mathewhe/aqua_rat huggingface dataset:
Question: How many times does the minute hand and the second hand make a straight line?
(A) 21
(B) 2823
(C) 2822
(D) 2832
(E) 2833
Rationale: D
2832
make a straight line 59 x 2 times = 118 times.
24 hours in a day, so in a day minutes and second hand make a straight line
24 x 118 times = 2832 times.
Answer: (D) 2832
Question: When 5 + 1 = 56, 6 + 1 = 67, 7 + 1 = 78, then 8 + 1 = ?
(A) 85
(B) 98
(C) 89
(D) 105
(E) 129
Rationale: 5 + 1 => 5 x 1 = 5 & 5 + 1 = 6 => 5 & 6 => 56
6 + 1 => 6 x 1 = 6 & 6 + 1 = 7 => 6 & 7 => 67
7 + 1 => 7 x 1 = 7 & 7 + 1 = 8 => 7 & 8 => 78
Then 8 + 1 => 8 x 1 = 8 & 8 + 1 = 9 => 8 & 9 => 89
Answer : C
Answer: (C) 89
Question: Dacid obtained 96, 95, 82, 97 and 95 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
(A) 79
(B) 93
(C) 88
(D) 88
(E) 75
Rationale: Average = (96+ 95+ 82+ 97+95)/5
= 465/5 = 93.
Answer:B
Answer: (B) 93
Question: There are 8 red, 7 blue and 6 green balls, 1 ball is picked up randomly thenwhat is the probability that neither blue nor green?
(A) 2/31
(B) 3/41
(C) 4/45
(D) 4/57
(E) 8/21
Rationale: Total number of balls = (8 + 7 + 6) = 21
Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.
Therefore, n(E) = 8.
P(E) = 8/21.
Answer: (E) 8/21
Question: What is the sum W of all 3 digit numbers that leave a remainder of '2' when divided by 3?
(A) 897
(B) 164,850
(C) 164,749
(D) 149,700
(E) 156,720
Rationale: The series is => 101+...998
Number of terms => 300
sum => 300/2 * [101+998]
hence sum W=> 164850 i.e. option B
Answer: (B) 164,850
Question: Company T produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company T last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
(A) 8/22
(B) 4/22
(C) 6/22
(D) 7/22
(E) 5/22
Rationale: # of basic stereos was 3/4 of total and # of deluxe stereos was 1/4 of total, let's assume total=16, then Basic=12 and Deluxe=4.
Now, if time needed to produce one Deluxe stereo is 1 unit than time needed to produce one Basic stereo would be 7/5 units. Total time for Basic would be 12*1=12 and total time for Deluxe would be 4*7/5=28/5 --> total time for both of them would be 12+28/5=88/5 --> deluxe/total=28/5 / 88/5= 28/88 =7/22
D
Answer: (D) 7/22
Question: Steve traveled the first 2 hours of his journey at 40 mph and the last 4 hours of his journey at 80 mph. What is his average speed of travel for the entire journey?
(A) 53.33 mph
(B) 56.67 mph
(C) 60 mph
(D) 64 mph
(E) 66.67 mph
Rationale: Average Speed = Total distance/ Total time = (40 * 2 + 80 * 4)/(2 + 4) = 400/6 = 66.6
Answer: E
Answer: (E) 66.67 mph
Question: A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 29 m * 2 m * 0.75 m?
(A) 29000
(B) 27908
(C) 78902
(D) 25000
(E) 27991
Rationale: 29 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x
29 = 1/100 * x => x
= 29000
Answer: A
Answer: (A) 29000
Question: 34.99 + 240.016 + 23.98 = ?
(A) 298.986
(B) 298.694
(C) 289.496
(D) 289.469
(E) 298.964
Rationale: 34.99
240.016
+ 23.98
--------
298.986
Answer is A.
Answer: (A) 298.986
Question: An analysis of the monthly incentives received by 5 salesmen : The mean and median of the incentives is $7000. The only mode among the observations is $12,000. Incentives paid to each salesman were in full thousands. What is the difference between the highest and the lowest incentive received by the 5 salesmen in the month?
(A) $4000
(B) $13,000
(C) $9000
(D) $5000
(E) $11,000
Rationale: The arithmetic mean of the incentives is $7000.
The median of the incentives is also $7000.
There is only one mode and the mode is $12,000.
Let their incentives be a, b, c, d, and e such that a ≤ b ≤ c ≤ d ≤ e
Therefore, the median of these values is 'c'.
So, c = $7000.
The sum of their incentives a + b + c + d + e = 5 * 7000 = $35,000
There is only one mode amongst these 5 observations.
The mode is that value that appears with the maximum frequency.
Hence, $12,000 is the incentive received by the most number of salesmen.
The incentive that c has got is $7000
So, the incentive received by d and e has to be greater than or equal to $7000
But the mode is $12,000
So, d and e should have got $12,000 each.
Therefore, c + d + e = 7000 + 12,000 + 12,000 = $31,000
Hence, a + b = 35,000 - 31,000 = $4000
As there is only one mode, the incentives received by a and b have to be different
So, a received $1000 and b received $3000.
Maximum incentive : $12,000
Minimum incentive : $1000
Difference between maximum and minimum incentive : $11,000
Answer E
Answer: (E) $11,000
Question: In how many of ways can 5 balls be placed in 5 tins if any number of balls can be placed in any tin?
(A)  5C4
(B)  5P4
(C)  54
(D)  4^5
(E)  5^5
Rationale: Now, each of the 5 different balls has 5 choices (5 tins to go to), so total # of distribution is 5*5*5*5*5=5^5.
Answer: E.
Answer: (E)  5^5
Question: A baker charges Q dollars for a birthday cake. Next week, she intends to earn 320 dollars selling cakes. If she were to reduce the price of the cake by 20 percent, she would have to sell two more cakes to earn the same amount of revenue. How many cakes does she intend to sell next week?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: We're told that by selling cakes at Q dollars/cake, a baker will make $320.
Reducing the price by 20% and selling 2 MORE cakes will also make her $320.
We're asked for the original number of cakes that the baker intends to sell.
$320 is a rather interesting number. Based on the answer choices, we're almost certainly dealing with integer values for the number of cakes AND the price per cake. As such, 6 is probably NOT going to be part of the solution (either as 4 and 6 cakes or as 6 and 8 cakes). As such, we can avoid Answers B and C....
Let's TEST ANSWER D: 8 cakes
IF....
Original cakes = 8
8(Q) = $320, so Q = $40/cake
20% off = $8 off = 40-8 = $32/cake
+2 more cakes = 8+2 = 10 cakes
10(32) = $320
This is an exact MATCH for what we were told, so this MUST be the answer.
Final Answer:
D
Answer: (D) 8
Question: A man saves Rs 500 at the end of each year and lends the money at 5% compound interest. How
much will it become at the end of 3 years.
(A) Rs 662
(B) Rs 1665.01
(C) Rs 1662.02
(D) Rs 1655.06
(E) None of these
Rationale: Explanation:
=[500(21/20×21/20×21/20)+500(21/20×21/20)+500(21/20)]=1655.06
Answer: D
Answer: (D) Rs 1655.06
Question: Because he’s taxed by his home planet, Mork pays a tax rate of 30% on his income, while Mindy pays a rate of only 20% on hers. If Mindy earned 3 times as much as Mork did, what was their combined tax rate?
(A)  32.5%
(B)  34%
(C)  35%
(D)  36%
(E)  22.5%
Rationale: Say Morks income is - 100
So tax paid will be 30
Say Mindys income is 3*100 = 300
So tax paid is 20% * 300 = 60
Total tax paid = 30+60 = 90.
Combined tax % will be 90/100+300 = 22.5%
Answer: (E)  22.5%
Question: The probability that a number selected at random from the first 50 natural numbers is a composite number is?
(A) 11/15
(B) 13/15
(C) 17/25
(D) 25/17
(E) 11/25
Rationale: Explanation:
The number of exhaustive events = ⁵⁰C₁ = 50.
We have 15 primes from 1 to 50.
Number of favorable cases are 34.
Required probability = 34/50 = 17/25
C
Answer: (C) 17/25
Question: Walking with 4/5 of my usual speed, I arrive at the bus stop 9 minutes later than normal. How many minutes does it take to walk to the bus stop at my usual speed?
(A) 24
(B) 28
(C) 32
(D) 36
(E) 40
Rationale: Let t = usual time = distance / usual speed
t + 9 = distance / (4* usual speed/5) = (5 * distance) / (4 * usual speed) = 5t/4
t = 36
The answer is D.
Answer: (D) 36
Question: A fair sided die labeled 1 to 6 is tossed three times. What is the probability the sum of the 3 throws is 16?
(A) 1/6
(B) 7/216
(C) 1/36
(D) 9/216
(E) 11/216
Rationale: the total number of possible outcomes is, of course, 6^3.
Fortunately, there are only two combinations of three dice throws that will give you a sum of 16:
5, 5, 6
4, 6, 6
(I have a hard time remembering a real GMAT question that would give you 12, as the number of potential combinations is indeed inordinately large and difficult to map out.)
However, our denominator counts out the number of throwing sequences (permutations) and not just combinations, so we will need to do the same. Effectively there are three throwing sequences for either combination:
6, 5, 5
5, 6, 5
5, 5, 6
4, 6, 6
6, 4, 6
6, 6, 4
So 6 throwing sequences we want divided by 6^3 throwing sequences we could get gives us 1/(6^2) or 1/36.
ANSWER:C
Answer: (C) 1/36
Question: Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
(A) Rs.190
(B) Rs.180
(C) Rs.220
(D) Rs.230
(E) Rs.250
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 550
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 550
⇒ y[12/10 + 1] = 550
⇒ 22y/10 = 550
⇒ 22y = 5500
⇒ y = 5500/22 = 500/2 = Rs.250
E)
Answer: (E) Rs.250
Question: Two trains start from A & B and travel towards each other at
speed of 60kmph and 70kmph resp. At the time of the meeting the
second train has traveled 200km more than the first.the distance
between them.
(A) 2200 km
(B) 2400 km
(C) 2600 km
(D) 2800 km
(E) 3000 km
Rationale: Let the distance traveled by the first train be x km
then distance covered by the second train is x + 200km
x/60 = x+200 / 70
x= 1200
so the distance between A & B is x + x + 200 = 2600 km
Answer is C.
Answer: (C) 2600 km
Question: A shopkeeper bought 600 oranges and 400 bananas. He found 15% of oranges and 6% of bananas were rotten. Find the percentage of fruits in good condition?
(A) 92.5%
(B) 88.6%
(C) 85.2%
(D) 96.8%
(E) 78.9%
Rationale: Total number of fruits shopkeeper bought = 600 + 400 = 1000
Number of rotten oranges = 15% of 600
= 15/100 × 600
= 9000/100
= 90
Number of rotten bananas = 6% of 400
= 24
Therefore, total number of rotten fruits = 90 + 24= 114
Therefore Number of fruits in good condition = 1000 - 114 = 886
Therefore Percentage of fruits in good condition = (886/1000 × 100)%
= (88600/1000)%
= 88.6%
Answer:B
Answer: (B) 88.6%
Question: The average weight of 8 persons increases by 1.5 kg. If a person weighing 65 kg is replaced by a new person, what could be the weight of the new person?
(A) 76 kg
(B) 77 kg
(C) 76.5 kg
(D) Data inadequate
(E) None of these
Rationale: total weight increases = 8 × 1.5 = 12 kg
so the weight of new person = 65 + 12 = 77 kg
Answer B
Answer: (B) 77 kg
Question: There are two numbers. If 10% of the first number is added to the second number, then the second number increases to its five-fourth. What is the ratio of the first number to the second number?
(A) 3 : 2
(B) 2 : 7
(C) 8 : 5
(D) 5 : 2
(E) 6 : 5
Rationale: Let the two numbers be x and y.
(1/10) * x + y = (5/4) * y
(1/10) * x = (1/4) * y
x/y = 10/4 = 5/2
The answer is D.
Answer: (D) 5 : 2
Question: If two typists can type two pages in two minutes, how many typists will it take to type 72 pages in nine minutes?
(A) 3
(B) 4
(C) 6
(D) 16
(E) 36
Rationale: In 2 minutes 2 typists type 2 pages which means that in 9 minutes they will type 9 pages but to type 72 pages (8 times) we need 8 times more typists i.e. 2 x 8 = 16 typists.
D
Answer: (D) 16
Question: A grocery store bought some mangoes at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of 9 for a dollar. What was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes?
(A) 1:4
(B) 1:5
(C) 3:2
(D) 1:2
(E) 2:5
Rationale: The cost price of a mango = 1/5 dollars.
The selling price of a mango from the first stack = 1/3 dollars --> the profit from one mango = 1/3 - 1/5 = 2/15 = 4/30 dollars.
The selling price of a mango from the second stack = 1/9 dollars --> the loss from one mango = 1/5 - 1/9 = 4/45 dollars.
The profit from one mango from the first stack is 4 times the loss from one mango from the second stack.
the ratio is 4/30*45/4 =3:2
C
Answer: (C) 3:2
Question: Find the odd man out.
2, 5, 10, 17, 26, 37, 50, 64
(A) 33
(B) 38
(C) 27
(D) 64
(E) 20
Rationale: Explanation:
(1*1)+1 , (2*2)+1 , (3*3)+1 , (4*4)+1 , (5*5)+1 , (6*6)+1 , (7*7)+1 , (8*8)+1
But, 64 is out of pattern.
Answer: D) 64
Answer: (D) 64
Question: (35423+7164+41720)-(317x89)=?
(A) 28213
(B) 84307
(C) 50694
(D) 54094
(E) None of them
Rationale: =(84307)-317x89
=84307-(317x(90-1))
=84307-(317x90-317)
=84307-28213
=54094
Answer is D
Answer: (D) 54094
Question: Jane and Ashley take 8 days and 40 days respectively to complete a project when they work on it alone. They thought if they worked on the project together, they would take fewer days to complete it. During the period that they were working together, Jane took an eight day leave from work. This led to Jane's working for four extra days on her own to complete the project. How long did it take to finish the project ?
(A) 14 Days
(B) 15 Days
(C) 16 Days
(D) 18 Days
(E) 20 Days
Rationale: Let us assume that the work is laying 40 bricks.
Jane = 5 bricks per day
Ashley = 1 brick per day
Together = 6 bricks per day
Let's say first 8 days Ashley works alone,
No of bricks = 8
Last 4 days Jane works alone,
No. of bricks = 20
Remaining bricks = 40 - 28= 12
So together, they would take 12/6 =2
Total no. of days = 8 + 4 + 2 = 14
Answer is A
Answer: (A) 14 Days
Question: Today is Sunday. The day after 59 days will be
(A) Monday
(B) Wednesday
(C) Saturday
(D) Sunday
(E) None of these
Rationale: Explanation :
59 days = 8 weeks 3 days = 3 odd days
Hence if today is Sunday, After 59 days, it will be = (Sunday + 3 odd days)
= Wednesday. Answer : Option B
Answer: (B) Wednesday
Question: A can finish a piece of work in 4 days. B can do it in 14 days. They work together for two days and then A goes away. In how many days will B finish the work?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 2/4 + (2 + x)/14 = 1 => x = 5 days
Answer: B
Answer: (B) 5
Question: In how many words can be formed by using all letters of the word BHOPAL
(A) 420
(B) 520
(C) 620
(D) 720
(E) None of these
Rationale: Explanation:
Required number
=6!=6∗5∗4∗3∗2∗1=720
Option D
Answer: (D) 720
Question: If,
1 * 3 * 5 = 16
3 * 5 * 7 = 38
Then find,
5 * 7 * 8 =?
(A) 65
(B) 68
(C) 61
(D) 80
(E) 77
Rationale: (8 * 7) + 5 = 61
C
Answer: (C) 61
Question: A and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.35000, find their shares?
(A) s.14000, Rs.15020
(B) s.14000, Rs.15700
(C) s.10000, Rs.21090
(D) s.10000, Rs.21000
(E) s.14000, Rs.21000
Rationale: The ratio of their profits A:B
= 8:12 = 2:3
Share of A in the total profit
= 2/5 * 35000
= Rs.14000 Share of A in the total profit = 3/5 * 35000
= Rs.21000
Answer: E
Answer: (E) s.14000, Rs.21000
Question: What are the last two digits of (301*402*502*604*646*547*448*349)^2
(A)  96
(B)  76
(C)  56
(D)  36
(E)  16
Rationale: ((301*402*502*604*646)*(547*448*349))^2
If you observe above digits, last digit are: 1,2,2,4,6,7,8,9; 3&5 are missing; so I have rearranged them so that multiplication will be easy for me as initial 4 digits have last two digits as 01,02,02,04,46 and final three as 47*48*49.
Solving for only last two digits and multiplying them we get:( (04*04*46)(56*49))^2 = (36*44)^2=84^2=56
Hence answer is C
Answer: (C)  56
Question: If x ≠ 0 and (y^2 − xy)/x=y-x, which of the following expressions is equal to its opposite?
(A) x^2
(B) x^2 – y^2
(C) y^2
(D) (y + x)^2
(E) (x – y)^2
Rationale: (y^2 − xy)/x=y-x
=> y^2 − xy = xy -x^2
=> x^2 - 2xy + y^2 = 0
=> (x-y)^2 = 0
Answer E
Answer: (E) (x – y)^2
Question: If x and y are positive integers, and x^3*y^4 = 432, which of the following is the value of xy?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: 432 = 2^4*3^3
xy = 2*3 = 6
The answer is C.
Answer: (C) 6
Question: What is remainder of the division (1125*1127*1129)/12?
(A) 0
(B) 3
(C) 1
(D) 2
(E) 4
Rationale: remainder will be number/ 100 here as the divisor is two digit number = 12.
hence checking for the last two digits = 5*7*9 = 15
Thus remainder = 3.
Answer : B
Answer: (B) 3
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 10 years ago was 20 years. The present age of the husband is:
(A) 20 years
(B) 34 years
(C) 60 years
(D) 30 years
(E) 35 years
Rationale: D
30 years
Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.
Sum of the present ages of wife and child = (20 x 2 + 10 x 2) years = 60 years.
Husband's present age = (90 - 60) years = 30 years.
Answer: (D) 30 years
Question: James Horner is having two coins in his hand. Out of the two coins, one is a real coin and the second one is a faulty one with Tales on both sides. He blind folds himself choose a random coin and tosses it in the air. The coin falls down with Tale facing upwards.
What is the probability that this is the faulty coin?
(A) 3/6
(B) 2/3
(C) 1/3
(D) 3/5
(E) 1/8
Rationale: B
2/3
While tossing the coins in this case only two cases are favorable:
1) A1 (H) A2 (H)
2) A2 (H) A1 (H)
3) B1 (H) B2 (T)
4) B2 (T) B1 (H)
Since the fourth case is not feasible, the probability is 2/3.
Answer: (B) 2/3
Question: Find the compound interest on $30000 in 2years at 4% per annum, the interest being compounded half-yearly?
(A) $645.56
(B) $824.32
(C) $954.26
(D) $2472.96
(E) $1020.45
Rationale: Principle = $10000
Rate = 2% half yearly = 4 half years
Amount = 30000*(1 + 2/100)^4 = 30000 * 51/50 * 51/50 * 51/50 * 51/50
= $32472.96
C.I. = 32472.96-10000 = $2472.96
Answer is D
Answer: (D) $2472.96
Question: An investor bought two shares of stock, which he sold for $36 each. If he had a profit of 20% on one of the shares and a loss of 20% on the other share, then on the sale of both shares combined, the investor had:
(A) a profit of $5
(B) a profit of $3
(C) a loss of $3
(D) a loss of $5
(E) neither a profit nor a loss
Rationale: The cost of the first stock was 36/1.2=30, so the profit from it is 6.
The cost of the second stock was 36/0.8=45, so loss from it is 9.
Overall the loss is $3.
The answer is C.
Answer: (C) a loss of $3
Question: An engineer undertakes a project to build a road 15 km long in 300 days and employs 35 men for the purpose. After 100 days, he finds only 2.5 km of the road has been completed. Find the (approximate) number of extra men he must employ to finish the work in time.
(A) a. 43
(B) b. 53
(C) c. 55
(D) d. 68
(E) e. 60
Rationale: 35 workers working already
Let x be the total men required to finish the task in next 200 days
2.5 km done hence remaining is 12.5 km
Also, work has to be completed in next 200 days (300 - 100 = 200)
We know that, proportion of men to distance is direct proportion
and, proportion of men to days is inverse proportion
Hence, X = (35 * 12.5 * 100) / (2.5 * 200)
thus, X = 87.5 that is approximately 88
Thus, more men needed to finish the task = 88-35=53
hence Answer is B
Answer: (B) b. 53
Question: In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole?
(A) 33
(B) 787
(C) 18
(D) 10
(E) 87
Rationale: Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps.
The distance to be covered is equal to the length of the train.
Required time t = d/s = 100/10 = 10 sec.
Answer:D
Answer: (D) 10
Question: Find the value of (19 + 43/151) × 151
(A) 2924
(B) 2916
(C) 2614
(D) 2912
(E) 2215
Rationale: =(19 + 43/151) × 151
=(2869+ 43)/151× 151
=2912/151× 151
=2912
Answer is D.
Answer: (D) 2912
Question: What is the probability that a 4 person committee chosen at random from a group consisting of 3 men, 7 women, and 5 children contains exactly 1 woman?
(A) 56/195
(B) 77/832
(C) 11/77
(D) 308/1411
(E) 22/832
Rationale: Total possible selections = 4 out of 15 group members = 15C4
Favorable selections = 1 out of 7 women and 3 out of 8 (= 3 men + 5 children) = 7C1 * 8C3
Thus the required probability = 7C1*8C3 / 15C4 = 56/195. Thus A is the correct answer.
Answer: (A) 56/195
Question: What decimal fraction is 90 ml of a litre ?
(A) .9
(B) .009
(C) .09
(D) 0.09
(E) None of these
Rationale: Answer
Required fraction = 90/1000
= 9/100
= .09
Correct Option: C
Answer: (C) .09
Question: A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 99 feet, and the sum of the lengths of the painted sides is 3737 feet, find out the area of the parking space in square feet?
(A) 126 sq. ft
(B) 64 sq. ft.
(C) 100 sq. ft.
(D) 102 sq. ft.
(E) 120 sq. ft.
Rationale: Explanation:
length =9 feet
breadth =37−9/2=14feet
Area =9×14=126 square feet
Answer: Option A
Answer: (A) 126 sq. ft
Question: The graphs of the two equations y = a x 2 + b x + c and y = A x 2 + B x + C, such that a and A have different signs and that the quantities b 2 - 4 a c and B 2 - 4 A C are both negative,
(A) intersect at two points
(B) intersect at one point
(C) do not intersect
(D) none of the above
(E) Cannot be determined
Rationale: Solution
Since a and A have different signs the graphs of the two equations are parabolas opening in diffent directions: If one opens up the other opens down. Also since b 2 - 4 a c and B 2 - 4 A C are both negative, none of the parabola cuts the x axis. This means that each one of these parabolas is either above the x axis or below the x axis and therefore do not intersect.
Answer C
Answer: (C) do not intersect
Question: A train running at the speed of 60 km/hr crosses a pole in 3 seconds. Find the length of the train.
(A) 60
(B) 50
(C) 75
(D) 100
(E) 120
Rationale: :
Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 3 = 50 meter
Answer:B
Answer: (B) 50
Question: Steve traveled the first 2 hours of his journey at 40 mph and the last 3 hours of his journey at 100 mph. What is his average speed of travel for the entire journey?
(A) 60 mph
(B) 56.67 mph
(C) 53.33 mph
(D) 64 mph
(E) 76 mph
Rationale: Answer
Average speed of travel = Total distance travelled/Total time taken
Total distance traveled by Steve = Distance covered in the first 2 hours + distance covered in the next 3 hours.
Distance covered in the first 2 hours = speed * time = 40 * 2 = 80 miles.
Distance covered in the next 3 hours = speed * time = 100 * 3 = 300 miles.
Therefore, total distance covered = 80 + 300 = 380 miles.
Total time taken = 2 + 3 = 5 hours.
Hence, average speed = Total distance travelled/Total time taken=380/5 = 76 miles per hour.
Choice E
Answer: (E) 76 mph
Question: A man can row downstream at 26 kmph and upstream at 22 kmph. Find the speed of the man in still water and the speed of stream respectively?
(A) 24, 2
(B) 12, 6
(C) 15, 3
(D) 14, 4
(E) None of these
Rationale: Explanation:
Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 26 --- (1)
and x - y = 22 --- (2)
From (1) & (2) 2x = 48 => x = 24, y = 2.
Answer: Option A
Answer: (A) 24, 2
Question: Two dogsled teams raced across a 400-mile course in Alaska. Team A finished the course in 4 fewer hours than team B. If team A’s average speed was 5 miles per hour greater than that of team B, what was team B’s average speed, in miles per hour?
(A) 12
(B) 15
(C) 18
(D) 20
(E) 25
Rationale: Let v be team B's average speed.
Time = Distance/Rate and the time difference was 4 hours.
400/v - 400/(v+5)= 4
400v + 2000 - 400v = 4(v)(v+5)
500 = (v)(v+5)
(20)(25) = (v)(v+5)
v = 20 mph
The answer is D.
Answer: (D) 20
Question: If 10! - 2*(5!)^2 is divisible by 10^n, what is the greatest value of n?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: =10∗9∗8∗7∗6∗5!−2∗5!∗5∗4∗3∗2∗1
=5!∗10∗3∗8(125)
=5∗(2∗2)∗3∗2∗(5∗2)∗24∗5∗5∗5
=5∗2∗5∗2∗5∗2∗5∗2∗24∗5∗3
=10^4∗2^4∗5∗3
=10^4∗5∗2∗12∗3
=10^5∗36
Answer: E
Answer: (E) 5
Question: The tens digit of a two-digit number is two more than its unit digit. The two-digit number is 7 times the sum of the digits. Find the units digits?
(A) 1
(B) 2 digits
(C) 3
(D) 4
(E) 5
Rationale: Let the two-digit number be 10a + b
a = b + 2 --- (1)
10a + b = 7(a + b) => a = 2b
Substituting a =
2b in equation (1), we get
2b = b + 2 => b = 2
Hence the units digit is: 2.
ANSWER:B
Answer: (B) 2 digits