MU-NLPC/Calc-aqua_rat huggingface dataset:
6 is the remainder when a certain positive integer is divided by 8. If the said integer is divided by 10, you have a remainder of 4. What will be leftover if the integer is divide by 50?
Choose the correct answer:	A) 0	B) 6	C) Between 10 and15, inclusive	D) 20	E) Between 1 and 5, inclusive

Solution: Let the integer be n   8n+6= 10nx+4   Start 8n+6 -->14, 22, 30,38,46,54...   Of these only 54 fit the description 10nx+4. The remainder when divided by 50 is 4. So answer is E).   Answer = Between 1 and 5, inclusive)
Answer: E
In a 200 meters race A beats B by 56 m or 7 seconds. A's time over the course is:  Choose the correct choice from the following options
A) 22 seconds
B) 12 seconds
C) 10 seconds
D) 18 seconds
E) 28 seconds

Solution: B runs 56 m in 7 sec.   => B runs 200 m in 7/56*200= 
7/56*200 = 25
25 seconds   Since A beats B by 7 seconds, A runs 200 m in (25-7)= 
(25-7) = 18
18 seconds   Hence, A's time over the course= 18 seconds   ANSWER:18 seconds
Answer: D
A committee of 5 people is to be selected from 9 people. How many different committees are possible?
Select
A) 28
B) 40
C) 56
D) 129
E) 336

Solution: Because the order does not matter in selecting 5 people for the committee, this is a combination question.   The number of ways to select 5 people from 9 = 9C5 = 9!/5!*4! = 129. Hence 129.
Answer: D
Okeydokey paid 5 apples at the Apple Investment Booth for an unopened box of earthworms. Artichokey paid 7 apples towards the same lot. The booth pays off earthworms proportional to the apples invested. The box turned out to contain 60 earthworms. How many of them should Okeydokey receive?
Answers:  A) 25  B) 27  C) 28  D) 29  E) 30

Solution: I1 = 5   I2 = 7   I1 share 5 parts & I2 share 7 parts   Total 12 parts -----> 60   ----> 1 part -------> 5   I1 share = 5 parts -----> 25   25
Answer: A
In the faculty of Reverse-Engineering, 226 second year students study numeric methods, 423 second year students study automatic control of airborne vehicles and 134 second year students study them both. How many students are there in the faculty if the second year students are approximately 60% of the total?	Pick one:
A) 858.	B) 545.	C) 618.	D) 644.	E) 666.

Solution: Answer is A :858   Solution : Total number of students studying both are 423 + 226 - 134= 
423 + 226 - 134 = 515
515 (Subtracting the 134 since they were included in the both the other numbers already).   So 60% of total is 515, so 100% is approx. 858.
Answer: A
10 : 4 seconds :: ? : 6 minutes Answers:
A) 10
B) 15
C) 20
D) 25
E) 30

Solution: 10*6=4*x   x=15   ANSWER:15
Answer: B
If x is an integer and y = 4x + 4, which of the following CANNOT be a divisor of y? Choose the correct choice from the following choices:
A) 6 B) 5 C) 4 D) 7 E) 8

Solution: For any value of x, the expression 4x + 4 would never be divisible by 3,6,9...... onwards   So answer = 6 = 6
Answer: A
Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?  Choose the correct choice from the following answers:
A) 27
B) 29
C) 36
D) 29
E) 62

Solution: Let the speed of each train be x m/sec.   Then, relative speed of the two trains = 2x m/sec.   So, 2x = (120 + 120)/12 => x = 10   Speed of each train = 10 m/sec.   = 10 * 18/5 =- 36 km/hr.   Answer:36
Answer: C
In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together  Choose the correct choice from the following answers:  A) 233  B) 3787  C) 720  D) 238  E) 271

Solution: Explanation:   The word 'OPTICAL' contains 7 different letters.   When the vowels OIA are always together, they can be supposed to form one letter.   Then, we have to arrange the letters PTCL (OIA).   Now, 5 letters can be arranged in 5! = 120 ways.   The vowels (OIA) can be arranged among themselves in 3! = 6 ways.   Required number of ways = (120 x 6) = 720.   Answer: 720) 720
Answer: C
If x = - |x| , then which one of the following statements could be true?
I. x = 0
II. x < 1
III. x > 0
Choices
A) None	B) I only	C) III only	D) I and II	E) II and III

Solution: Answer copied from NOVA guide   Statement I could be true because ± 0 = −(+0) = −(0) = 0 .   Statement II could be false because 1/2= −(+1/2)=−1/2   Now, if one side of an equation is always negative, then the other side must always be negative,   otherwise the opposite sides of the equation would not be equal.   Since Statement III is the opposite of Statement II, it must be false. But let’s show this explicitly:   Suppose x were positive. Then x = x, and the equation x = ± x becomes x = –x. Dividing both sides of this equation by x yields 1 = –1. This is contradiction.   Hence, x cannot be positive. The answer is (I only).
Answer: B
A and B together can 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?
Choose the correct choice from the following answers:
A) 6 days B) 7 days C) 8 days D) 9 days E) 10 days

Solution: Sol. (A + B)'s 1 day's work = (1/4). A's 1 day's work = (1/12).   B's 1 day's work =((1/4)-(1/12))=(1/6)   Hence, B alone can complete the work in 6 days.   Option 6 days
Answer: A
Given that f(1) = 1 and f(2) = 1. If f(n) = f(n+1) - f(n - 1), then find the value of f(8)−f(7)+f(5)f(7)−f(6)−f(4)
Answers:
A) 13/2
B) 13/9
C) 13/1
D) 13/6
E) 13/4

Solution: f(n) = f(n+1) - f(n - 1)   ⇒⇒ f(n - 1) = f(n + 1) = f(1)   f(8) - f(7) = f(6) and f(7) - f(6) = f(5)   ⇒⇒f(n + 1) = f(n) + f(n - 1)   ⇒⇒f(3) = f(2) + f(1) = 1 + 1= 
1 + 1 = 2
2   ⇒⇒f(4)= f(3) + f(2) = 2 + 1= 
2 + 1 = 3
3   ⇒⇒f(5)= f(4) + f(3) = 3 + 2= 
3 + 2 = 5
5   ⇒⇒ f(6)= f(5) + f(4) = 5 + 3= 
5 + 3 = 8
8   f(8)−f(7)+f(5)f(7)−f(6)−f(4)=f(6)+f(5)f(5)−f(4)=8+55−3=13/2   13/2nswer:13/2
Answer: A
Three candidates contested an election and received 1136, 7636 and 16000 votes respectively. What percentage of the total votes did the winning candidate get?
Choose the correct choice from the following options:
A) 46%  B) 66%  C) 74%  D) 63%  E) 68%

Solution: 66%   16000/(1136 + 7636 + 16000) = 66%.
Answer: B
A student chose a number, multiplied it by 2, then subtracted 148 from the result and got 110. What was the number he chose? Answers
A) 90 B) 129 C) 120 D) 160 E) 200

Solution: Solution:   Let x be the number he chose, then   2*x*148=110   2x=258   x=129   correct answer 129
Answer: B
In a local election, 2400 people were to vote for Party A or Party B. Party A was bound to win the election. However, on Election Day, 33% of the voters of Party A were kidnapped. Party B was also able to influence the remaining Party A voters and thus double the strength of its voters. In this way, Party A lost by a majority which was half of that by which it would have won had the elections been fair. How many people finally voted for Party A and Party B?	Choose the most appropriate option
A) 600(A), 1200(B)	B) 300(A), 600(B)	C) 450(A), 900(B)	D) 600(A), 900(B)	E) None of these

Solution: DETAILED SOLUTION   Easiest way to solve this question is through options:   a) If 600 voted for A and 1200 voted for B then   Before influencing, A –   600 + 600= 
  600 + 600 = 1_200
1200, B – 1200 – 600= 600(As half of B’s vote were through influencing)   Before kidnapping, A – 1200 + a∗12 of 1200 = 1800 (As 1/3 of A’s voters were kidnapped which is half of the 2/3 that remained)   Thus, total voter initially = 1800 (A) + 600 (B) = 2400   Thus option a) fits the scenario given in the question completely.   Therefore,   600(, 1200(B)nswer – (a)   Correct 600(, 1200(B)nswer:600(, 1200(B)
Answer: A
Three friends had dinner at a restaurant. When the bill was received, Akshitha paid 3/4 as much as Veena paid and Veena paid 1/2 as much as Lasya paid. What fraction of the bill did Veena pay ? Choose the correct option:  A) 4/15  B) 3/12  C) 3/11  D) 3/10  E) 3/14

Solution: Let Veena paid x,   so Akshitha paid 3x/4 , and Lasya paid 2x,   So total bill paid is given by   x+(3x/4) +2x = 1, we get   i.e. x = 4/15   4/15nswer: 4/15
Answer: A
In a apartment, 10% of the people speak English, 20% speak Hindi and 30% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?	Choose the most appropriate option.
A) 1/3  B) 2/3  C) 2/5  D) 2/7  E) 1/10

Solution: P (1/10) = 10 / 100 = 3 / 10 , P (H) = 30 / 100 = 3 / 10 and P (1/10 âˆ© H) = 30 / 100 = 3 / 10   P (1/10 or H) = P (1/10 U H)   = P (1/10) + P (H) - P (1/10 âˆ© H)   = (1 / 10) + (3 / 10) - (3 / 10) = 4 / 10 = 1/10   1/10
Answer: E
Of 1000 surveyed students, 20% of those who read book A also read book B and 25% of those who read book B also read book A. If each student read at least one of the books, what is the difference between the number of students who read only book A and the number of students who read only book B?	Choose the correct choice from the following answers.
A) 120  B) 125  C) 130  D) 145  E) 155

Solution: Say the number of students who read book A is A and the number of students who read book B is B.   Given that 20% of those who read book A also read book B and 25% of those who read book B also read book A, so the number of students who read both books is 0.2A=0.25B --> A=1.25B.   Since each student read at least one of the books then {total}={A}+{B}-{Both} --> 1000=1.25B+B-0.25B --> B=500, A=1.25B=625 and {Both}=0.25B=125.   The number of students who read only book A is {A}-{Both}=625-125= 
625-125 = 500
500;   The number of students who read only book B is {B}-{Both}=500-125= 
500-125 = 375
375   The difference is 500-375= 
500-375 = 125
125.   Answer: 125.
Answer: B
The remainder of the division of a number by 63 is 27. What will be the remainder when that number is divided by 9?
Please explain
Choose the correct answer:  A) 4  B) 5  C) 0  D) 7  E) 8

Solution: The easiest way to solve this question is by plugging in a number. Here are the steps I followed:   1) Choose a number X that when divided by 63 gives you 27 as a remainder. So I did x = 63 + 27= 
63 + 27 = 90
90. (90/63= 1R27)   2) Divide that number by 9. 90/9 = 10R0   Since the remainder is 0, the correct answer is choice 0.
Answer: C
There is a 75% chance that Tigers will not win at all during the whole season. There is a 25% chance that Germany will not play at all in the whole season. What is the greatest possible probability that the Tigers will win and Germany will play during the season?	Select the correct option: A) 55% B) 60% C) 70% D) 75% E) 80%

Solution: There is a 75% chance that Tigers will not win at all during the whole season   We can infer that there is 25% chance Tigers will win .   Similarly There is a 25% chance that Germany will not play at all in the whole season   We can also infer that there is 75% chance that Germany will play.   Answer 75%
Answer: D
If x is three times larger than n , and if 2n+3 is 20% of 25, what is the value of ?  Choose the correct option:  A) 1  B) 2  C) 3  D) 6  E) 12

Solution: Then the wordings of question are misleading. Moreover, it'd also be a bad way to convey x=4n, if it really wanted to convey so.   From other questions that I have seen, proper wordings could be:   If x is three times as large as n   OR simply,   If x is three times n.3
Answer: C
f(x) is a function such that f(x) + 3f(8 - x) = x for all real numbers x. Find the value of f(2). Select the correct option:
A) 5
B) 4
C) 3
D) 2
E) 1

Solution: f(x) + 3f(8 - x) = x : given   f(2) + 3f(6) = 2 : x = 2 above   f(6) + 3f(2) = 6 : x = 6 above   f(6) = 6 - 3f(2) : solve equation C for f(6)   f(2) + 3(6 - 3f(2)) = 2 : substitute   f(2) = 2 : solve above equation.   correct answer is 2) 2
Answer: D
If x and y are integers such that x^2-2x+2y+3=2x^2-3x+y+1, we can deduce that y is	Choose the correct choice from the following answers
A) not an even
B) an even
C) a perfect square
D) an odd
E) a prime

Solution: x^2 - 2x + 2y + 3 = 2x^2 - 3x + y + 1   y = x^2 - x - 2   y = (x-2)(x+1) (Note that one factor is even and one factor is odd.)   Then y must be even.   The answer is an even.
Answer: B
If n = 2lk, where l and k are distinct prime numbers greater than 2, how many different positive even divisors does n have, including n ?	Select the correct option.
A) Two
B) Three
C) Four
D) Six
E) Eight

Solution: Answer - 'C' - Four.   For a number 2lk with primes lk,there will be four even divisors - 2,2*l,2*k,2*l*k
Answer: C
Beginning in Town A, Biker Bob rides his bike 10 miles west, 5 miles north, 5 miles east, and then 15 miles north, to Town B. How far apart are Town A and Town B? (Ignore the curvature of the earth.)  Choose the correct choice from the following choices.
A) 22 miles
B) 20.62 miles
C) 25 miles
D) 26 miles
E) 28 miles

Solution: Using Pythagoras we have one side i,e total distance traveled in north direction = 15+5= 
15+5 = 20
20m   other being the base ie distance traveled west- distance traveled eat=10- 5= 
10- 5 = 5
5 m   now this third side or the distance between town A and Town 20.62 miles=20^2+ 5^2=sq root 425=20.62 mile   Answer : 20.62 miles
Answer: B
The average of first five multiples of 8 is :  Answers
A) 3  B) 9  C) 12  D) 15  E) 24

Solution: Solution   Average = 8(1+2+3+4+5)/5 =120/5= 
120/5 = 24
24 Answer 24
Answer: E
A box contains eleven bulbs out of which six are defective. If six bulbs are chosen at random, find the probability that all the six bulbs are defective? Choose the correct choice.
A) 1/450  B) 1/422  C) 1/429  D) 1/136  E) 1/462

Solution: Out of eleven, five are good and six are defective. Required probability   = 6C6/11C6   = 1/462   Answer:1/462
Answer: E
The population of a town is 8000. It decreases annually at the rate of 10% p.a. What will be its population after 3 years?
Select
A) 5100 B) 5120 C) 5200 D) 5400 E) 5832

Solution: Formula :   ( After =100 denominator   Ago = 100 numerator)   8000 Ã— 90/100 Ã— 90/100 x 90/100= 5832   Answer :5832
Answer: E
A man spends 2/5 of his salary on house rent, 3/10 of his salary on food, and 1/8 of his salary on conveyance. if he has Rs 1400 left with him, find his expenditure on food and conveyance
Choose one
A) 3200
B) 3400
C) 3600
D) 3800
E) 4000

Solution: If his salary is x, then   x- x*(2/5 +3/10+1/8) =1400   x(1- 33/40) =1400   x= 1400*40/7= 
1400*40/7 = 8_000
Rs 8000   Expenditure on food and conveyance= 8000*3/10+ 8000*1/8 = 2400+1000= 
2400+1000 = 3_400
3400   ANSWER:3400
Answer: B
If average temperature of june,july and august is 31,and july,august september is 30. find tempearture of september if temperature of june is 29.	Choose the correct choice.
A) 26
B) 27
C) 28
D) 29
E) 30

Solution: june+july+aug=31*3= 
31*3 = 93
93---(i)   july+aug+sep=30*3= 
30*3 = 90
90---(ii)   subtracting (ii) from (i)   june-sep=3   there4 September=29-3= 
29-3 = 26
26   26NSWER:26
Answer: A
If 6111309× 3145208 × K^2 is divisible by 3, which of the following could be the value of K?
Choose the correct choice from the following answers:
A) 30
B) 4
C) 5
D) 66
E) All of these

Solution: The first term divisible by 3, so any term could be the third term.   Answer =(All of these)
Answer: E
A starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business?	Choose the correct choice from the following choices: A) 2400 B) 2677 C) 2168 D) 2669 E) 2668

Solution: 1200 * 12: x * 9 = 2:3   x = 2400   2400nswer: 2400
Answer: A
Mohit sold an article for $15000. Had he offered a discount of 10% on the selling price, he would have earned a profit of 8%. What is the cost price of the article?
Choose the correct option.
A) 12500	B) 25000	C) 15000	D) 18000	E) 17000

Solution: Let the CP be $x.   Had he offered 10% discount, profit = 8%   Profit = 8/100 x and hence his SP = x + 8/100 x = $1.08x = 15000 - 10/100(15000) = 15000 - 1500= 
15000 - 1500 = 13_500
$13500=> 1.08x = 13500   => x = 12500   12500
Answer: A
P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?  Choose the correct option
A) 5 5/11	B) 5 6/11	C) 6 5/11	D) 6 6/11	E) 5 4/11

Solution: P can complete the work in (12 x 8) hrs. = 96 hrs.   Q can complete the work in (8 x 10) hrs. = 80 hrs.   Work done by P's per hour =1/96   Work done by Q's per hour =1/80   P and Q work together per hour=1/96 + 1/80=11/480   Both P and Q will finish the work in 480/11 hrs   Number of days of 8 hours each =480/11 x 1/8=60/11 days=5 5/11 days   5 5/11
Answer: A
In a certain neighborhood, there are half as many beige houses as white houses, and 7 times as many white houses as brown houses. What is the ratio of the number of brown houses to the number of beige houses?	Pick one:  A) 3:5  B) 1:4  C) 3:1  D) 2:7  E) 5:2

Solution: The ratio of beige:white:brown = 7:14:2   The answer is 2:7.
Answer: D
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
Choose the correct choice from the following answers:	A) 22	B) 24	C) 26	D) 20	E) 18

Solution: Let number of hens =h   number of cows =c   Number of heads =48   ⇒h+c=48 ⋯(1)   Number of feet =140   ⇒2h+4c=140   ⇒h+2c=70 ⋯(2)   (2)−(1) gives   2c−c=70−48   ⇒c=22   Substituting the value of c in (1), we get   h+22=48   ⇒h=48−22=26   h+22=48⇒h=48−22=26   i.e., number of hens =26   Answer: 26
Answer: C
Two years ago, Sam put $1,000 into a savings account. At the end of the first year, his account had accrued $100 in interest bringing his total balance to $1,100. The next year, his account balance increased by 10%. At the end of the two years, by what percent has Sam's account balance increased from his initial deposit of $1,000 ?	Choices:  A) 19%  B) 20%  C) 21%  D) 22%  E) 25%

Solution: investment 1000 dollars   1 st year total gained = 100   total amount end of first year = 1100   second year account increased by 10 % = 1100*0.1= 
1100*0.1 = 110
110   therefore total amount by second year end= 1210   so total percentage increase in money = (1210-1000)*100/1000= 
(1210-1000)*100/1000 = 21
21 %   ANSWER:21%
Answer: C
If the tens digit of positive integers m, y are 6, how many values of the tens digit of 2(m+y) can be there? Choose the correct option.
A) 2 B) 3 C) 4 D) 5 E) 6

Solution: If the tens digit of positive integers m, y are 6, how many values of the tens digit of 2(m+y) can be there?   A. 2   B. 3   C. 4   D. 5   E. 6   -> If m=y=60, 2(m+y)=240 is derived. If m=y=69, 2(m+y)=276 is derived, which makes 4,5,6,7 possible for the tens digit. Therefore, the answer is 4.
Answer: C
A jar contains 3 black, 3 white and 1 green balls. If you pick two balls at the same time, what's the probability that one ball is black and one is white?	Select
A) 2/7
B) 5/7
C) 4/7
D) 3/7
E) 1/2

Solution: P(1st black, 2nd white) = 3/7*3/6 = 9/42;   P(1st white, 2nd black) = 3/7*3/6 = 9/42.   P = 9/42 + 9/42 = 18/42 = 3/7.   Answer: 3/7.
Answer: D
A man buys an article for 12% less than its value and sells it for 12% more than its value. His gain or loss percent is:  Choices
A) no profit, no loss  B) 20% profit  C) less than 25% profit  D) more than 25% profit  E) None

Solution: Let the article be worth Rs. x.   C.P. 88% of Rs. x = Rs. 88x/100   S.P. = 112% of Rs. x = Rs. 112x/100   Gain = (112x/100 - 88x/100) = Rs.6x/25   Gain % = 6x/25 * 100/88x * 100 = 27 3/11 % > 25%   ANSWER:more than 25% profit
Answer: D
If log8 x + log 8 1/6 = 1/3, then the value of x is: Select
A) 12  B) 16  C) 18  D) 24  E) 26

Solution: log8 x + log8 (1/6) = 1/3   => (log x/ log 8) + (log 1/6 / log 8) = log (81/3) = log 2   => log x = log 2 – log 1/6 = log (2*6/1)= 
(2*6/1) = 12
log 12   12NSWER:12
Answer: A
For what value of x between − 6 and 6, inclusive, is the value of x^2 − 10x + 16 the greatest?	Choose the correct choice from the following answers: A) − 6 B) − 2 C) 0 D) 2 E) 6

Solution: we can see from the statement that two terms containing x, x^2 will always be positive and -10x will be positive if x is -ive..   so the equation will have greatest value if x is -ive, and lower the value of x, greater is the equation.   so -6 will give the greatest value..   ans − 6
Answer: A
A man can reach certain place in 50hours. If he reduces his speed by 1/10th, he goes 100km less in time. Find his speed? Choose the correct answer
A) 20km/hr
B) 30km/hr
C) 40km/hr
D) 50km/hr
E) 60km/hr

Solution: Let the speed be x km/hr   50x-50* 9/10 *x = 100   50x - 45x = 100   5x = 100   x = 20km/hr   20km/hrnswer is 20km/hr
Answer: A
In how many years does a sum of Rs. 3000 yield a simple interest of Rs. 12500 at 15% p.a.?
Pick one:
A) 27.7 years	B) 26.7 years	C) 25.7 years	D) 24.7 years	E) 23.7 years

Solution: T = (100 * 12500)/(15 * 3000) = 27.7 years   27.7 yearsNSWER:27.7 years
Answer: A
John and David can finish a job together in 2 hours. If John can do the job by himself in 3 hours, what percent of the job does David do?
Select.
A) 36.33% B) 33.33% C) 39.33% D) 40.33% E) 33%

Solution: You can also plug in numbers. For example, Bob and Alice work at a donut factory and make 18 donuts which is the job ( I picked this as a SMART number).   John on his own works  18/3= 
 18/3 = 6
6 donuts per hour.   John and David work   18/2= 
  18/2 = 9
9 donuts per hour so David works 3 donuts/hour   To find out the percentage, David works 3 donuts/hr x 2 hours= 6 donuts per hour.   Therefore 6 donuts/18donuts = 1/3 = 33.33%   Answer : 33.33%
Answer: B
What is the Compound Interest on Rs.6500 at 5.5% p.a. compounded half-yearly for 1 year.	Choose the correct choice from the following
A) 369.42 B) 762.42 C) 162.42 D) 362.42 E) 333.42

Solution: Compound interest : A = P(1 + r/n)nt   A = 6,862.42   C.I. >> 6,862.42 - 6500 >> Rs. 362.42   Answer:362.42
Answer: D
Plane leaves from Chelsea every 25 minutes from West Ham airport. Air hostess told Frank Lampard that the plane had left 25 minutes ago and the next plane for Chelsea will leave at 7:00 p.m. At what time air hostess convey this information to Frank Lampard?	Choose the correct choice from the following:
A) 5:35 p.m  B) 6:00 p.m  C) 7:00 p.m  D) 8:35 p.m  E) 9:00 p.m

Solution: Explanation:   Time of Frank Lampard last missed plane = 7:00 p.m - 25 min = 6:35 p.m   As this information has been given to Frank Lampard 25 minutes after the plane has already left, the air hostess gave the information at 6:35 p.m + 25 min = 7:00 p.m   Answer 7:00 p.m
Answer: C
By travelling at 40 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?
Select the correct option:
A) 20 kmph B) 24 kmph C) 22 kmph D) 28 kmph E) 29 kmph

Solution: A   20 kmph   Let the time taken to reach the destination be 3x hours. Total distance = 40 * 3= 
40 * 3 = 120
120x km   He covered 2/3 * 120= 
2/3 * 120 = 80
80x km in 1/3 * 3x= x hours So, the remaining 40x km, he has to cover in 2x hours. Required speed = 40x/2x = 20 kmph.40 /2= 
40 /2 = 20
20 kmph.
Answer: A
The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 24,000 is made? Choose one
A) 328897 B) 120000 C) 877888 D) 277768 E) 188871

Solution: The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000   SP such that a profit of Rs. 24,000 is made = 96,000 + 24,000 = Rs. 1,20,000   Answer: 120000
Answer: B
K = wxyz, where w, x, y, z are prime numbers. Not including 1 and K, how many factors does K have?	Pick
A) 7
B) 14
C) 21
D) 28
E) 35

Solution: Suppose w = 2, x = 3, y = 5 and z = 7. Then wxyz = 210.   To find out how many factors 210 has, go through different combinations of the prime factors as follows. You don't even need to calculate the answers but I have done so here:   (factor #1) 2   (factor #2) 3   (factor #3) 5   (factor #4) 7   (factor #5) 2 x 3 = 6   (factor #6) 2 x 5 = 10   (factor #7) 2 x 7 = 14   (factor #8) 2 x 3 x 5= 30   (factor #9) 2 x 3 x 7 = 42   (factor #10) 2 x 5 x 7 = 70   (factor #11) 3 x 5 = 15   (factor #12) 3 x 7 = 21   (factor #13) 3 x 5 x 7 = 105   (factor #14) 5 x 7 = 35   Since we are not including 1 and 210, answer = 14   ANSWER:14
Answer: B