divelab/Sys2Bench huggingface dataset:
Question: At a certain stage of a soccer tournament, the score ratio of teams A, B and C was 3:4:5. Eventually, the score ratio of A to B has doubled while the score ratio of A to C has halved. If the final score of team C was 40, what was the final score D of team B?
Options:
A)1)8
B)2)10
C)3)20
D)4)40
E)5)80
Rationale: A to B = 3 : 4
So, on doubling we get 6 : 4
A to C = 3 : 5
So, on halving we get 1.5 : 5 or 3 : 10 or 6 : 20
So final ratio = 6 : 4 : 20.
If 20x = 40
4x = 8
Hence, answer is A
Answer: A
Question: If n > 0 , which of the following must be true?
I n^2 < 1
II	n - n^2 > 0
III	2n - 1 > 0
Options:
A)I only
B)II only
C)III only
D)I and II only
E)none
Rationale: I. False for all values of n except 1
When n = 1 ; n^2 = 1
II. False for all values of n except 1
When n = 1 ; n - n^2 = 1 - 1 =>0
III	True for all values of n
Hence the correct answer will be (C)
Answer: C
Question: x=2+2^(2/3)+2^(1/3), then what is the value of x^3-6x^2+6x? here X^Y indicates X to the power Y.
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: Given that x = 2 + 2^(2/3) + 2^(1/3)
so x - 2 = 2^(2/3) + 2^(1/3)
or (x-2)^3 = [2^(2/3)+2^(1/3)]^3
or x^3 - 8 - 6x(x-2) = 2^2 + 2^1 + 3*[2^{(2/3)+(1/3)}[2^(2/3)+2^(1/3)
or x^3 - 8 - 6x^2 + 12x = 4 + 2 + 6(x-2)
or x^3 - 8 -6x^2 + 12x = 6 + 6x - 12
or x^3 - 6x^2 +6x = 2
ANSWER:A
Answer: A
Question: A rectangular cube has a volume of 11 cubic feet. If a similar cube is twice as long, twice as wide, and twice as high, then the volume, in cubic feet of such cube is?
Choices
Options:
A)24
B)48
C)64
D)88
E)100
Rationale: Lets say the sides of the rectangular cube are x, y and z. Problem states volume is 11.
i.e,
x*y*z = 11.
If every side is increased twice as before. then new volume is
2x*2y*2z = 8*(x*y*z) = 8*11 = 88.
Answer is D
Answer: D
Question: A certain roller coaster ride has fewer than 110 people waiting in line to board. If riders are let on only in groups of 5 there will be 2 riders that do not get on. If riders are let on only in groups of 6 all riders will be able to get on the roller coaster. Which of the following could be the number of people in the line?
Options:
A)7
B)22
C)52
D)67
E)72
Rationale: Total number of riders = 5p + 2 or 6q.
The first number that fits in is 12. Numbers following will be 12 + multiple of 30 ( LCM of 5 and 6).
Therefore, the total number of riders will be 30k+12.
12, 42, 72, 102 are the only possibilities as the number of riders is fewer than 110.
Among the given options 72 is the answer.
ANSWER:E
Answer: E
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 8% from the list price. It may be sold at a profit of 25% on the cost price?
Options:
A)60.5
B)69.5
C)64.5
D)62.5
E)22.5
Rationale: CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(92/100) = 59.375
MP = 64.5
Answer:C
Answer: C
Question: There are 6 different travelers who each have a choice of vacationing at one of 10 different destinations. What is the probability that all 6 travelers will end up vacationing at the same destination?
Options:
A)0.1
B)0.001
C)0.0002
D)1.0e-05
E)0.0001
Rationale: Prob that traveler 1 will choose 1st place(any particular place) out 10 places = 1/10
Prob that traveler 2 will choose same place out 10 places = 1/10
......
Total = 1/10 * ... 1/10 (6 times)
= 1/10^6
But this can happen for all of the 10 places.
So Prob = 10/(10^6) = 1/10^(6-1)
=0.00001
Answer - D
Answer: D
Question: Two teams participating in a competition had to take a test in a given time. Team
B chose the easier test with 300 questions, and team A the difficult test with 10%less questions. Team A completed the test 3 hours before schedule while team B completed it 6 hours before schedule. If team B answered 7 questions more than
team A per hour, how many questions did team A answer per hour?
Options:
A)16
B)17
C)18
D)19
E)20
Rationale: If t hrs is normal time,
then
270/(t-3) + 7 = 300/(t-6)
so t = 18
so Qns done by team A per hour = 270/15 = 18 qns.
ANSWER:C
Answer: C
Question: There is 7 friends (A1, A2, A3....A7).If A1 have to have shake with all without repeat. How many handshakes possible?
Options:
A)6
B)21
C)28
D)7
E)9
Rationale: only A1 have to hand shake,so A1 can hand shake with remaining 6 person.
ANSWER:A
Answer: A
Question: Speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph. A man rows to a place at a distance of 7380 km and comes back to the starting point. The total time taken by him is:
Options:
A)914.2 hours
B)937.1 hours
C)915 hours
D)905 hours
E)915 hours
Rationale: Explanation:
Speed downstream = (16 + 2) = 18 kmph
Speed upstream = (16 - 2) = 14 kmph
Total time taken = 7380/18 + 7380/14 = 410 + 527.1 = 937.1 hours
Answer: Option B
Answer: B
Question: Of the employees in a company, 30 % are female who have a master degree. If 50 % of the female employees do not have a master degree, what percent of the employees in the company are female?
Options:
A)50%
B)70%
C)60%
D)66%
E)65%
Rationale: Let E be total no. of employees and F be total no of female employees.
Question asked what is F/E X 100%?
No. of female employees with Masters = 0.3 x E (From the question)
No. of female employees without masters = 0.5 x F (From the question)
Therefore No. of female employees with masters = F - 0.5 F = 0.5 F
The 2 expressions equal each other therefore 0.5F = 0.3E; F/E = 0.3/0.5 = 60%
Ans: C
Answer: C
Question: At a party, every two people shook hands once. How many people
attended the party if there were 66 handshakes?
Options:
A)12
B)22
C)33
D)65
E)67
Rationale: If there are n people at the party, then each of the n people will shake hands
with n -1 other people. Since each handshake accounts for a handshake that each of two
people have made (i.e., since there are two people involved with each handshake), the total
number of handshakes the n people will make is n(n-1)=2. (Alternatively, the number
of handshakes is the number of ways of choosing 2 people from among n people, which is
-n
2 =n(n-1)=2.) Hence, we have n(n-1)=2 = 66 = 12 11=2, so n = 12.
correct answer A
Answer: A
Question: What is 982*982?
Options:
A) 964,169
B) 964,219
C) 964,324
D) 975,019
E) 975,369
Rationale: if you take a base of 1000 then 982 is 18 less than 1000
to get the product of 982 x 982 write like this
982- 18( as 18 less than base1000)
982- 18
now 18 x 18 = 324
and 982-18 = 964
so 982 x 982 = 964324 ... (bingo the answer is C . you can even have a shortcut ...... 18 x 18 = 324 ... only answer choice has last three digits as 324.. so no need to calculate 982-18 . after you get 18 x 18 you can straight way pick answer choice C.
Answer: C
Question: 852.68 âˆ’ 4.0 + 108.98 = ? âˆ’ 2132.54
Options:
A)6078.58
B)6078.08
C)6258.58
D)6088.58
E)None
Rationale: Option 'B'
Answer: B
Question: The cost of 2 chairs and 3 tables is Rs.1400. The cost of 3 chairs and 2 tables is Rs.1200. The cost of each table is more than that of each chair by?
Options:
A)228
B)287
C)277
D)188
E)200
Rationale: Explanation:
2C + 3T = 1400 --- (1)
3C + 2T = 1200 --- (2)
Subtracting 2nd from 1st, we get
-C + T = 200 => T - C = 200
Answer:E
Answer: E
Question: The distance between Delhi and Mathura is 110 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?
Options:
A)11
B)10
C)88
D)17
E)22
Rationale: D = 110 – 20 = 90
RS = 20 + 25 = 45
T = 90/45 = 2 hours
8 a.m. + 2 = 10 a.m.
Answer: B
Answer: B
Question: What was the difference between the total monthly salary of Arun in all the years together and Suman's monthly income in the year 2007 ?
Options:
A)23
B)33
C)25
D)26
E)27
Rationale: Answer:B
Answer: B
Question: Positive integer n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 5. If n is greater than 30, what is the remainder that n leaves after division by 35?
Options:
A)3
B)12
C)18
D)22
E)28
Rationale: The theory says:
if a # x is devided by y and leave the positive # r as the remainder then it can also leave negative # (r-y) as the remainder.
e.g:
9 when devided by 5 leves the remainder 4 : 9=5*1+4
it can also leave the remainder 4-5 = -1 : 9=5*2 -1
back to the original qtn:
n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 5
==> n leaves a remainder of -2 (i.e. 4-6) after division by 6 and a remainder of -2 (i.e. 3-5) after division by 5
==> n when devided by 5 and 6 leaves the same remainder -2.
what is n?
LCM (5,6)-2 = 30-2 = 28
CHECK: 28 when devided by 6 leaves the remainder 4 and when devided by 5 leaves the remainder 3
However, the qtn says n > 30
so what is the nex #, > 28, that can give the said remainders when devided by 6 and 5
nothing but 28 + (some multiple of 6 and 5) as thissome multiple of 6 and 5will not give any remainder when devided by 5 or 6 but 28 will give the required remainders.
hence n could be anything that is in the form 28 + (some multiple of 6 and 5)
observe thatsome multiple of 6 and 5is always a multiple of 30 as LCM (5,6) = 30.
hence when n (i.e. 28 + some multiple of 6 and 5) is devided by 30 gives the remainder 18.
C
Answer: C
Question: Charlie, a painter, has 9 jars of paint: 4 are Red, 2 are yellow, and the rest are brown. Charlie will combine 3 jars of paint into a new container to make a new colour, which he will name according to the following conditions: 1) C1, if the paint contains 2 jars of brown paint and no red paint 2) C2, if the paint contains 3 jars of brown paint. 3) J1, if the paint contains at least 2 jars of red paint 4) J2, if the paint contains exactly 1 jar of red paint What is the probability that the new colour will be a shade of J (J1 or J2)?
Options:
A)21/37
B)37/21
C)37/42
D)42/37
E)74/42
Rationale: the probability that it would be J1 or J2 is same as 1-()probability that it is C1 or C2
For C1-3C2(Brown)*2C1(Yellow)=3*2=6
For C2-3C3(all brown)=1
Total=9C3=84
1-7/84=77/84= 37/42
Answer : C
Answer: C
Question: A can do a piece of work in 28 days which B can do in 12 days. B worked at it for 9 days. A can finish the remaining work in ?
Options:
A)3 days
B)5 days
C)6 days
D)7 days
E)11 days
Rationale: B's 9 day's work = 9 x (1/12) = 3/4
Remaining work = (1 - 3/4) = 1/4
1/4 work is done by A in = 28 x (1/4) = 7 days.
answer : D
Answer: D
Question: A is thrice as efficient as B and is, therefore, able to finish a piece of work 10 days earlier than B. In how many days A and B will finish it together?
Options:
A)7/5
B)2/7
C)9
D)1/5
E)2
Rationale: Explanation:
WC = 3:1
WT = 1:3
x 3x
1/x â€“ 1/3x = 1/10
x = 20/3
3/20 + 1/20 = 1/5 days.
Answer:D
Answer: D
Question: John paid a sum of money for purchasing 20 pens, which he recovered in full when he sold 10 of them. What was his percentage of profit or loss per pen?
Options:
A)100%
B)150%
C)90%
D)80%
E)95%
Rationale: A
100%
If the sum he paid whilst purchasing 20 pens = A,
Then the Cost Price of each pen = A/20.
Since the amount he got whilst selling 10 pens is also = A
Then the Selling Price of each pen = A/10.
Since Selling Price > Cost Price, he made a profit.
Profit per pen = Selling Price - Cost Price = A/10 -A/20= A/20.
Profit percentage per pen = Profit per pen / Cost per pen x 100 = (A/20) / (A/20) x 100 = 100%
Answer: A
Question: By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?
Options:
A)27%
B)25%
C)21%
D)85%
E)24%
Rationale: SP = CP + g
150 SP = 150 CP + 30 SP
120 SP = 150 CP
120 --- 30 CP
100 --- ? => 25%
Answer:B
Answer: B
Question: The compound interest earned on a sum for the second and the third years are $1400 and $1512 respectively. What is the rate of interest?
Options:
A)5%
B)6%
C)7%
D)8%
E)9%
Rationale: 1512 - 1400 = 112 is the rate of interest on $1400 for one year.
The rate of interest = (100 * 112) / (1400) = 8%
The answer is D.
Answer: D
Question: Which of the following inequalities is always true for any real number 'x' and 'y'?
Options:
A)|x-y| < |x| +|y|
B)|x + y| > |y| + |x|
C)|x + y| <= |x| + |y|
D)|x - y| <= |x| - |y|
E)|x - y| > |x| - |y|
Rationale: The answer is (C). One of the fundamental properties of absolute value, which is subadditivity, essentially means that evaluating the function for the sum of two elements (numbers) always returns something less than or equal to the sum of the function's values at each element; therefore, |x + y| <= |x| + |y|
Answer: C
Question: A man gains 20% by selling an article for a certain price. If the sells it at double the price, the percentage of profit will be:
Options:
A)327
B)140
C)277
D)178
E)112
Rationale: Let C.P. = Rs. x.
Then, S.P. = Rs. (12% of x) = Rs. 6x/5
New S.P. = 2 * 6x/5 = Rs. 12x/5
Profit = 12x/5 - x = Rs. 7x/5
Profit = 7x/5 * 1/x * 100 = 140%.\
Answer: D
Answer: D
Question: What is the ratio between perimeters of two squares one having 3 times the diagonal then the other?
Options:
A)3:6
B)3:9
C)3:5
D)3:1
E)3:2
Rationale: d = 3d d = d
a√2 = 3d a√2 = d
a = 3d/√2 a = d/√2 => 3:1
Answer: D
Answer: D
Question: If a committee of 3 people is to be selected from among 4 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?
Options:
A)20
B)32
C)50
D)80
E)120
Rationale: Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) each to send onerepresentativeto the committee: 4C3=4.
But these 3 chosen couples can send two persons (either husband or wife): 2*2*2=2^3=8.
Total # of ways: 4C3*2^3=32.
Answer: B.
Answer: B
Question: When 5% is lost in grinding wheat, a country has to import 20 million bags; but when only 2% is lost, it has to import only 15 million bags. Find the quantity of wheat, which grows in the country?
Options:
A)133 1/3 m
B)150 m
C)106 2/3 m
D)166 2/3 m
E)168 2/3 m
Rationale: 5% - 2% = 3%
3% ---- 5
100% ---- ? => 166 2/3
ANSWER:D
Answer: D
Question: If m/21 is an integer, then each of the following must be an integer EXCEPT
Options:
A)5/2
B)4
C)3
D)2
E)1
Rationale: Now plug m =21 into the answer choices:
A. (21- 28)/7 = -1. This is an integer
B. (21+ 21)/7 = 6. This is an integer
C. 14(21)/98 = 3. This is an integer
D. (21^2 - 49)/49 = 8. This is an integer
E. (21+ 14)/14 = 5/2. This is NOT an integer
Answer: A
Answer: A
Question: Find out the wrong term in the series 5, 10, 50, 500, 25000, 3000000
Options:
A)15,000,000
B)12,500,000
C)9,000,000
D)3,00,000
E)60,000
Rationale: Explanation:
Each number with in the series is the product of the two numbers that proceed it.
So, if (5 * 10 = 50) , then (500 * 25000 = 12,500,000). 12,500,000 should replace 3000000.
Answer: B) 12,500,000
Answer: B
Question: The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is:
Options:
A)36.5
B)35
C)34
D)33
E)32.5
Rationale: Correct sum = (36 * 50 + 48 - 23) = 1825.
Correct mean = 1825/50 = 36.5
ANSWER A
Answer: A
Question: The larger of two negative consecutive even integers 2t and 2(t-1) is multiplied by 7 and then added to the smaller of the two original integers. Which of the following represents this operation?
Options:
A)16t-2
B)8t-2
C)-2
D)3
E)-2-4t^2
Rationale: larger of 2t-2, 2t (when they are negative) is 2t. the smallest of 2t and 2t-2 when they are positive is 2t-2.
therefore 7* 2t + 2t-2 = 16t-2.
option A.
Answer: A
Question: Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 40 white marbles. How many red marbles could be in bag A?
Options:
A)8
B)3
C)4
D)6
E)8
Rationale: 6 is the answer.
Bag A-
R:W:B = 2:6:9
Let W in bag A be 6K
Bab B -
R:W = 1:3
Let W in bag B be 4k
W = 30 = 6K+4k=> k =40/10 =4
Total Red's in bag A will be 2K = 8
A
Answer: A
Question: Arun got 30% of the maximum marks in an examination and failed by 10 marks. However, Sujith who took the same examination got 40% of the total marks and got 15 marks more than the passing marks. What were the passing marks in the examination?
Options:
A)90
B)250
C)85
D)75
E)65
Rationale: Explanation:
Let x is the maximum marks of the examination
Marks that Arun got = 30 % of x = 30x/100
Given that Arun failed by 10 marks
⇒Minimum Pass Mark = 30x/100 + 10......(Equation 1)
Marks that Sujith got = 40 % of x = 40x/100
Given that Sujith got 15 marks more than the passing marks
⇒40x100=Minimum Pass Mark +15
⇒Minimum Pass Mark =40 x100 −15......(Equation 2)
From equations 1 and 2, we have
30 x 100 + 10 = 40x/100 − 15
⇒10x/100 = 10 + 15 = 25
⇒x/10 = 25
⇒ x = 10 × 25 = 250
⇒Maximum marks of the examination = x = 250
Substituting the value of x in Equation 1, we have
Minimum Pass Mark = 30x/100 + 10 = 30 × 250/100 + 10 = 75 + 10 = 85
Answer: Option C
Answer: C
Question: We had $350 left after spending 30% of the money that we took for shopping. How much money did we start with?
Options:
A)$440
B)$460
C)$480
D)$500
E)$520
Rationale: Let x be the amount of money we started with.
0.7x = 350
x = 500
The answer is D.
Answer: D
Question: The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?
Options:
A)18 2/18%
B)18 2/11%
C)18 2/31%
D)18 4/11%
E)16 2/11%
Rationale: 13 CP = 11 SP
11 --- 2 CP
100 --- ? =>18 2/11%
Answer: B
Answer: B
Question: If n = 3p, where p is a prime number greater than 2, how many different positiveevendivisors does n have, including n ?
Options:
A) Two
B) Three
C) Four
D) Six
E) Eight
Rationale: This is an interesting question because we are immediately given the option to insert any prime number we wish for p. Since this is a problem-solving question, and there can only be one correct answer, we can select any value for p, as long as it is a prime number greater than 2. We always want to work with small numbers, so we should select 3 for p. Thus, we have:
n = 4 x 3
n = 12
Next we have to determine all the factors, or divisors, of P. Remember the term factor is synonymous with the term divisor.
1, 12, 6, 2, 4, 3
From this we see that we have 4 even divisors: 12, 6, 2, and 4.
If you are concerned that trying just one value of p might not substantiate the answer, try another value for p. Let’s say p = 5, so
n = 4 x 5
n = 20
The divisors of 20 are: 1, 20, 2, 10, 4, 5. Of these, 4 are even: 20, 2, 10 and 4. As we can see, again we have 4 even divisors.
No matter what the value of p, as long as it is a prime number greater than 2, n will always have 4 even divisors.
The answer is B.
Answer: B
Question: If P= {multiplies of 3 between 1 and 20}, Q = {even natural number upto 15} , find the intersection of the two given set P and Q.
Options:
A)P∪Q= {6,12}
B)P∩Q= {6,12}
C)P∩Q= {10,12}
D)P∪Q= {10,12}
E)P∪Q= {8,10}
Rationale: P= {3,6,9,12,15,18}, Q= {2,4,6,8,10,12,14}
Intersection of P and Q is the largest set containing only those elements which are common to both the given sets P and Q. correct answer : (B) P∩Q= {6,12}
Answer: B
Question: 46080, 3840, 384, 48, 8, 2, ?
Options:
A)1
B)1⁄64
C)1⁄8
D)None of these
E)1/32
Rationale: Explanation :
46080 ÷ 12 = 3840
3840 ÷ 10 = 384
384 ÷ 8 = 48
48 ÷ 6 = 8
8 ÷ 4 = 2
2 ÷ 2 = 1
Answer : Option A
Answer: A
Question: A, B and C rents a pasture for Rs.950. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
Options:
A)295
B)199
C)676
D)156
E)122
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 950= 295
Answer: A
Answer: A
Question: In a group of ducks and cows, the total number of legs are 28 more than twice the number of heads. Find the total number of cows.
Options:
A)12
B)14
C)16
D)18
E)20
Rationale: Let the number of ducks be d
and number of cows be c
Then, total number of legs = 2d + 4c = 2(d + 2c)
total number of heads = c + d
Given that total number of legs are 28 more than twice the number of heads
=> 2(d + 2c) = 28 + 2(c + d)
=> d + 2c = 14 + c + d
=> 2c = 14 + c
=> c = 14
i.e., total number of cows = 14
Answer is B.
Answer: B
Question: A box contains 2 white balls and 4 red ball. in how many ways can 3 balls be drawn from the box , if at least one black ball is to be included i the draw ?
Options:
A)32
B)48
C)64
D)96
E)None
Rationale: Solution
We have many (1 black and 2 non-black) or (2 black and 1 non-black) or (3 black).
So, Required number of ways = (3 C 1 × 6 C 2) + (3 C 2 × 6 C 1) + (3 C 3)
= ( 3x 6x 5/2x1) + ( 3x 2/2x1x 6) + 1 = (45 + 18 + 1) = 64.
Answer C
Answer: C
Question: If the height of a cone is increased by 120% then its volume is increased by?
Options:
A)100
B)777
C)998
D)729
E)120
Rationale: 120%
Answer:E
Answer: E
Question: Find the average of all prime numbers between 60 and 90
Options:
A)45
B)55
C)69
D)65
E)77
Rationale: Prime numbers between 60 and 90 are 67, 71, 73, 79, 83, 89
Required average = (67+ 71+ 73+ 79+ 83+ 89)/6 = 462/6 = 77
Answer is E
Answer: E
Question: An egg seller sells his eggs only in the packs of 3 eggs, 6 eggs, 9 eggs, 12 eggs etc., but the rate is not necessarily uniform. One day Raju (which is not the same egg seller) purchased at the rate of 3 eggs for a rupee and the next hour he purchased equal number of eggs at the rate of 6 eggs for a rupee. Next day he sold all the eggs at the rate of 9 eggs for Rs. 2. What is his percentage profit or loss?
Options:
A)10% loss
B)11.11% loss
C)3% loss
D)2.5 % profit
E)None of These
Rationale: Solution: CP of one egg in first case = 1/3 = 33.33 paise
CP of one egg in second case = 1/6 = 16.66 paise
Average CP = (33.33 +16.66)/2 = 25 paise
Selling price of 9 eggs = Rs. 2
SP of one egg = 200/9
Profit or loss = [(25 - (200/9))*100]/25
Profit or loss = -11.11. (loss)
Answer: Option B
Answer: B
Question: Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
Options:
A)50
B)77
C)55
D)43
E)12
Rationale: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 46 - 36 = 10 km/hr.
= 10 * 5/18 = 25/9 m/sec.
2x/36 = 25/9 => x = 50.
Answer: A
Answer: A
Question: A is twice efficient than B. A and B can both work together to complete a work in 7 days. Then find in how many days A alone can complete the work?
Options:
A)10.9
B)10.5
C)10.8
D)10.1
E)80.1
Rationale: Ans: Let us assume A can do 2 units of work each day, then B can do only 1 unit a day. If both can complete the work in 7 days, total work done by these two togeter = (2 + 1 ) x 7 = 21 units
If these 21 units to be done by A alone, then he will take 21 / 2 = 10.5 days.
\Answer:B
Answer: B
Question: In a public show 50 % of the seats were filled. If there were 600 seats in the hall, how many seats were vacant?
Options:
A)100
B)110
C)120
D)300
E)150
Rationale: 50 % of 600
= 50/100 × 600
= 300
Therefore, the number of vacant seats = 600 - 300 = 300.
Answer:D
Answer: D
Question: Which of the following numbers is not prime?
Options:
A)5-3
B)11+12
C)31-2
D)4+6
E)1000-3
Rationale: 2 can be factored out of both 4 and 6. --> 4+6= 2*(2+3). The correct answer is D.
Answer: D
Question: A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
Options:
A)230 m
B)245 m
C)260 m
D)275 m
E)295 m
Rationale: Relative speed = (120 + 80) km/hr
= 200 x 5/18
= 500/9 m/sec
Then, (x+270)/9 = 500/9
--> x + 270 = 500
--> x = 230.
Answer : A.
Answer: A
Question: {130, 280, 250, n}
Which of the following could be the median of the 4 integers listed above?
I. 160
II. 210
III. 250
Options:
A)I only
B)II only
C)I and II only
D)II and III only
E)I, II, and III
Rationale: If 160 is the median, (n+250) / 2 = 160. Then n = 70. But n < 130, so 160 can not be the median.
If 210 is the median, (n+250) / 2 = 210. Then n = 170. Thus 210 can be the median.
If 250 is the median, (n+250) / 2 = 250. Then n = 250. Thus 250 can be the median.
The answer is D.
Answer: D
Question: What will be the acute angle between hands of a clock at 2 : 30?
Options:
A)105°
B)115°
C)95°
D)135°
E)None of these
Rationale: At 2'O Clock, Minute Hand will be 10 × 6 = 60°
behind the Hour Hand.
In 30 minutes, Minute Hand will gain (51⁄2)° × 30
= 150 + 15 = 165°
∴ Angle between Hour Hand and Minute Hand
= 165 – 60 = 105°
Answer A
Answer: A