divelab/Sys2Bench huggingface dataset:
Question: A tank is filled in eight hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?
Options:
A)28
B)99
C)27
D)26
E)11
Rationale: Explanation:
1/A + 1/B + 1/C = 1/8 (Given)
Also given that A = 2B and B = 2C
=> 1/2B + 1/B + 2/B = 1/8
=> (1 + 2 + 4)/2B = 1/8
=> 2B/7 = 8
=> B = 28 hours.
Answer:A
Answer: A
Question: On dividing 144 by a number, the quotient is 13 and the remainder is 1. Find the divisor.
Options:
A)A)11
B)B)14
C)C)16
D)D)18
E)E)22
Rationale: d = (D-R)/Q
= (144 - 1)/13
= 143/13 = 11
A)
Answer: A
Question: Find large number from given question. The difference of 2 numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
Options:
A)1345
B)1450
C)1440
D)1546
E)1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Large number = 270+1365 = 1635
E
Answer: E
Question: P and Q invested in a business. The profit earned was divided in the ratio 2 : 3. If P invested Rs 40000, the amount invested by Q is
Options:
A)40000
B)50000
C)60000
D)70000
E)None of these
Rationale: Explanation :
Let the amount invested by Q = q
40000 : q = 2 : 3
=> 40000/q = 2/3
=> q = 40000 * (3/2) = 60000. Answer : Option C
Answer: C
Question: What is the largest 4 digit number exactly divisible by 50?
Options:
A)4676
B)4678
C)9950
D)9504
E)9936
Rationale: Largest 4 digit number = 9999
9999 ÷ 50 = 199, remainder = 49
Hence largest 4 digit number exactly divisible by 50
= 9999 - 49 = 9950
answer :C
Answer: C
Question: 2500÷10÷5=?
Options:
A)43
B)37
C)50
D)33
E)32
Rationale: 2500 ÷ 10 = 250
250 ÷ 5= 50
Answer is C
Answer: C
Question: A football field is 7200 square yards. If 1200 pounds of fertilizer are spread evenly across the entire field, how many pounds of fertilizer were spread over an area of the field totaling 3600 square yards?
Options:
A)450
B)600
C)750
D)2400
E)3200
Rationale: Answer A) 9600 yards need 1200 lbs
1 Yard will need 1200/7200 = 1/6 lbs
3600 Yards will need 1/6* 3600 Yards = 600lbs
B
Answer: B
Question: Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P,Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?
Options:
A)6/11
B)5/11
C)7/11
D)8/11
E)9/11
Rationale: Explanation:
Solution 1
Part of the tank filled by pipe A in 1 minute =1/30
Part of the tank filled by pipe B in 1 minute=1/20
Part of the tank filled by pipe C in 1 minute =1/10
Here we have to find the proportion of the solution R.
Pipe C discharges chemical solution R.
Part of the tank filled by pipe C in 3 minutes =3 X 1/10 = 3/10
Part of the tank filled by pipe A,B,C together in 1 minute =1/30 + 1/20 +1/10=11/60
Part of the tank filled by pipe A,B,C together in 3 minute =3 X 11/60 =11/20
Required proportion =(3/10) / (11/20)=3 X 20 / 10 X 11 = 6 /11.
ANSWER IS A
Answer: A
Question: In a village of 100 households, 65 have at least one DVD player, 75 have at least one cell phone, and 35 have at least one MP3 player. If x and y are respectively the greatest and lowest possible number of households that have all three of these devices, x – y is:
Options:
A)60
B)55
C)45
D)35
E)25
Rationale: Am I missing something here??? it seems straightforward......
The obvious maximum that have all 3 is 35, because you are limited by the SMALLEST number.
The minimum is simply the sum of the max of each people who DONT have the product, so:
100-75 = 25 don't have Cell
100-65 = 35 don't have DVD
and 100-35 = 65 don't have MP3
SO a total of 25+35+65 = 125 combined who might NOT have SOME combination of the 3 products. So subtract that from 100, to give you the minimum of the people who COULD have all 3 and you get 100-125 = -25.
35+25 = 60
A
Answer: A
Question: P is three times as fast as Q and working together, they can complete a work in 8 days. In how many days can Q alone complete the work?
Options:
A)32 days
B)16 days
C)13 days
D)15 days
E)19 days
Rationale: B
16 days
P = 3Q
P + Q = 3Q + Q = 4Q
These 4Q people can do the work in 8 days, which means Q can alone do the work in 4*8 =32 days.
Answer : A
Answer: A
Question: Suppose that f(x) is a function such that for every real number x,i)f(x)+f(1-x) = 13 and (ii) f(1+x) = 3+f(x). Then f(x)+f(-x)
must equal
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: Since (ii) holds for every real number x, it will remain valid if we replace x with
-x. Therefore, f(1-x) = 3+f(-x). Now, from (i), 13 = f(x)+f(1-x) = f(x)+3+f(-x)
so that f(x) + f(-x) = 13-3 = 10. (Observe that f(x) = 3x + 4 satisfies the conditions
in the problem.)
correct answer C
Answer: C
Question: Given that a “24-inch pizza” means circular pizza with a diameter of 12 inches, changing from an 12-inch pizza to a 24-inch pizza gives you approximately what percent increase in the total amount of pizza?
Options:
A)300
B)500
C)670
D)800
E)125
Rationale: area of 12 inch pizza= 6*6*pi=36 pi
area of 24 inch pizza =12*12*pi=144 pi
108/36*100=300% increase
hence answer is A
Answer: A
Question: Which one of the following option is the closest in the meaning to the word given below..
MITIGATE
Options:
A)Diminish
B)Divulge
C)Dedicate
D)Denote
E)Deno2S
Rationale: Explanation:
Mitigate means to make something less severe. Divulge means reveal. Denote means indicate. Diminish means to make or to cause something to become less in size, importance etc.
Answer: A
Answer: A
Question: Sonika deposited Rs.6000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 2% more. She would get how much?
Options:
A)9660
B)6560
C)7560
D)9560
E)8560
Rationale: (6000*3*2)/100 = 360
9200
--------
9560
ANSWER:D
Answer: D
Question: The average of first 10 natural numbers is?
Options:
A)7.7
B)5.5
C)9.0
D)9.6
E)5.9
Rationale: Explanation:
Sum of 10 natural no. = 110/2 = 55
Average = 55/10 = 5.5
Answer:B
Answer: B
Question: A number has exactly 32 factors out of which 4 are not composite. Product of these 4 factors (which are not composite) is 30. How many such numbers E are possible?
Options:
A)2
B)4
C)6
D)3
E)Not possible
Rationale: Firstly , we should note that 1 is NEITHER a prime nor a composite number.The first composite number is 4.Thus, when the problem states that there are 4 factors that are not composite, these nos are 1,2,3,5. Thus, the given number = 2^a*3^b*5^c. Also, (a+1)*(b+1)*(c+1) = 32. We can break down 32 into 3 integers as : 2*2*8 or 4*4*2
Also, the only possible combinations for a,b,c are : 3,3,1 OR 1,1,7. Thus, each combination has 3 possible orders and we have a total E of 6 possibilities.
C.
Answer: C
Question: A car travels first 160 km at 75 km/hr and the next 160 km at 90 km/hr. What is the average speed for the first 320 km of the tour?
Options:
A)71.11
B)71.12
C)71.1
D)71.17
E)81.81
Rationale: Car travels first 160 km at 75 km/hr
Time taken to travel first 160 km = distancespeed=160/75
Car travels next160 km at 90 km/hr
Time taken to travel next 160 km = distancespeed=160/90
Total distance traveled = 160+160=2×160
Total time taken = 160/75+160/90
Average speed = Total distance traveled/Total time taken=320/(160/75+160/90)=81.81 km/hr
Answer:E
Answer: E
Question: Of the final grades received by the students in a certain math course, 1/5 are A's, 1/4 are B's, 1/2 are C's, and the remaining 20 grades are D's. What is the number of students in the course?
Options:
A) 80
B) 110
C) 160
D) 200
E) 400
Rationale: We start by creating a variable for the total number of students in the math course. We can say:
T = Total number of students in the math course
Next, we can use variable T in an equation that we translate from the given information. We are given that, of the final grades received by the students in a certain math course, 1/5 are A's, 1/4 are B's, 1/2 are C's, and the remaining 20 grades are D's. Since this represents all the grades in the class, it represents all the students in the class. Thus we know:
#A’s + #B’s + #C’s + #D’s = Total number of students in the class
1/5(T) + ¼(T) + ½(T) + 20 = T
We can multiply the entire equation by 20 to cancel out the denominators of the fractions and we have:
4T + 5T + 10T + 400 = 20T
19T + 400 = 20T
400 = T
There are a total of 400 students in the math class.
Answer is E.
Answer: E
Question: Q' = 3Q - 3, what is the value of (4')' ?
Options:
A) 48
B) 57
C) 66
D) 72
E) 81
Rationale: (4')'=(3*4-3)'=9'=9*9-9=72
Answer D
Answer: D
Question: The forth proportional to 6,8,15 is?
Options:
A)15
B)12
C)18
D)20
E)24
Rationale: Let the fourth proportional to 6,8,15 be x
then 6:8::15:x
6x = 8*15
x = 20
Answer is D
Answer: D
Question: A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
Options:
A)356
B)352
C)350
D)359
E)358
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 39 = 50/3
3(x + 300) = 1950 è x = 350m.
Answer: Option C
Answer: C
Question: A train 450 m long is running at a speed of 68 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train?
Options:
A)5 sec
B)39 sec
C)27 sec
D)15 sec
E)18 sec
Rationale: Speed of the train relative to man = (68 - 8) kmph
= (60* 5/18) m/sec = (50/3)m/sec
Time taken by the train to cross the man
= Time taken by It to cover 450 m at 50/3 m / sec = 450 *3/ 50 sec = 27 sec
Answer : C.
Answer: C
Question: The greatest number of four digits which is divisible by 21, 35, 49 and 63
Options:
A)6612
B)6615
C)6610
D)6611
E)5671
Rationale: Explanation:
The greatest four digit number is 9999
L.C.M of 21, 35, 49 and 63 is 6615.
On dividing 9999by 6615, the remainder is 3384
Required number is 9999 - 3384 is 6615
Answer: Option B
Answer: B
Question: If by selling an article for Rs.60, a person loses 1/7 of money, what would he have gained or lost % by selling it for Rs.77?
Options:
A)5%
B)10%
C)12%
D)15%
E)17%
Rationale: Sol. CP - = EC7 = 70 1-7 6 77-70 % Profit = 100 = 10%
B
Answer: B
Question: In a class of 140 students, 60% of them passed. By what percent is the number of students who passed more than the number of failed students?
Options:
A)90%
B)20%
C)80%
D)50%
E)20%
Rationale: Number of students passed = 60% of 140
= 60/100 * 140 = 84
Number of students failed
= 140 - 84 = 56.
Required percentage
= 28/56 * 100 = 50%.
Answer:D
Answer: D
Question: S:E = 1:3
E:M = 3:5
------------
S:E:M = 3:9:15
3/27 * 162 = 18
Options:
A)18
B)16
C)16
D)17
E)19
Rationale: S:E = 1:3
E:M = 3:5
------------
S:E:M = 3:9:15
3/27 * 162 = 18
Answer: A
Answer: A
Question: There is enough provisions for 9600 women in an army camp for 400 days. If there were 4800 men less, how long will the provision last?
Options:
A)799
B)800
C)801
D)802
E)803
Rationale: We have, M1D1 = M2D2
9600*400= 4800* D2
D2 = 9600*400/4800 = 800 days.
ANSWER:B
Answer: B
Question: A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of this son is
Options:
A)21 years
B)22 years
C)23 years
D)24 years
E)25 years
Rationale: Explanation:
Let's Son age is x, then Father age is x+24.
=> 2(x+2) = (x+24+2)
=> 2x+4 = x+26
=> x = 22 years
Answer: Option B
Answer: B
Question: Find the one which does not belong to that group ?
Options:
A)36
B)71
C)62
D)12
E)57
Rationale: Explanation:
41, 43, 47 and 53 are prime numbers, but not 57.
Answer:E
Answer: E
Question: The speed of a boat in still water is 18 kmph. What is the speed of the stream if the boat can cover 48 km downstream or 32 km upstream in the same time?
Options:
A)4 kmph
B)5 kmph
C)6 kmph
D)7 kmph
E)8 kmph
Rationale: X = the speed of the stream
(18 + X) / (18 - X) = 2/1
18+ X = 36 - 2X
3X = 18
X = 6 km/hour
If the speed of the stream is 6km/hour, then the 'downstream' speed of the boat is 18+6 = 24km/hour and the 'upstream' speed of the boat is 18-6 = 12km/hour. In that way, if the boat traveled for 2 hours, it would travel 2x24 = 48km downstream and 2x12 = 24km/hour upstream.
Answer : C
Answer: C
Question: What is the difference between the place value and the face value of 7 in the numeral 297832?
Options:
A)None of these
B)5993
C)994
D)5994
E)995
Rationale: Explanation:
Place value of 6 = 7000
Face value of 6 = 7
Difference = 6000 - 7 = 5993
Answer: B
Answer: B
Question: When the oil from a circular cylinder leaked, the formula for the speed of the leak is V = kh^2, where h was the height of the remaining oil and k was constant. If the height of the cylinder is 2, the speed of the leak is Vâ€™, When the height of the oil remaining is 10, what was the speed of the leak, in terms of Vâ€™?
Options:
A)2Vâ€™
B)25Vâ€™
C)Vâ€™/2
D)Vâ€™/4
E)Vâ€™
Rationale: When h=2 v=V'
So V' = k.4
Hence k = V'/4
Now when h=10
v=(V'/4).10^2
v=V'.100/4
v=25V'
Ans : B
Answer: B
Question: Subtracting 10% from X is the same as multiplying X by what number?
Options:
A)80%
B)90%
C)10%
D)50%
E)60%
Rationale: Explanation:
X - (10/100) X = X * ?
? = 90%
ANSWER IS B
Answer: B
Question: A 10-by-9 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?
Options:
A)The volume of the cylinder with height 10 is 90/pi cubic inches greater than the volume of the cylinder with height 6.
B)The volume of the cylinder with height 9 is 90/pi cubic inches greater than the volume of the cylinder with height 10.
C)The volume of the cylinder with height 10 is 90pi cubic inches greater than the volume of the cylinder with height 6.
D)The volume of the cylinder with height 9 is 90pi cubic inches greater than the volume of the cylinder with height 10.
E)The volume of the cylinder with height 9 is 240/pi cubic inches greater than the volume of the cylinder with height 10.
Rationale: Pretty straightforward. Plug in the values to compute the volume of the cylinder. Keep in mind 9 and 10 are the circumference of the base and not the radius. B is the right answer.
Answer: B
Question: Eric, Nick and Archi make contributions to the Society Of Nature Protection in the ratio of 5:3:2.5. If altogether they contribute 5250 Nis, how much more money does Nick contribute than Archi?
Options:
A)128 Nis
B)212 Nis
C)234 Nis
D)250 Nis
E)288 Nis
Rationale: E:N:A 5:3:2.5
so total = 5x + 3x + 2.5 x = 10.5 x = 5250
so x = 500
Nick Contribution is 0.5 more than Archi so 0.5 x =0.5 * 500 = 250
So D. 250 Nis is the correct answer
Answer: D
Question: The sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers?
Options:
A)180
B)282
C)267
D)287
E)207
Rationale: Let the five numbers be P, Q, R, S and T.
=> P + Q + R + S + T = 655.
(P + Q)/2 = 85 and R = 125
P + Q = 170 and R = 125
P + Q + R = 295
S + T = 655 - (P + Q + R) = 360
Average of the last two numbers
= (S + T)/2 = 180
Answer:A
Answer: A
Question: The average weight of a group of boys is 30 kg. After a boy of weight 45 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
Options:
A)14
B)15
C)16
D)17
E)18
Rationale: Let the number off boys in the group originally be x.
Total weight of the boys = 30x
After the boy weighing 45 kg joins the group, total weight of boys = 30x + 45
So 30x + 45 = 31(x + 1) = > x = 14.
Answer: A
Answer: A
Question: In a two-digit, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:
Options:
A)24
B)26
C)42
D)46
E)none
Rationale: Let the ten's digit be x.
Then, unit's digit = x + 2.
Number = 10x + (x + 2) = 11x + 2.
Sum of digits = x + (x + 2) = 2x + 2.
(11x + 2)(2x + 2) = 144
22x2 + 26x - 140 = 0
11x2 + 13x - 70 = 0
(x - 2)(11x + 35) = 0
x = 2.
Hence, required number = 11x + 2 = 24
Answer = A
Answer: A
Question: The ratio between the present ages of P and Q is 5:7 respectively.If the difference between Q’s present age and P’s age after 6 years is 2,what is the total of P’s and Q’s present ages ?
Options:
A)48 years
B)52 years
C)56 years
D)Cannot be determined
E)None of these
Rationale: Solution
Let the present ages of P and Q be 5x years and 7x years respectively.
Then,7x -(5x +6)=2 ⇔ 2x =8 ⇔ x=4.
∴ Required sum =5x +7x =12x =48 years. Answer A
Answer: A
Question: 58, 52, 46, 40, 34, ... ?
Options:
A)20
B)22
C)28
D)27
E)32
Rationale: Each number is 6 less than the previous number.
58-6=52
52-6=46
46-6=40
40-6=34
34-6=28
ANSWER:C
Answer: C
Question: Two years ago, John’s age was half of the age he will be in 8 years. How old is he now?
Options:
A)14years
B)15years
C)16years
D)12years
E)18years
Rationale: Let John=j,j-2=(j+8)/2,then j=12years
ANSWER:D
Answer: D
Question: If all the fractions 3/10, 1/16, 4/11, 2/9, 1/7, 5/14 and 5/24 arranged in descending order of their values, then which one will be the third?
Options:
A)1/16
B)2/9
C)3/10
D)4/11
E)None of these
Rationale: 3/10 = 0.3, 1/16 = 0.0625, 4/11 = 0.36, 2/9 = 0.22, 1/7 = 0.14, 5/14 = 0.36 and 5/24 = 0.21
4/11 > 5/14 > 3/10 > 2/9 > 5/24 > 1/7 > 1/16
3/10 will be the third.
ANSWER:C
Answer: C
Question: What is the remainder when 1250*1090*1045*1055 is divided by 18?
Options:
A)34
B)19
C)16
D)14
E)10
Rationale: OA is 'C'.
OE:
take the remainder from each of 1250/18, 1090/18 and so on..
1250/18 gives remainder = 8
1090/18 gives remainder = 10
1045/18 gives remainder = 1
1055/18 gives remainder = 11
the net remainder is the product of above individual remainders. i.e = 8*10*1*11
break them into pairs 8*10/18 gives remainder 8
and 1*11/18 gives remainder 11
so 8*11/18 gives remainder 16.
Answer: C
Answer: C
Question: The captain of a cricket team of 11 players is 25 years old and the wicket-keeper is 3 years older. If the age of these two players are replaced by that of another two players, the average of the cricket team drops by 2 years. Find the average age of these two players.
Options:
A)15 years
B)15.5 years
C)17 years
D)16.5 years
E)None of the above
Rationale: Let average of team = x years
Then, 25 + 28 + S9 = 11x … (i)
where S9 is the sum of ages of remaining players
Also, Np + S9 = 11(x – 2) ,…(ii)
where Np is the sum of ages of new players
(i) – (ii) ⇒ 53 – Np = 22
⇒ Np = 31
∴ Average age of new two players = 31⁄2 = 15.5 years
Answer B
Answer: B
Question: In the exam the average was found to be p mark. After deducting typographical error the average marks of 120 student reduced from 90 to 70 . Due to this the average came down by 12 marks. What was the number of students who took the exam?
Options:
A)100
B)120
C)200
D)130
E)160
Rationale: Explanation :
Number of student = (90-70) * 120/12 = 200
Answer : C
Answer: C
Question: For every integer n ≥ 3, the function g(n) is defined as the product of all the odd integers from 1 to n, inclusive. What is the value of g(106) – g(103)?
Options:
A)100
B)99
C)98
D)102
E)104
Rationale: g(106) = 1*3*5*7*9*...*99*101*103*105
g(103) = 1*3*5*7*9*...*99*101*103
g(106) - g(103) = 1*3*5*7*9*...*99*101*103*105 - 1*3*5*7*9*...*99*101*103 = 1*3*5*7*9*...*103*(105 - 1) = 1*3*5*7*9*...*99*101*103*104
hence:E
Answer: E
Question: What is the area of square field whose side of length 14 m?
Options:
A)225
B)196
C)266
D)288
E)261
Rationale: 14 * 14 = 196 sq m
Answer: B
Answer: B
Question: By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?
Options:
A)42 6/8%
B)42 8/7%
C)482 6/7%
D)42 6/7%
E)42 1/7%
Rationale: SP = CP + g
50 SP = 50 CP + 15 SP
35 SP = 50 CP
35 --- 15 CP gain
100 --- ? => 42 6/7%
Answer:D
Answer: D
Question: A man swims downstream 60 km and upstream 100 km taking 10 hours each time, what is the speed of the man in still water?
Options:
A)24
B)42
C)6
D)8
E)12
Rationale: 60 --- 10 DS = 6
? ---- 1
100 ----10 US = 10
? ---- 1 M = ?
M = (10 + 6)/2 = 8
Answer:D
Answer: D
Question: A positive integer is called "square-Free" if it has no factor that is the square of an integer greater than 1. If n is an even square-free integer, which of the following must also be square free?
Options:
A)n/2
B)2n
C)n+2
D)n^2
E)none of the above
Rationale: Per definition a square-free integer has primes in power of 1. For example 5^3 is NOT square-free because it's a multiple of 5^2.
We are told that n=2k, since n itself is square-free, then k also must be square-free --> n/2=k.
Answer: A.
number for n. Say n=2, then among A, B, C, and D, only A (n/2=1) will be square free.
Answer: A
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
Options:
A)228
B)278
C)120
D)998
E)232
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6 = 120 m.
Answer: C
Answer: C
Question: Cost of 16 mirror and 8 comb is Rs.368 and the cost of 4 mirror and 4 comb is Rs.96. Find the cost of each mirror?
Options:
A)10
B)12
C)20
D)21
E)22
Rationale: Let the cost of each pen and pencil be 'p' and 'q' respectively.
16m + 8c = 368 --- (1)
4m + 4c = 96
8m + 8c = 192 --- (2)
(1) - (2) => 8p = 176
=> m = 22
E
Answer: E
Question: Find the greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively.
Options:
A)127
B)157
C)147
D)137
E)None of them
Rationale: Required number = H.C.F. of (1657 - 6) and (2037 - 5) = H.C.F. of 1651 and 2032
_______
1651 ) 2032 ( 1 1651
1651_______
381 ) 1651 ( 4
1524_________
127 ) 381 ( 3
381
0
Required number = 127.
Answer is A.
Answer: A
Question: There are 5 people and 3 chairs. In how many different ways people can occupy the chairs?
Options:
A)60
B)70
C)80
D)90
E)100
Rationale: number of ways = 5*4*3 = 60
Answer is A
Answer: A
Question: A certain ski shop sells pairs of gloves in 13 different colors. If one pair of each color is dropped in a bag and a store clerk reaches in to draw two individual gloves simultaneously and at random, what is the probability that she draws two gloves of the same color?
Options:
A)1/144
B)1/143
C)1/25
D)1/23
E)1/12
Rationale: there are 13 different colours sothere are 13 pairs of gloves dropped..
first can be any of 26..so 26/26..
second has to be its pair, which will be just one out of remaining 25.. 1/25..
overall prob=26/26*1/25= 1/25..
C
Answer: C
Question: Of the eight participants in a certain competition, half are male, and half of the males are younger than 18 years of age. If half of the female competitors are also younger than 18 years of age, into how many distinct groups of 4 competitors could the participants be divided if each group must contain two males under 18 years of age and 2 females over 18 years of age?
Options:
A)1
B)4
C)6
D)9
E)20
Rationale: M under 18 - 2
F above 18 - 2
How many distinct groups can be formed now: 2c2 * 2c2 = 1
Answer : A
Answer: A
Question: Mike weighs twice as much as Mary. Mike's weight is 50% of Michelle's weight. Alan weighs 40% of Charlie's weight. Charlie weighs 180% of Mary's weight. Which of these 5 people weighs the highest?
Options:
A)Mary
B)Mike
C)Michelle
D)Alan
E)Charlie
Rationale: Mary < Mike < Michelle
Alan < Charlie
Let x be Mary's weight.
Michelle's weight is 4x and Charlie's weight is 1.8x.
The answer is C.
Answer: C
Question: A certain stock exchange designates each stock with a two-letter or three-letter code, where each letter is selected from the 26 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes without using the letters A or Z?
Options:
A)13.8
B)14,400
C)15,000
D)15,600
E)16,200
Rationale: The number of two-letter codes is 24*24=576.
The number of three-letter codes is 24*24*24=13,824.
The total number of codes is 576+13,824=14,400.
The answer is B.
Answer: B
Question: If difference between compound interest and simple interest on a sum at 10% P.a. for 2 years is Rs.51 then sum is
Options:
A)Rs.5000
B)Rs.5100
C)Rs.5800
D)Rs.6000
E)Rs.6200
Rationale: p(r/100)^2=C.I-S.I
P(10/100)^2=51
5100
ANSWER:B
Answer: B
Question: In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
Options:
A)60
B)65
C)63
D)70
E)75
Rationale: Req 7C5*3C2==>63
ANSWER C
Answer: C