mathewhe/aqua_rat huggingface dataset:
Question: 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?
(A) 0
(B) 6
(C) Between 10 and15, inclusive
(D) 20
(E) Between 1 and 5, inclusive
Rationale: 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 = E)
Answer: (E) Between 1 and 5, inclusive
Question: In a 200 meters race A beats B by 56 m or 7 seconds. A's time over the course is:
(A) 22 seconds
(B) 12 seconds
(C) 10 seconds
(D) 18 seconds
(E) 28 seconds
Rationale: B runs 56 m in 7 sec.
=> B runs 200 m in 7/56*200 = 25 seconds
Since A beats B by 7 seconds, A runs 200 m in (25-7) = 18 seconds
Hence, A's time over the course = 18 seconds
ANSWER:D
Answer: (D) 18 seconds
Question: A committee of 5 people is to be selected from 9 people. How many different committees are possible?
(A) 28
(B) 40
(C) 56
(D) 129
(E) 336
Rationale: 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 D.
Answer: (D) 129
Question: 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?
(A) 25
(B) 27
(C) 28
(D) 29
(E) 30
Rationale: I1 = 5
I2 = 7
I1 share 5 parts & I2 share 7 parts
Total 12 parts -----> 60
----> 1 part -------> 5
I1 share = 5 parts -----> 25
A
Answer: (A) 25
Question: 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?
(A) 858.
(B) 545.
(C) 618.
(D) 644.
(E) 666.
Rationale: Answer is A :858
Solution : Total number of students studying both are 423 + 226 - 134 = 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) 858.
Question: 10 : 4 seconds :: ? : 6 minutes
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
Rationale: 10*6=4*x
x=15
ANSWER:B
Answer: (B) 15
Question: If x is an integer and y = 4x + 4, which of the following CANNOT be a divisor of y?
(A) 6
(B) 5
(C) 4
(D) 7
(E) 8
Rationale: For any value of x, the expression 4x + 4 would never be divisible by 3,6,9...... onwards
So answer = 6 = A
Answer: (A) 6
Question: 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?
(A) 27
(B) 29
(C) 36
(D) 29
(E) 62
Rationale: 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:C
Answer: (C) 36
Question: In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together
(A) 233
(B) 3787
(C) 720
(D) 238
(E) 271
Rationale: 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: C) 720
Answer: (C) 720
Question: If x = - |x| , then which one of the following statements could be true?
I. x = 0
II. x < 1
III. x > 0
(A)  None
(B)  I only
(C)  III only
(D)  I and II
(E)  II and III
Rationale: 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 (B).
Answer: (B)  I only
Question: 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?
(A) 6 days
(B) 7 days
(C) 8 days
(D) 9 days
(E) 10 days
Rationale: 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 A
Answer: (A) 6 days
Question: 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)
(A) 13/2
(B) 13/9
(C) 13/1
(D) 13/6
(E) 13/4
Rationale: 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 = 2
⇒⇒f(4) = f(3) + f(2) = 2 + 1 = 3
⇒⇒f(5) = f(4) + f(3) = 3 + 2 = 5
⇒⇒ f(6) = f(5) + f(4) = 5 + 3 = 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
Answer:A
Answer: (A) 13/2
Question: Three candidates contested an election and received 1136, 7636 and 16000 votes respectively. What percentage of the total votes did the winning candidate get?
(A) 46%
(B) 66%
(C) 74%
(D) 63%
(E) 68%
Rationale: B
16000/(1136 + 7636 + 16000) = 66%.
Answer: (B) 66%
Question: A student chose a number, multiplied it by 2, then subtracted 148 from the result and got 110. What was the number he chose?
(A) 90
(B) 129
(C) 120
(D) 160
(E) 200
Rationale: Solution:
Let x be the number he chose, then
2*x*148=110
2x=258
x=129
correct answer B
Answer: (B) 129
Question: 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?
(A) 600(A), 1200(B)
(B) 300(A), 600(B)
(C) 450(A), 900(B)
(D) 600(A), 900(B)
(E) None of these
Rationale: 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 = 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,
Answer – (a)
Correct Answer:A
Answer: (A) 600(A), 1200(B)
Question: 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 ?
(A) 4/15
(B) 3/12
(C) 3/11
(D) 3/10
(E) 3/14
Rationale: 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
Answer: A
Answer: (A) 4/15
Question: 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?
(A) 1/3
(B) 2/3
(C) 2/5
(D) 2/7
(E) 1/10
Rationale: P (E) = 10 / 100 = 3 / 10 , P (H) = 30 / 100 = 3 / 10 and P (E âˆ© H) = 30 / 100 = 3 / 10
P (E or H) = P (E U H)
= P (E) + P (H) - P (E âˆ© H)
= (1 / 10) + (3 / 10) - (3 / 10) = 4 / 10 = 1/10
E
Answer: (E) 1/10
Question: 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?
(A) 120
(B) 125
(C) 130
(D) 145
(E) 155
Rationale: 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=500;
The number of students who read only book B is {B}-{Both}=500-125=375
The difference is 500-375=125.
Answer: B.
Answer: (B) 125
Question: 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
(A) 4
(B) 5
(C) 0
(D) 7
(E) 8
Rationale: 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 = 90. (90/63 = 1R27)
2) Divide that number by 9. 90/9 = 10R0
Since the remainder is 0, the correct answer is choice C.
Answer: (C) 0
Question: 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?
(A)  55%
(B)  60%
(C)  70%
(D)  75%
(E)  80%
Rationale: 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 D
Answer: (D)  75%
Question: If x = 2, then what is the value of 8x √x3 – x2
(A) 32
(B) 48
(C) 16√2
(D) 90
(E) 60
Rationale: Explanation:
Given: x = 2
8 * 2 √23 – 22
16√8-4
16√4
16 * 2 = 32
ANSWER: A
Answer: (A) 32
Question: If x is three times larger than n , and if 2n+3 is 20% of 25, what is the value of ?
(A) 1
(B) 2
(C) 3
(D) 6
(E) 12
Rationale: 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.C
Answer: (C) 3
Question: f(x) is a function such that f(x) + 3f(8 - x) = x for all real numbers x. Find the value of f(2).
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
Rationale: 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 D) 2
Answer: (D) 2
Question: If x and y are integers such that x^2-2x+2y+3=2x^2-3x+y+1, we can deduce that y is
(A) not an even
(B) an even
(C) a perfect square
(D) an odd
(E) a prime
Rationale: 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 B.
Answer: (B) an even
Question: 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 ?
(A)  Two
(B)  Three
(C)  Four
(D)  Six
(E)  Eight
Rationale: 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)  Four
Question: 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.)
(A) 22 miles
(B) 20.62 miles
(C) 25 miles
(D) 26 miles
(E) 28 miles
Rationale: Using Pythagoras we have one side i,e total distance traveled in north direction = 15+5=20m
other being the base ie distance traveled west- distance traveled eat=10- 5= 5 m
now this third side or the distance between town A and Town B=20^2+ 5^2=sq root 425=20.62 mile
Answer : B
Answer: (B) 20.62 miles
Question: The average of first five multiples of 8 is :
(A) 3
(B) 9
(C) 12
(D) 15
(E) 24
Rationale: Solution
Average = 8(1+2+3+4+5)/5 =120/5 =24 Answer E
Answer: (E) 24
Question: 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?
(A) 1/450
(B) 1/422
(C) 1/429
(D) 1/136
(E) 1/462
Rationale: Out of eleven, five are good and six are defective. Required probability
= 6C6/11C6
= 1/462
Answer:E
Answer: (E) 1/462
Question: 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?
(A) 5100
(B) 5120
(C) 5200
(D) 5400
(E) 5832
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
8000 Ã— 90/100 Ã— 90/100 x 90/100= 5832
Answer :E
Answer: (E) 5832
Question: Evaluate: 11 + sqrt(- 4 + 6×4÷3) =?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: According to order of operations, inner brackets first where 6×4÷3 is first calculated since it has a multiplication and a division.
6×4÷3 = 24÷3 = 8
Hence
11 + sqrt(- 4 + 6×4÷3) = 11 + sqrt(- 4 + 8)
= 11 + sqrt(4) = 11 + 2 = 13
correct answer D)13
Answer: (D) 13
Question: 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
(A) 3200
(B) 3400
(C) 3600
(D) 3800
(E) 4000
Rationale: If his salary is x, then
x- x*(2/5 +3/10+1/8) =1400
x(1- 33/40) =1400
x= 1400*40/7 = Rs 8000
Expenditure on food and conveyance = 8000*3/10+ 8000*1/8 = 2400+1000 = 3400
ANSWER:B
Answer: (B) 3400
Question: 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.
(A) 26
(B) 27
(C) 28
(D) 29
(E) 30
Rationale: june+july+aug=31*3=93---(i)
july+aug+sep=30*3=90---(ii)
subtracting (ii) from (i)
june-sep=3
there4 September=29-3=26
ANSWER:A
Answer: (A) 26
Question: If 6111309× 3145208 × K^2 is divisible by 3, which of the following could be the value of K?
(A) 30
(B) 4
(C) 5
(D) 66
(E) All of these
Rationale: The first term divisible by 3, so any term could be the third term.
Answer =(E)
Answer: (E) All of these
Question: 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?
(A) 2400
(B) 2677
(C) 2168
(D) 2669
(E) 2668
Rationale: 1200 * 12: x * 9 = 2:3
x = 2400
Answer: A
Answer: (A) 2400
Question: 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?
(A) 12500
(B) 25000
(C) 15000
(D) 18000
(E) 17000
Rationale: 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 = $13500
=> 1.08x = 13500
=> x = 12500
A
Answer: (A) 12500
Question: 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?
(A) 5 5/11
(B) 5 6/11
(C) 6 5/11
(D) 6 6/11
(E) 5 4/11
Rationale: 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
A
Answer: (A) 5 5/11
Question: 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?
(A) 3:5
(B) 1:4
(C) 3:1
(D) 2:7
(E) 5:2
Rationale: The ratio of beige:white:brown = 7:14:2
The answer is D.
Answer: (D) 2:7
Question: A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be
(A) 22
(B) 24
(C) 26
(D) 20
(E) 18
Rationale: 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: C
Answer: (C) 26
Question: 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 ?
(A) 19%
(B) 20%
(C) 21%
(D) 22%
(E) 25%
Rationale: 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 = 110
therefore total amount by second year end = 1210
so total percentage increase in money = (1210-1000)*100/1000 = 21 %
ANSWER:C
Answer: (C) 21%
Question: 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
Rationale: 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 C.
Answer: (C) 4
Question: 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?
(A) 2/7
(B) 5/7
(C) 4/7
(D) 3/7
(E) 1/2
Rationale: 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: D.
Answer: (D) 3/7
Question: 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:
(A) no profit, no loss
(B) 20% profit
(C) less than 25% profit
(D) more than 25% profit
(E) None
Rationale: 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:D
Answer: (D) more than 25% profit
Question: If log8 x + log 8 1/6 = 1/3, then the value of x is:
(A) 12
(B) 16
(C) 18
(D) 24
(E) 26
Rationale: 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)= log 12
ANSWER:A
Answer: (A) 12
Question: For what value of x between − 6 and 6, inclusive, is the value of x^2 − 10x + 16 the greatest?
(A) − 6
(B) − 2
(C) 0
(D) 2
(E) 6
Rationale: 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 A
Answer: (A) − 6
Question: 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?
(A) 20km/hr
(B) 30km/hr
(C) 40km/hr
(D) 50km/hr
(E) 60km/hr
Rationale: Let the speed be x km/hr
50x-50* 9/10 *x = 100
50x - 45x = 100
5x = 100
x = 20km/hr
Answer is A
Answer: (A) 20km/hr
Question: In how many years does a sum of Rs. 3000 yield a simple interest of Rs. 12500 at 15% p.a.?
(A) 27.7 years
(B) 26.7 years
(C) 25.7 years
(D) 24.7 years
(E) 23.7 years
Rationale: T = (100 * 12500)/(15 * 3000) = 27.7 years
ANSWER:A
Answer: (A) 27.7 years
Question: 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?
(A) 36.33%
(B) 33.33%
(C) 39.33%
(D) 40.33%
(E) 33%
Rationale: 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 = 6 donuts per hour.
John and David work 18/2 = 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 : B
Answer: (B) 33.33%
Question: What is the Compound Interest on Rs.6500 at 5.5% p.a. compounded half-yearly for 1 year.
(A) 369.42
(B) 762.42
(C) 162.42
(D) 362.42
(E) 333.42
Rationale: Compound interest : A = P(1 + r/n)nt
A = 6,862.42
C.I. >> 6,862.42 - 6500 >> Rs. 362.42
Answer:D
Answer: (D) 362.42
Question: 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?
(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
Rationale: 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 C
Answer: (C) 7:00 p.m
Question: 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?
(A) 20 kmph
(B) 24 kmph
(C) 22 kmph
(D) 28 kmph
(E) 29 kmph
Rationale: A
20 kmph
Let the time taken to reach the destination be 3x hours. Total distance = 40 * 3x = 120x km
He covered 2/3 * 120x = 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.
Answer: (A) 20 kmph
Question: 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?
(A) 328897
(B) 120000
(C) 877888
(D) 277768
(E) 188871
Rationale: 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: B
Answer: (B) 120000
Question: K = wxyz, where w, x, y, z are prime numbers. Not including 1 and K, how many factors does K have?
(A) 7
(B) 14
(C) 21
(D) 28
(E) 35
Rationale: 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:B
Answer: (B) 14
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?
(A) 3/5
(B) 3/2
(C) 3/8
(D) 3/9
(E) 3/1
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2.
Answer: B
Answer: (B) 3/2
Question: A man purchases 8 pens for Rs.9 and sells 9 pens for Rs.8, how much profit or loss does he make?
(A) 20.98
(B) 20.93
(C) 20.95
(D) 20.92
(E) 20.91
Rationale: 81 ---- 17
100 ----- ? è 20.98%los
Answer: A
Answer: (A) 20.98