divelab/Sys2Bench huggingface dataset:
Question: If the positive integer X is divisible by 3, 6, and 12, then which of the following must X be divisible by?
I. 12
II. 35
III. 46
Options:
A)III
B)II only
C)I and II only
D)II and III only
E)I only
Rationale: Answer = E
LCM of 3, 6, 12 = 12
Answer = 12
Answer : E
Answer: E
Question: A monkey ascends a greased pole 22 meters high. He ascends 2 meters in the first minute and then slips down 1 meter in the alternate minute. If this pattern continues until he climbs the pole , in how many minutes would he reach at the top of the pole ?
Options:
A)40th minute
B)41st minute
C)43rd minute
D)42nd minute
E)45th minute
Rationale: The money is climbing 1meter in 2min. This pattern will go on till he reaches 20meters. I mean this will continue for first 20*2=40mins. he would have reached 20meters. After that he will climb 2meters and he will reach the pole. So total time taken = 40 + 1 = 41mins.
So, asnwer will be B
Answer: B
Question: Raghav borrows Rs.2550 to be paid back with compound interest at the rate of 4% per annum by the end of 2 years in two equal yearly instalments. How much will each instalment be ?
Options:
A)Rs.1275
B)Rs.1283
C)Rs.1352
D)Rs.1377
E)Rs.1577
Rationale: Let the value of each instalment be Rs.x.
x/(1+4/100) + x/(1+4/100)2 = 2550 = 25x/26 + 625x/676 = 2550
1275x = 2550 *676
x = (2550*676)/1275 = 1352.
ANSWER:C
Answer: C
Question: If the number 761 * 829 is completely divisible by 9, then the smallest whole number in place of * will b
Options:
A)4
B)5
C)3
D)8
E)9
Rationale: Sum of digits = (7 + 6 + 1 + x + 8 + 2 + 9) = (33 + x), which must be divisible by 9.
x = 3.
C)
Answer: C
Question: b.	Last Night lottery winning numbers followed this pattern: 25, 22, 20, 19, 16, 14, 13, 10, 8, 7, ? What is the last winning number?
Options:
A)6
B)3
C)4
D)5
E)7
Rationale: The sequence progresses -3, -2, -1 repeated; The last winning number is 4.
Ans C = 4
Answer: C
Question: Exactly 3/7 of the people in the room are under the age of 21, and exactly 5/12 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21?
Options:
A)21
B)35
C)36
D)60
E)65
Rationale: The total number of the people in the room must be a multiple of both 7 and 12 (in order 3/7 and 5/12 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 7 and 12, which is 84.
Since, the total number of the people in the room is greater than 50 and less than 100, then there are 84 people in the room.
Therefore there are 3/7*84=36 people in the room under the age of 21.
Answer: C.
Answer: C
Question: The ratio of numbers is 5:6 and their H.C.F is 4. Their L.C.M is:
Options:
A)12
B)16
C)24
D)48
E)120
Rationale: Let the numbers be 5x and 6x.
Then their H.C.F = x. So, x = 4.
So, the numbers are 20 and 24.
L.C.M of 20 and 24 = 120.
ANSWER:E
Answer: E
Question: The number '7' is the prime followed by a cube.
Is there any other number sharing the same quality?
Options:
A)No
B)Yes
C)May be
D)None of above
E)Do know
Rationale: A
No
7 is the only prime followed by a cube.
Assume that n3-1 is a prime for some n.
N3-1 will be equal to (n−1)(n2+n+1)
Now, n-1 divides n3-1.
If n-1>1, then we will have a contradiction to n3-1 being a prime.
Answer: A
Question: A man sells an article at 15% loss. Had he sold it for Rs. 350/- more he could have gained 20%. What is the cost price of the article?
Options:
A)Rs.420/-
B)Rs.400/-
C)Rs.460/-
D)Rs.1000/-
E)None of these
Rationale: Explanation:
Short cut method:
Loss =====> 15 %
Profit ====> 20 %
~
----------------
35 % ---------> Rs. 350/-
100 % --------> Rs. 1000/-
Answer: Option D
Answer: D
Question: If 20 men can build a wall 56 meters long in 6 days , what length of a similar wall can be built by 35 men in 3 days?
Options:
A)44
B)48
C)45
D)47
E)49
Rationale: Let the required length be x meters
More men, More length built (Direct proportion)
Less days, Less length built (Direct Proportion)
Men 20:35 and Days 6:3::56:x
Therefore (20 x 6 x (X))=(35 x 3 x 56)
x=(35x3x56)/120=49
Hence, the required length is 49 m.
Answer is E.
Answer: E
Question: X does a work in 20 days. Y does the same work in 30 days. In how many days they together will do the same work?
Options:
A)10
B)12
C)20
D)30
E)15
Rationale: X's 1day's work= 1/20
Y's 1 day's work=1/30
(X+Y)'s 1day's work= (1/20+1/30)=1/12
both together will finish the work in 12 days.
correct option is B
Answer: B
Question: The average age of a class is 15.8 years. The average age of the boys in the class is 16.4 years and that of the girls is 15.4 years. What is the ratio of boys to girls in the class?
Options:
A)1 : 2
B)3 : 4
C)2 : 3
D)3:2
E)None of these
Rationale: Let number of boys = x ; Let number of girls = y
Total numbers of students = x + y
(x + y) × 15.8 = 16.4x + 15.4y
0.6x = 0.4y
x/y = 0.4/0.6 = 2/3
ANSWER:C
Answer: C
Question: Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 50 years. What will be the age of the B ten years hence?
Options:
A)39
B)23
C)28
D)96
E)100
Rationale: Let the present ages of A, B and C be a, b and c respectively.
Given, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1)
(b + c)/2 = 50 => b + c = 100 --- (2)
Answer: E
Answer: E
Question: What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years?
Options:
A)1 : 3
B)2 : 3
C)1 : 2
D)3 : 2
E)1 : 4
Rationale: Let the principal be P and rate of interest be R%.
Required ratio =
(P x R x 6)/100 DIVIDED BY	(P x R x 9)/100
=	6PR/9PR	=	6/9	= 2 : 3.
ANSWER : B
100
9PR 9
Answer: B
Question: A money lender lends Rs.2000 for six months at 20% p.a. rate. It the interest is reckoned quarterly than find the amount given after time limit?
Options:
A)2205
B)2888
C)2669
D)2770
E)2771
Rationale: A = 2000(21/20)2 = 2205
Answer: A
Answer: A
Question: Taylor is making a bracelet. He Starts with 4 blue knots, 5 red knots, and 2 yellow knots, in that order, and repeats the pattern until there is no more string. If the last Knot is yellow which of the following could be the total number of knots on the bracelet.
Options:
A)87
B)90
C)95
D)97
E)102
Rationale: Repeating sequence = 4 + 5 + 2 = 11.
As the pattern ends in Y this could be the 10th thread or 11 thread (both are yellow)
Out of the answer choices, correct on should be a multiple of 11(since 11 threads are repeating) and if not, multiple of 11 + 10 (since 11 threads are repeating and last sequence end at first yellow)
none of the options is a direct multiple of 11 and only option that is multiple of 11; + 10 is 87 (11*7) + 10
Hence, answer is A
Answer: A
Question: Last year Jackie saved 5% of her annual salary. This year, she made 10% more money than last year, and she saved 8% of her salary. The amount saved this year was what percent of the amount she saved last year?
Options:
A)56%
B)76%
C)158%
D)176%
E)188%
Rationale: Assuming Annual salary of last year = 100
5 % Salary Saving (last year) would give = (5/100) * 100 = 5
she made 10% more money than last year = 110 (This year Salary)
8 % Salary saving this year = (8/100) * 110 = 88/10 = 8.8
(Amount saved this year/Amount saved last year) * 100= (8.8/5) * 100 = 8.8 * 20 = 176 %
ANSWER:D
Answer: D
Question: Using all the letters of the word "BUTTON", how many words can be formed, which begin with B and end with N?
Options:
A)9
B)24
C)7
D)5
E)3
Rationale: There are five letters in the given word.
Consider 6 blanks ....
The first blank and last blank must be filled with B and N all the remaining three blanks can be filled with the remaining 4 letters in 4! ways.
The number of words = 4! = 24.
Answer:B
Answer: B
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?
Options:
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
Question: In a 200 meters race A beats B by 56 m or 7 seconds. A's time over the course is:
Options:
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
Question: A committee of 5 people is to be selected from 9 people. How many different committees are possible?
Options:
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
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?
Options:
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
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?
Options:
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
Question: 10 : 4 seconds :: ? : 6 minutes
Options:
A)10
B)15
C)20
D)25
E)30
Rationale: 10*6=4*x
x=15
ANSWER:B
Answer: B
Question: If x is an integer and y = 4x + 4, which of the following CANNOT be a divisor of y?
Options:
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
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?
Options:
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
Question: In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together
Options:
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
Question: If x = - |x| , then which one of the following statements could be true?
I. x = 0
II. x < 1
III. x > 0
Options:
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
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?
Options:
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
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)
Options:
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
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?
Options:
A)46%
B)66%
C)74%
D)63%
E)68%
Rationale: B
16000/(1136 + 7636 + 16000) = 66%.
Answer: B
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?
Options:
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
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?
Options:
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
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 ?
Options:
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
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?
Options:
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
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?
Options:
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
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
Options:
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
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?
Options:
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
Question: If x = 2, then what is the value of 8x √x3 – x2
Options:
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
Question: If x is three times larger than n , and if 2n+3 is 20% of 25, what is the value of ?
Options:
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
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).
Options:
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
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
Options:
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
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 ?
Options:
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
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.)
Options:
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
Question: The average of first five multiples of 8 is :
Options:
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
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?
Options:
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
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?
Options:
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
Question: Evaluate: 11 + sqrt(- 4 + 6×4÷3) =?
Options:
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
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
Options:
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
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.
Options:
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
Question: If 6111309× 3145208 × K^2 is divisible by 3, which of the following could be the value of K?
Options:
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
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?
Options:
A)2400
B)2677
C)2168
D)2669
E)2668
Rationale: 1200 * 12: x * 9 = 2:3
x = 2400
Answer: A
Answer: A
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?
Options:
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
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?
Options:
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
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?
Options:
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
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
Options:
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