divelab/Sys2Bench huggingface dataset:
Question: Hitesh is 40 years old and Ronnie is- 60 years old. How many years ago was the ratio of their ages 3:5 ?
Options:
A)5 years
B)10 years
C)20 years
D)15 years
E)25 years
Rationale: Suppose, the ratio was 3 : 5, x years ago.
Then,
(40-x)/(60-x)=3/5
=5 (40 - x) = 3 (60 - x)
=200-5x =180-3x
=2x = 20
= x = 10.
Answer: B
Answer: B
Question: Evaluate the expression
m - (m - n) : (-2) ⋅ (-5) when m = -4, n = -6
Options:
A)8
B)9
C)5
D)7
E)6
Rationale: Solution:
m - (m - n) : (-2) ⋅ (-5) = (-4) - [-4 - (-6)] : (-2) ⋅ (-5) = -4 - 2 : (-2) ⋅ (-5) = -4 - (-1) ⋅ (-5) = -4 - (+5) = -9
Answer B
Answer: B
Question: The average age of three boys is 15 years and their ages are in proportion 3:5:7. What is the age in years of the youngest boy?
Options:
A)8
B)9
C)7
D)5
E)4
Rationale: 3x + 5x + 7x = 45
x =3
3x = 9
Answer:B
Answer: B
Question: A certain board game has a row of squares numbered 1 to 100. If a game piece is placed on a random square and then moved 13 consecutive spaces in a random direction, what is the probability the piece ends no more than 13 spaces from the square numbered 49?
Options:
A)28%
B)27%
C)30%
D)37%
E)17%
Rationale: No more than 13 spaces from 49 means in the rangefrom 49-13=36 to 49+13=62, inclusive. Total numbers in this range 62-36+1=27, the probability favorable/total=27/100
Answer: B
Answer: B
Question: Walking at the rate of 4 kmph a man cover certain distance in 2 hr 45 min. Running at a speed of 16.5 kmph the man will cover the same distance in.
Options:
A)12 min
B)40 min
C)60 min
D)30 min
E)45 min
Rationale: dist = 4*22/4 = 22km
new speed = 16.5 kmph
=>D/S = 11/16.5 = 40 min
ANSWER B
Answer: B
Question: A garrison of 3300 men had provisions for 32 days, when given at the rate of 860 gms per head. At the end of 7 days, a reinforcement arrives and it was for that the provisions wi1l last 17 days more, when given at the rate of 826 gms per head, What is the strength of the reinforcement?
Options:
A)1900
B)1600
C)1300
D)1500
E)1700
Rationale: The problem becomes:
3300 men taking 850 gms per head have provisions for (32 - 7) or 25 days,
How many men taking 825 gms each have provisions for 17 days?
Less ration per head, more men	(Indirect Proportion)
Less days, More men	(Indirect Proportion)
Ration 825 : 850
Days 17: 25 } : : 3300 : x
(825 x 17 x x) = 850 x 25 x 3300 or x = (850 x 25 x 3300)/(825 x 17)=5000
Strength of reinforcement = (5500 - 3300) = 1700.
Answer is E.
Answer: E
Question: In a friendship gang Aravind has 2 gang, in how many ways can he invite one or more of the gang to his house?
Options:
A)25
B)49
C)3
D)87
E)36
Rationale: Aravind can select one or more than one of his 8 gang.
=> Required number of ways = 2^2 – 1= 3.
C
Answer: C
Question: Shyam visited Ram during his brief vacation. In the mornings they both would go for yoga. In the
evenings they would play tennis. To have more fun, they indulge only in one activity per day, i.e.
either they went for yoga or played tennis each day. There were days when they were lazy and
stayed home all day long. There were 24 mornings when they did nothing, 14 evenings when they stayed at home, and a total of 22 days when they did yoga or played tennis. For how many days Shyam stayed with Ram?
Options:
A)32
B)24
C)30
D)None of these
E)Cannot be determined
Rationale: Explanation :
Let ,
P days : they play tennis.
Y days : they went to yoga.
T days : total duration for which Ram and Shyam were together.
=> P + Y = 22.
Also, (T - Y ) = 24 & (T - P) = 14.
Adding all of them,
2T = 22 + 24 + 14
=> T = 30 days.
Answer : C
Answer: C
Question: A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A?
Options:
A)240
B)882
C)727
D)199
E)212
Rationale: (3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 630 = 240
Answer: A
Answer: A
Question: If 36 men do a work in 70 days, in how many days will 40 men do it?
Options:
A)64
B)63
C)65
D)66
E)67
Rationale: 36 * 70 = 40 * x
x = 63 days
Answer: B
Answer: B
Question: During a certain season, a team won 85 percent of its first 100 games and 50 percent of its remaining games. If the team won 70 percent of its games for the entire season, what was the total number of games that the team played?
Options:
A)180
B)175
C)156
D)150
E)105
Rationale: We are first given that a team won 85 percent of its first 100 games. This means the team won 0.85 x 100 = 85 games out of its first 100 games.
We are next given that the team won 50 percent of its remaining games. If we use variable T to represent the total number of games in the season, then we can say T – 100 equals the number of remaining games in the season. Thus we can say:
0.5(T – 100) = number of wins for remaining games
0.5T – 50 = number of wins for remaining games
Lastly, we are given that team won 70 percent of all games played in the season. That is, they won 0.7T games in the entire season. With this we can set up the equation:
Number of first 100 games won + Number of games won for remaining games = Total Number of games won in the entire season
85 + 0.5T – 50 = 0.7T
35 = 0.2T
350 = 2T
175 = T
Answer is B.
Answer: B
Question: The sum of all two digit numbers divisible by 5 is
Options:
A)945
B)545
C)745
D)645
E)845
Rationale: Required numbers are 10,15,20 . . . . . 95
This is an A.P. in which a=10,d=5 and l=95.
Let the number of terms in it be n.Then t=95
So a+(n-1)d=95.
10+(n-1)*5=95,
10+5n-5=95
5+5n=95
5n=95-5
n = 90/5
then n=18.
Required sum
=n/2(a+l)
=18/2(10+95)
=945
Answer is A.
Answer: A
Question: Find the principle on a certain sum of money at 5% per annum for 3 1/5 years if the amount being Rs.1160?
Options:
A)Rs.1000
B)Rs.1100
C)Rs.1010
D)Rs.10000
E)None of these
Rationale: Explanation:
1160 = P [1 + (5*16/5)/100]
P= 1000
Answer: Option A
Answer: A
Question: A pump will fill a tank in 3 hours. Because of a leak in the tank, it took 3 hours 30 min to fill the tank. In what time the leak can drain out all the water of the tank and will make tank empty ?
Options:
A)20 hrs
B)21 hrs
C)22 hrs
D)23 hrs
E)24 hrs
Rationale: work done for 1 hr without leak = 1/3
work done with leak = 31/2 ==>7/2
work and leak in 1 hr = 2/7
work leak in 1 hr = 1/3 - 2/7 = 1/21
so 21 hrs
ANSWER B
Answer: B
Question: At present the ratio between the ages of Arun and Deepak is 4:3. After 6years, Arun's age will be 26 years. What is the age of Deepak at present?
Options:
A)15
B)21
C)23
D)12
E)25
Rationale: Let the present ages of Arun and Deepak be 4x years and 3x years respectively
4x+6 = 26
4x = 20
x = 5
Deepak's age = 3x = 15years
Answer is A
Answer: A
Question: A class consists of 100 students, 20 of them are girls and 80 boys; 20 of them are rich and remaining poor; 40 of them are fair complexioned. The probability of selecting a fair complexioned rich girl is
Options:
A)2/125
B)1/59
C)1/56
D)1/54
E)1/53
Rationale: The probability of selecting girl is: 20/100 = 1/5
The probability of selecting rich is: 20/100 = 1/5
The probability of selecting fair complexioned is: 40/100 = 2/5
Three are independent;probability of rich and fair complexioned girl is:
(1/5) Ã—(1/5) Ã— (2/5) = 2/125
Answer: A
Answer: A
Question: Express 25 mps in kmph?
Options:
A)22
B)88
C)90
D)21
E)24
Rationale: 25 * 18/5 = 90 kmph
Answer: C
Answer: C
Question: At Company K, 15 percent of the employees are secretaries and 60 percent are salespeople. If there are 25 other employees of Company K, how many employees does Company K have?
Options:
A) 160
B) 180
C) 190
D) 200
E) 100
Rationale: Let the total number of employees in the company be x
% of secretaries = 15%
% of salespeople = 60%
% of of employees other than secretaries and salespeople = 100 - 75 = 25%
But this number is given as 25
so 25% of x = 25
x = 100
Therefore there a total of 100 employees in the company K
Correct answer - E
Answer: E
Question: A committee of 6 is chosen from 5 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed?
Options:
A)150
B)700
C)1404
D)2620
E)3510
Rationale: The only cases possible are :
1. 2 men and 4 women : 5C2 * 5C4 = 50
2. 3 men and 3 women: 5C3*5C3 = 100
Rest of the cases will either have 1 or 0 men (not allowed) or will have 1 or 2 or 0 women (not allowed)
Total possible combinations = 50+100 = 150. Thus A is the correct answer.
Answer: A
Question: How many even multiples of 45 are there between 449 and 901?
Options:
A)5
B)6
C)9
D)10
E)11
Rationale: 450 = 10*45
900 = 20*45
The even multiples are 45 multiplied by 10, 12, 14, 16, 18, and 20 for a total of 6.
The answer is B.
Answer: B
Question: If a number T between 0 and 1 is selected at random, which of the following will the number most likely be between?
Options:
A)0 and 3/20
B)3/20 and 1/5
C)1/5 and 1/4
D)1/4 and 3/10
E)3/10 and 1/2
Rationale: The number T will most likely be between the largest range.
A. 0 and 3/20 --> range 3/20;
B. 3/20 and 4/20 --> range 1/20;
C. 4/20 and 5/20 --> range 1/20;
D. 5/20 and 6/20 --> range 1/20;
E. 6/20 and 10/20 --> range 4/20.
Answer: E.
Answer: E
Question: How many ways are there to split a group of 8 girls into two groups of 4 girls each? (The order of the groups does not matter)
Options:
A)30
B)40
C)35
D)45
E)50
Rationale: the combination is 8C4 /2
= 8!/4!*4! *2 = 35
C
Answer: C
Question: 49 members attended the party. In that 22 are males, 27 are females. The shake hands are done between males, females, male and female. Total 12 people given shake hands. How many such kinds of such shake hands are possible?
Options:
A)66
B)291
C)26
D)29
E)11
Rationale: If only 12 people shaked their hands, then total hand shakes are 12C212C2 = 66
Answer:A
Answer: A
Question: A Laptop was sold at a loss of 10%. If it was sold for Rs.5000 more, there would have been a gain of 10%. What is the cost price?
Options:
A)Rs.18000
B)Rs.21000
C)Rs.22000
D)Rs.20000
E)Rs.25000
Rationale: 90%
110%
--------
20% ---- 5000
100% ---- ? => Rs.25000
Answer: E
Answer: E
Question: What is the remainder when 1271 * 1276 * 1277 *1285 is divided by 12?
Options:
A) 0
B) 1
C) 11
D) 9
E) 4
Rationale: 1271*1275*1277*1285 = (1272 - 1)(1272 + 4)(1284 - 7)(1284 + 1) = (multiple of 12 - 1)(multiple of 12 + 3)(multiple of 12 - 7)(multiple of 12 + 1)
Now, if we expand this expression all terms but the last one will have a multiple of 12 in them, thus will leave no remainder upon division by 12, the last term will be (-1)(4)(-7)(1) = 28. Thus the question becomes: what is the remainder upon division of 28 by 12? The answer to this question is 4.
Answer: E
Answer: E
Question: A reading list for a certain course consists of 10 books, of which 4 are poems and the rest are novels. Each student is required to read a selection of 4 books from the list, including at most 1 novels. How many selections of 4 books satisfy the requirements?
Options:
A)90
B)115
C)130
D)144
E)195
Rationale: Ans: B
Solution: Selection requires at most 2 novels, means=
0N4P + 1N3P + 2N2P
6c0*4c4+ 6c1*4c3 + 6c2*4c2 +6c3*4c1
= 1+ 24 + 90+80
= 195
Ans: E
Answer: E
Question: Martin has to secure 80% marks to clear his exam of class 9th.
He got 200 marks and failed by 200 marks.
What is the maximum marks ?
Options:
A)500
B)505
C)510
D)515
E)525
Rationale: A
500
To pass the exam ravish needs 200 + 200 = 400 marks.
=> (400/80) *100 = 500
Answer: A
Question: 96 can be expressed as a product of primes as
Options:
A)2 × 2 × 3 × 3 × 3 × 7
B)2 × 3 × 3 × 3 × 7 × 7
C)2 × 2 × 2 × 2 × 2 × 3
D)2 × 3 × 3 × 3 × 3 × 7
E)None of these
Rationale: Explanation:
It is clear that 96 = 2 × 2 × 2 × 2 × 2 × 3
Answer: Option C
Answer: C
Question: S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk–1 + 2(10k–1). If p is the sum of the first 30 terms of S, what is the tenth digit of p, counting right to left from the units digit?
Options:
A)1
B)2
C)4
D)6
E)9
Rationale: C
Sum of unit digits of first 30 terms = 60
Sum of tens digits of first 30 terms = 58
Sum of thousands digits of first 30 terms = 56
and so on..
p1 = 0
p2 = (6+58) = 4
p3 = (6+56) = 2
p4 = (6+54) = 0
p5 = (6+52) = 8
p6 = (5+50) = 5
p7 = (5+48) = 3
p8 = (5+46) = 1
p9 = (5+44) = 9
p10= (4+42) = 6
ANSWER : D
Answer: D
Question: Vijay bought 160 shirts at the rate of Rs. 225 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?
Options:
A)Rs.282
B)Rs.229
C)Rs.208
D)Rs.285
E)Rs.229
Rationale: Total CP per shirt = 225 + 1400/160 + 1.75 + 320/160 = Rs. 237.5
SP = CP[(100 + profit%)/100]
= 237.5 * [(100 + 20)/100]
= Rs.285.
Answer:D
Answer: D
Question: An accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 1 o'clock in the afternoon?
Options:
A)30
B)60
C)90
D)120
E)150
Rationale: The hour hand will move 5/12 of a circle.
(5/12)*360 = 150 degrees.
The answer is E.
Answer: E
Question: In a throw of dice what is the probability of geÆ«ng number greater than 4
Options:
A)1/2
B)1/3
C)1/5
D)1/6
E)None of these
Rationale: Explanation:
Number greater than 4 is 5 & 6, so only 2 number
Total cases of dice = [1,2,3,4,5,6]
So probability = 2/6 = 1/3
Answer: B
Answer: B
Question: A certain sum of money at simple interest amounted Rs.840 in 10 years at 3% per annum, find the sum?
Options:
A)338
B)277
C)229
D)646
E)261
Rationale: 840 = P [1 + (10*3)/100]
P = 646
Answer:D
Answer: D
Question: If x+y=5, and x=15/y, what is the value of x^2+y^2?
Options:
A)12
B)14
C)16
D)18
E)10
Rationale: x^2 + y^2 should make you think of these formulas:
(x+y)(x+y) = x^2+y^2+2xy
We already know (x+y) = 5 and x*y = 15
(x+y)(x+y) = (5)(5) = x^2+y^2+2*(15)
x^2+y^2 = 25 - 15 = 10
Answer : E
Answer: E
Question: If k is the greatest positive integer such that 3^k is a divisor of 24! then k =
Options:
A)3
B)4
C)5
D)6
E)10
Rationale: 24/3=8
24/9=2
8+2 =10
k=10
Answer: E
Answer: E
Question: The sum of three consecutive multiples of 3 is 72. What is the largest number?
Options:
A)21
B)24
C)27
D)36
E)39
Rationale: Let the numbers be 3x, 3x + 3 and 3x + 6.
Then,
3x + (3x + 3) + (3x + 6) = 72
9x = 63
x = 7
Largest number = 3x + 6 = 27.
ANSWER:C
Answer: C
Question: 3 boys and 7 girls can complete John work in 10 days . But 4 boys and 6 girls need 8 days to complete the same work . In how many days will 10 girls complete the same work?
Options:
A)10 days
B)20 days
C)40 days
D)56 days
E)65 days
Rationale: Work done by 4 boys and 6 girls in 1 day = 1/8
Work done by 3 boys and 7 girls in 1 day = 1/10
Let 1 man does m work in 1 day and 1 woman does w work in 1 day. The above equations can be written as
4m + 6w = 1/8 ---(1)
3m + 7w = 1/10 ---(2)
Solving equation (1) and (2) , we get m=11/400 and w=1/400
Amount of work 10 girls can do in John day = 10 × (1/400) = 1/40
Ie, 10 girls can complete the work in 40 days
C
Answer: C
Question: What is the greatest possible (straight line) distance, between any two points on a hemisphere of radius 4?
Options:
A)n/8
B)0.8
C)8
D)18
E)π
Rationale: Maximum distance straight line is diameter
d = 2r = 8..
ANS option C.
Answer: C
Question: The pilot of a small aircraft uses 60 gallons of fuel to fly 300 miles. At this rate, how many gallons of fuel are needed for a 700 mile flight?
Options:
A)140
B)155
C)160
D)170
E)175
Rationale: Number of gallons of fuel per mile = 300 /60 = 5 gallons per mile
Number of gallons of fuel for a 700 mile flight = 700/5 = 140
ANSWER:A
Answer: A
Question: If the integer n has exactly four positive divisors, including 1 and n, how many positive divisors does n^3 have?
Options:
A)16
B)11
C)10
D)20
E)9
Rationale: take the example of 6...
it has 4 positive divisors (1,2,3,4)
Now, take the example of 216 ...
it has 16 divisors..
so A is the ans
Answer: A
Question: An escalator moves towards the top level at the rate of 12 ft.sec and its length is 160 feet. If a person walks on the moving escalator at the rate of 8 feet per second towards the top level, how much time does he take to cover the entire length.
Options:
A)10sec
B)8sec
C)9sec
D)7sec
E)12sec
Rationale: Explanation :
Time taken to cover the entire length = tot.dist/resultant speed = 160/ (12+8) = 8sec
Answer : B
Answer: B
Question: The value of 489.1375 x 0.0483 x 1.956/0.0873 x 92.581 x 99.749 is closest to:
Options:
A)0.04
B)0.08
C)0.07
D)0.06
E)0.05
Rationale: = 489.1375 x 0.0483 x 1.956/0.0873 x 92.581 x 99.749
= 489 x 0.05 x 2/0.09 x 93 x 100
= 489/9 x 93 x 10
= 163/279 x 1/10
= 0.58/10
= 0.058 (or) 0.06.
Answer is D.
Answer: D
Question: The simple form of the ratio 8/5:2/3 is?
Options:
A)12:5
B)12:7
C)7:12
D)5:7
E)4:7
Rationale: 8/5:2/3 = 12:5
Answer: A
Answer: A
Question: John has on his shelf two books of poetry, six novels, and two reference works. Suppose from these ten books, we were to pick two books at random. What is the probability that we pick one novel and one reference work?
Options:
A)1/2
B)2/5
C)3/10
D)7/20
E)4/15
Rationale: When we are picking two books, one novel and one reference work, we could either pick a novel first and then a reference book or pick a reference book and then a novel. Therefore the answer is 6/10*2/9 + 2/10*6/9 = 4/15.
Answer: E.
Answer: E
Question: The cost of 4 bags and 12 purses is Rs.1600, what is the cost of 10 bags and 30 purses?
Options:
A)Rs.3600
B)Rs.4000
C)Rs.3800
D)Rs.3900
E)None of these
Rationale: Explanation:
Cost of 4 bags + 12 purses = Rs.1600
Multiply each term by 5/2, we get,
Cost of 10 bags + 30 purses = Rs.4000.
Answer: Option B
Answer: B
Question: When positive integer n is divided by 7, the remainder is 1. When n is divided by 11, the remainder is 5. What is the smallest positive integer k such that k+n is a multiple of 77?
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: n = 7p + 1 = 11q + 5
n+6 = 7p + 7 = 11q + 11
n+6 is a multiple of 7 and 11, so it is a multiple of 77.
The answer is C.
Answer: C
Question: Starting with 0, a mathematician labels every non-negative integer as one of five types: alpha, beta, gamma, delta, or epsilon, in that repeating order as the integers increase. For instance, the integer 8 is labeled delta. What is the label on an integer that is the sum of an alpha raised to the seventh power and a delta raised to the seventh power?
Options:
A)alpha
B)beta
C)gamma
D)delta
E)epsilon
Rationale: Let the alpha be 5k and let the delta be 5j+3.
(5k)^7 + (5j+3)^7 which has the form 5k+2, which is a gamma.
The answer is C.
Answer: C
Question: Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
Options:
A)11 1/9
B)11 1/4
C)19 1/9
D)11 1/2
E)11 1/41
Rationale: 3/12 + x/15 = 1
x= 11 1/4
Answer: B
Answer: B
Question: Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is?
Options:
A)60 gallons
B)100 gallons
C)120 gallons
D)180 gallons
E)200 gallons
Rationale: Explanation:
Work done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24) = - 1/40
Volume of 1/40 part = 3 gallons\
Volume of whole = 3 * 40 = 120 gallons.
ANSWER IS C
Answer: C
Question: A and B undertake to do a piece of work for Rs. 1200. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they finish it in 3 days. Find the share of B.
Options:
A)250
B)450
C)750
D)800
E)None of them
Rationale: C's 1 day's work = 1/3-(1/6+1/8)=24
A : B : C = Ratio of their 1 day's work = 1/6:1/8:1/24= 4 : 3 : 1.
A’s share = Rs. (1200 *4/8) = Rs.600, B's share = Rs. (1200 *3/8) = Rs. 450
C's share = Rs. [1200 - (300 + 225») = Rs. 150.
Answer is B
Answer: B
Question: Given two fair dice, what is the probability Q that the sum of their numbers is 4 if exactly one die shows a 3?
Options:
A)a) 2/11
B)b) 1/18
C)c) 3/11
D)d) 2/39
E)e) 1/5
Rationale: If exactly one die shows 3, there are 10 such combinations (given that we have 2 fair dice).
1:3, 2:3, 4:3, 5:3, 6:3,
3:1, 3:2, 3:4, 3:5, 3:6
The sum of numbers would be 4 for two events: 1:3, 3:1.the probability Q that the sum of their numbers is 4 if exactly one die shows a 3
2/11 would be the answer if 'at least one of the die shows a 3'.A
Answer: A
Question: 60 + 5 * 12 / (180/3) = ?
Options:
A)60
B)120
C)13
D)61
E)50
Rationale: Explanation:
60 + 5 * 12 / (180/3) = 60 + 5 * 12 / (60)
= 60 + (5 * 12)/60 = 60 + 1 = 61.
ANSWER IS D
Answer: D
Question: A brick measures 20cm*10cm*7.5cm how many bricks will be requiredfor a wall 25m*2m*0.75m ?
Options:
A)24000
B)23000
C)22000
D)25000
E)27000
Rationale: 25*2*0.75=20/100*10/100*0.75/100*X25=1/100*XX=25000Answer :D
Answer: D
Question: The New York Classical Group is designing the liner notes for an upcoming CD release. There are 10 soloists featured on the album, but the liner notes are only 5 pages long, and therefore only have room for 5 of the soloists. The soloists are fighting over which of them will appear in the liner notes, though not about which page they appear on. How many different combinations E of soloists can appear in the liner notes?
Options:
A)5!
B)10!/(5!5!)
C)10!/5!
D)10!
E)10!*5!
Rationale: Total Soloists to choose from = 10
Soloist Required = 5
Question : How many different combinations E of soloists can appear in the liner notes?
The language of the question clearly mentions that only the combinations need to be calculated
i.e. Arrangement of the Soloists does NOT matter(Refer theHighlightedpart of the question)
Method-1:
Total Ways to Choose 5 out of 10 soloists = 10C5 = 10! / (5!*5!)
Method-2:
No. of ways to select and arrange 5 soloist on 5 Page = 10*9*8*7*6
Since the arrangement of 5 selected Notes (which can happen in 5! ways) doesn't NOT matter,
Therefore total ways to pick 5 out of 10 soloists = 10*9*8*7*6 / 5! = 10*9*8*7*6 *5! / (5!*5!) = 10! / (5!*5!)
Answer: Option B
Answer: B
Question: The largest prime number is?
Options:
A)11
B)13
C)5
D)7
E)9
Rationale: The largest prime number is 13.
B)
Answer: B
Question: A collection of books went on sale, and 2/3 of them were sold for $3 each. If none of the 36 remaining books were sold, what was the total amount received for the books that were sold?
Options:
A)$216
B)$135
C)$90
D)$60
E)$54
Rationale: Since 2/3 of the books in the collection were sold, 1/3 were not sold. The 36 unsold books represent 1/3 of the total number of books in the collection, and 2/3 of the total number of books equals 2(36) or 72. The total proceeds of the sale was 72($3) or $216. The best answer is therefore A.
Answer: A.
Answer: A
Question: A die is rolled twice. What is the probability of getting a sum equal to 9?
Options:
A)2/3
B)2/9
C)1/3
D)1/9
E)2/5
Rationale: Total number of outcomes possible when a die is rolled = 6 (∵ any one face out of the 6 faces)
Hence, total number of outcomes possible when a die is rolled twice, n(S) = 6 × 6 = 36
E = Getting a sum of 9 when the two dice fall = {(3, 6), {4, 5}, {5, 4}, (6, 3)}
Hence, n(E) = 4
P(E) = n(E)/n(S)=4/36=1/9
Answer is E
Answer: E
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?
Options:
A)278
B)166
C)151
D)270
E)109
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 250)/26 = 20
x = 270 m.
Answer:D
Answer: D
Question: One of the following numbers can be marked out as the odd one out. can you find which one?
1) 680986879
2) 716089780
3) 820670987
4) 932967879
Options:
A)The odd number is 680986879
B)The odd number is 820670987
C)The odd number is 716089780
D)The odd number is 932967879
E)None
Rationale: Correct Answer : B
if you add up the first three digits of all the numbers, it adds up to 14 except for second option 820670987
Answer: B