years
(B) 30years
(C) 15years
(D) 24years
(E) 20years
Rationale: The required average = (125*23+162*25)/125+162 = 24 years
Answer is D
Answer: (D) 24years