divelab/Sys2Bench huggingface dataset:
Question: After a storm deposits 120 billion gallons of water into the city reservoir, the reservoir is 60% full. If the original contents of the reservoir totaled 240 billion gallons, the reservoir was approximately what percentage full before the storm?
Options:
A)40%
B)48%
C)54%
D)58%
E)65%
Rationale: When the storm deposited 120 billion gallons, volume of water in the reservoir = 240 + 120 = 360 billion gallons
If this is only 60% of the capacity of the reservoir, the total capacity of the reservoir = 360/0.6 = 600 billion gallons
Therefore percentage of reservoir that was full before the storm = (240/600)*100 = 40%
Option C
Answer: C
Question: A prize of $800 is to be distributed among 20 winners, each of whom must be awarded at least $20. If 2/5 of the prize will be distributed to 3/5 of the winners, what is the greatest possible individual award?
Options:
A)$200
B)$220
C)$280
D)$300
E)$340
Rationale: Total value of the prize =$800
Number of people = 20
2/5 of 800 (=$320) should be distributed among 3/5 of 20 (=12 people ) with each getting $20 each. Remaining money = 800-320 = $480. Now in order to 'maximize' 1 prize, we need to minimise the others and we have been given that each should get $20. Thus, minimising the remaining 7 people (=20-12-1. '-1' to exclude 1 that needs to be maximised) = 7*20=140.
Thus the maximum award can be = 480-140 = $340, hence E is the correct answer.
Answer: E
Question: A professional basketball player just signed a contract that has a 10% raise in base salary from last year to this year. The contract also has provisions for a performance bonus of up to $10,000. If he earns the maximum performance bonus, his new effective salary will be a 10.5% raise over last year's total salary, when he received no performance bonus. Assuming he earns the full performance bonus, what will be his new salary?
Options:
A)2,010,000
B)2,110,000
C)2,150,000
D)2,200,000
E)2,210,000
Rationale: let x=old salary
then (1+.10)*x+10,000 = (1+.105)*x
i.e. new base salary +10,000 = effective new salary
thus 1.1*x + 10,000 = 1.105*x
10,000 = .005*x
2,000,000 = x
thus the new effective salary is 1.105*2,000,000 = 2,210,000
E
Answer: E
Question: A train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
Options:
A)32 kmph
B)76 kmph
C)34 kmph
D)43 kmph
E)40 kmph
Rationale: S = (100 + 300)/45
= 400/45 * 18/5
= 32
Answer:A
Answer: A
Question: Nine highschool girls gather at the gym for a game of mini-foot ball. Three teams of 3 people each will be created. How many ways are there to create these 3 teams?
Options:
A)27
B)51
C)45
D)175
E)12
Rationale: Arrange the 6 boys in a straight line in 6! ways.
The first three form team 1, next three form team 2 and last three form team 3. But in each team, the boys are arranged in first, second third positions so you need to un-arrange them by dividing by 3! three times (once for each team). You get 6!/(2! * 2! * 2!)
Also, there are no distinct teams - team1, team2 and team3. You just have three teams. So you also need to un-arrange the three teams by dividing by another 3!.
You get 6!/(2! * 2! * 2!) * 2! = 45
Answer (C)
You get 6!/(2! * 2! * 2!) * 2!
Answer : C
Answer: C
Question: The tax on a commodity is diminished by 20% but its consumption is increased by 15%. Find the decrease percent in the revenue derived from it?
Options:
A)12%
B)14%
C)16%
D)20%
E)8%
Rationale: Explanation:
100 * 100 = 10000
80 * 115 = 9200
10000------- 800
100 ------- ? = 8%
E)
Answer: E
Question: A circle is circumscribed around a quadrilateral, and the quadrilateral is ABCD, What is the value of y when angle B is 75 degrees?
Options:
A)75
B)95
C)105
D)115
E)135
Rationale: An inscribed angle is an angle in a circle composed of two chords with a common endpoint, that is, an angle with its vertex on the circle. In this problem, all four lettered angles are inscribed angles.
An inscribed angle necessarily opens to intersect an arc (the technical word is to subtend an arc). The Inscribed Angle Theorem said that the measure of an inscribed angle is always half the measure of the arc it intersects, or subtends.
angle B = 75 degrees
Thus,
arc ADC = 150 degrees
A whole circle has 360 degrees of arc, so arc ABC should be the rest of the circle.
arc ABC = 360 - 150 = 210 degrees
The angle that intersects this arc, angle D, should have half this measure.
angle D = y = 210/2 = 105 degrees
Answer =(C)
Answer: C
Question: Jane makes toy bears. When she works with an assistant, she makes 89 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent?
Options:
A)20%
B)80%
C)110%
D)180%
E)200%
Rationale: Let's assume just Jane 40 bears per 40/hrs a week, so that is 1 bear/hr. With an assistant she makes 75.6 bears per 36 hours a week or 2.1 bears/hr ([40 bears * 1.89] / [40 hrs * .90]).
[(2.1 - 1)/1] * 100% = 110%
ANSWER:C
Answer: C
Question: The least number by which 72 must be multiplied in order to produce a multiple of 112, is:
Options:
A)6
B)12
C)14
D)18
E)20
Rationale: Required number is divisible by 72 as well as by 112, if it is divisible by their LCM, which is 1008.
Now, 1008 when divided by 72, gives quotient= 14.
Therefore, required number= 14.
Answer: C
Answer: C
Question: Which of the following is closer to √0.1+√0.15?
Options:
A)0.5
B)0.7
C)0.9
D)1.1
E)1.2
Rationale: √0.1+√0.15=approximately √0.09+√0.16=0.3+0.4=0.7 . Hence, the correct answer is B.
Answer: B
Question: As x increases from 165 to 163, which of the following must increase?
I. 2x - 5
II. 1 - 1/x
III. 1/(x^2 - x)
Options:
A) I only
B) III only
C) I and II
D) I and III
E) II and III
Rationale: I. 2x - 5 --> x increases from 165 to 163 --> 2x increases --> 2x - 5 increases. Correct.
II. 1 - 1/x --> x increases from 165 to 163 --> 1/x decreases --> 1 -1/x increases. Correct.
III. 1/(x^2 - x) --> x increases from 165 to 163 --> x^2-x increases --> 1/(x^2 - x) decreases.
Answer: C.
Answer: C
Question: What is the area of the square with the following coordinates: (x, y), (20, 20), (20, 9), (x, 9)?
Options:
A)121
B)132
C)144
D)156
E)169
Rationale: To find the area of a square, knowing the length of one side is sufficient.
From the coordinates given, we can see that one side equals 11.
The area is 11*11 = 121.
The answer is A.
Answer: A
Question: Thirty men can do a work in 24 days. In how many days can 20 men can do the work, given that the time spent per day is increased by one-third of the previous time?
Options:
A)27 days
B)77 days
C)88 days
D)66 days
E)22 days
Rationale: Let the number of hours working per day initially be x. we have M1 D1 H1
= M2 D2 H2
30 * 24 * x = 20 * d2 * (4x)/3
=> d2 = (30 * 24 * 3)/(24 * 4)
= 27 days.
Answer:A
Answer: A
Question: Ram's average (arithmetic mean) test score on 4 tests is 78. What must be the student's score on a 5th test for the Ram's average score on the 5 tests to be 80?
Options:
A) 80
B) 82
C) 84
D) 86
E) 88
Rationale: E. 88
Ram must score at least an 80 for sure. If he scores an 8, then he will need to score 2 pots for each of the 4 other tests tomake upthe difference. They each were at 78 (at least the average is, but this is a small point and doesn't matter to the answer). So 4 tests that were each 2 points short of the 80 average that is desired means the next test must be 8 points higher than the desired average, so 80+8 = 88.
Answer: E
Question: The weight of every type A widget is the same, the weight of every type B widget is the same, and the weight of every type C widget is the same. If the weight of 7 type A widgets is equal to the weight of 4 type B widgets, and the weight of 3 type B widgets is equal to the weight of 7 type C widgets. What is the ratio of the total weight of 1 type A widget and 1 type B widget, to the total weight of 1 type B widget and 1 type C widget?
Options:
A)5:4
B)7:6
C)9:8
D)11:10
E)13:12
Rationale: 3B = 7C and so B = 7C/3
7A = 4B and so A = 4B/7 = 4C/3
A+B = 4C/3 + 7C/3 = 11C/3
B+C = 7C/3 + C = 10C/3
The ratio of A+B:B+C = 11:10
The answer is D.
Answer: D
Question: A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation?
Options:
A)20
B)99
C)28
D)18
E)11
Rationale: Explanation:
There are three ladies and five gentlemen and a committee of 5 members to be formed.
Number of ways such that two ladies are always included in the committee = â¶Câ‚ƒ = (6 * 5 * 4)/6 = 20.
Answer:A
Answer: A
Question: In how many ways the letters of the word LOOC be arranged?
Options:
A)10
B)11
C)12
D)16
E)18
Rationale: In this four letters means 4! = 24 ways
But 'O' is repeated two times.
And thus we divide the final ways by 2. I.e. there are only 24/2 = 12 ways of arranging the letters of this word.
LOOK, LOKO, LKOO, KOOL, KOLO, KLOO, OOLK, OOKL, OLOK, OKOL, OLKO, OKLO = 12 Ways
C
Answer: C
Question: A closed cylindrical tank contains 36 pie cubic feet of water and its filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of water in the tank is 4 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?
Options:
A)0 feet
B)1 feet
C)2 feet
D)3 feet
E)4 feet
Rationale: 36 pie cubic feet of water and its filled to half tank's capacity...
volume of tank = 72 Pie cubic feet
height of tank = 4*2 = 8 feet ( since tank is placed upright on its circular base on level ground, the height of water in the tank is 4 feet.)
72 pie = pie * r2*8
r2=9
r = 3 feet
ANSWER:D
Answer: D
Question: The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 60 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam.
Options:
A)22
B)27
C)15
D)99
E)21
Rationale: Let the number of students who wrote the exam be x.
Total marks of students = 80 x.
Total marks of (x - 5) students = 90(x - 5)
80x - (5 * 60) = 90(x - 5)
150 = 10x => x = 15.Answer: C
Answer: C
Question: If the square root of p^2 is an integer, which of the following must be true?
I. p^2 has an odd number of factors
II. p^2 can be expressed as the product of an even number of prime factors
III. p has an even number of factors
Options:
A)I
B)II
C)III
D)I and II
E)II and III
Rationale: I. p^2 is a perfect square and a perfect square has pairs of factors and '1' with it. The total number of factors is odd
II. If p = 3 then p^2 = 9. The prime factors will always remain even as the p is an integer and the pairs have to come out of square root to make p an integer.
III. This is not true always. Let us say p = 4, it has three factors: 1, 2 and 4. Hence it will not hold true always.
Hence D is the answer.
Answer: D
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
Options:
A)22 sec
B)88 sec
C)48 sec
D)18 sec
E)9 sec
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 6/125 = 48 sec.
Answer:C
Answer: C
Question: Tom, working alone, can paint a room in 6 hours. Peter and John, working independently, can paint the same room in 3 hours and 4 hours, respectively. Tom starts painting the room and works on his own for one hour. He is then joined by Peter and they work together for an hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?
Options:
A)7/15
B)9/20
C)11/25
D)13/27
E)15/31
Rationale: Tom paints 1/6 of the room in the first hour.
Tom and Peter paint 1/6+1/3 = 1/2 of the room in the next hour for a total of 4/6.
The three people then paint the remaining 2/6 in a time of (2/6) / (3/4) = 4/9 hours
Peter worked for 13/9 hours so he painted 13/9 * 1/3 = 13/27 of the room.
The answer is D.
Answer: D
Question: The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
Options:
A)7%
B)4%
C)9%
D)42%
E)2%
Rationale: 65*(90/100)*((100-x)/100)
= 56.16
x = 4%
Answer:B
Answer: B
Question: What will come in place of the x in the following Number series? 12, 38, 116, 350, 1052, 3158, 9476, x
Options:
A)2643
B)5464
C)3456
D)7554
E)28430
Rationale: 12
12 Ã— 3 + 2 = 38
38 Ã— 3 + 2 = 116
116 Ã— 3 + 2 = 350
350 Ã— 3 + 2 = 1052
1052 Ã— 3 + 2 = 3158
3158 Ã— 3 + 2 = 9476
9476 Ã— 3 + 2 = 28430
E
Answer: E
Question: Find the simple interest on Rs.500 for 9 months at 6 paisa per month?
Options:
A)287
B)270
C)276
D)129
E)211
Rationale: I = (500*9*6)/100 = 270
Answer: B
Answer: B
Question: If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Joe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 45 miles ahead of Joe?
Options:
A)15
B)60
C)75
D)90
E)210
Rationale: This type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30-40 seconds for a difficult one.
Teena covers 55 miles in 60 mins.
Joe covers 40 miles in 60 mins
So teena gains 15 miles every 60 mins
Teena need to cover 7.5 +45 miles.
Teena can cover 7.5 miles in 30 mins
Teena will cover 45 miles in 180 mins
So answer 30+180= 210 mins.(ANSWER E)
Answer: E
Question: If P(A) = 6/17, P(B) = 5/17, and P(A ∪ B) = 4/17 Find P(B|A)?
Options:
A)2/3
B)3/5
C)2/7
D)3/7
E)4/9
Rationale: P(B|A) = P(A ∪ B)/P(A)
P(B|A) = (4/17)/(6/17) = 4/6 = 2/3.
A
Answer: A
Question: A bag contains 2 red, 2 green, and 3 white balls. Three balls are picked up one by one without replacement. What is the probability that there will be at least one red ball?
Options:
A)5/7
B)11/14
C)17/21
D)19/28
E)23/35
Rationale: P(no red balls) = 5/7*4/6*3/5 = 2/7
P(at least one red ball) = 1 - 2/7 = 5/7
The answer is A.
Answer: A
Question: If A is to be chosen at random from the set {8,1} and B is to be chosen at random from the set {2,7,9,6}, what is the probability that AB will be even?
Options:
A)5/9
B)5/4
C)3/8
D)9/7
E)2/5
Rationale: Method-1
AB will be even when
1) A is even and B is odd, Probability of A even is (1/2) and Probability of B odd is (2/4), so Probability of Case(1) = (1/2)*(2/4) = (2/8)
2) A is Odd and B is Even, Probability of A Odd is (1/2) and Probability of B Even is (2/4), so Probability of Case(2) = (1/2)*(2/4) = (2/8)
3) A is even and B is Even, Probability of A even is (1/2) and Probability of B Even is (2/4), so Probability of Case(1) = (1/2)*(2/4) = (2/8)
Total Favorable Probability = (2/8)+(4/8)+(4/8) = (10/8) = 5/4
Answer: option B
Answer: B
Question: If a^3 is divisible by 240 what is the least possible value of integer a?
Options:
A)12
B)30
C)60
D)90
E)120
Rationale: 240 can be written as (2^4)*3*5.
For a^3 to be divisible by 240 it should contain atleast 2^4 and 3 and 5 in its factors. We can leave out option A because 12 doesnt have 5 as one of its factor. Now if we check for option B, 30 can be written as 2*3*5, hence 30^3 will have 3 as the maximum power of 2, so we can leave out this option too.
Option C is the right answer if we follow the same method as we followed for other two previous options.
60 = (2^2)*3*5; 60^3 = (2^6)*(3^3)*(5^3). So it shows that 60^3 is divisible by 240 and hence the answer.
Answer : C
Answer: C
Question: If the price of bananas goes down by 10%, find the percentage of increase that a family should effect in its consumption so as not to increase expenditure on this account?
Options:
A)13(1/9)%
B)15(1/9)%
C)11(1/9)%
D)12(1/9)%
E)none of these
Rationale: Increase in consumption
= [(P/(100 - P)] X 100)%
= [(10/(100 - 10)] X 100)%
= 11(1/9)%
ANSWER:C
Answer: C
Question: A man distributed Rs. 100 equally among his friends. If there had been 5 more friends, each would have received one rupee less. How many friends had he ?
Options:
A)20
B)25
C)30
D)35
E)40
Rationale: firstly we have 20 friends and money wiill be distribute each of them 5 rupee
then 5 more friends
it means total no frnd=25 each recv 4 rupee
which means all recv 1 less rupee
ANSWER:B
Answer: B
Question: If (x - 1)^2 = 361, which of the following could be the value of x - 4?
Options:
A)17
B)15
C)-22
D)-24
E)-26
Rationale: (x - 1)^2 = 361
(x - 1) = 19 or -19
x = 20 or -18
x - 4 = 16 or -22
The answer is C.
Answer: C
Question: A car traveled 35% of the way from Town X to Town Y at an average speed of 35 mph. The car traveled at an average speed of v mph for the remaining part of the trip. The average speed for the entire trip was 50 mph. What is v in mph?
Options:
A)45
B)65
C)55
D)75
E)85
Rationale: Assume total distance = 100miles
Time taken for 35 miles = 35/35 = 1 hour
Time taken for the rest of the 65 miles = 65/v hours.
Average speed = 50
Therefore the total time needed = 2 hours.
2 = 1 + 65/v
Hence v = 65 mph
Answer : B
Answer: B
Question: If the average of 5 positive integers is 65 and the difference between the largest and the smallest of these 5 numbers is 10, what is the maximum value possible for the largest of these 5 integers?
Options:
A)50
B)52
C)59
D)68
E)73
Rationale: Sum of 5 Integer (a, b, c, d, e) = 5*65 = 325
e - a = 10
i.e. e = a+10
For e to be maximum remaining 4 MUST be as small as possible
Since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers
i.e. a+a+a+a+(a+10) = 325
i.e. 5a = 315
i.e. a = 63
i.e. Largest e = 63+10 = 73
Answer: option E
Answer: E
Question: A salesperson received a commission of 3 percent of the sale price for each of the first 100 machines that she sold and 4 percent of the sale price for each machine that she sold after the first 100. If the sale price of each machine was $10,000 and the salesperson received a $42,000 commission, how many machines did she sell?
Options:
A) 90
B) 103
C) 130
D) 115
E) 120
Rationale: First 100 machines = 3% commission = 0.03*100*10000 = 30000
Commission from sale of next machines = 42000 - 30000 = 12000
So 30 more machines..
Total = 130 machines
IMO C...
Answer: C
Question: In a class of 50 students, 20 play Basketball, 15 play Cricket and 11 play Football. 7 play both Basketball and Cricket, 4 play Cricket and Football and 5 play Basketball and football. If 18 students do not play any of these given sports, how many students play exactly two of these sports?
Options:
A)67
B)45
C)10
D)675
E)688
Rationale: Notice that7 play both Basketball and Cricket does not mean that out of those 7, some does not play Football too. The same for Cricket/Football and Basketball/Football.
[color=#ffff00]{Total}={Basketball}+{Cricket}+{Football}-{HC+CH+HF}+{All three}+{Neither}For more checkADVANCED OVERLAPPING SETS PROBLEMS
[/color]
50=20+15+11-(7+4+5)+{All three}+18 --> {All three}=2;
Those who play ONLY Basketball and Cricket are 7-2=5;
Those who play ONLY Cricket and Football are 4-2=2;
Those who play ONLY Basketball and Football are 5-2=3;
Hence, 5+2+3=10 students play exactly two of these sports.
Answer: C.
Answer: C
Question: Three pieces of timber 30 m, 35 m and 45 m long have to be divided into planks of the same length, What is the greatest possible length of each plank ?
Options:
A)7 m
B)4 m
C)5 m
D)6 m
E)None of these
Rationale: Answer
Greatest possible length of each plank = H.C.F of 30, 35, 45 = 5 m
Correct Option: C
Answer: C
Question: A software programmer does 30% of the work in 80% of the time, and 80% of the work in the remaining 20% of the time. If the code he writes is X lines long and he was given one month (30 days) to accomplish the task, then, assuming that the programmer works at a constant rate in each of the two stages, How many lines of code were written in the last two weeks, in terms of X?
Options:
A)13x /15
B)15x/15
C)7x/15
D)2x/30
E)13x/30
Rationale: Take X=30 lines
80% of 30 = 24 lines
20% of 30 = 6 lines
W - R - T
6 lines - r1 - 24 (first 80% of the 30 days)
24 lines - r2 - 6 ( last 20% of the 20 days)
r1 = 1/4r2 = 4
Now Work in last 14 days = 6 days programmer worked at r2 + 8days programmer worked at r1
=> 6 * 4 + 8 * 1/4 = 24 + 2 = 26
Insert, X=30 in all options => C is the answer.
Answer: C
Question: On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets rain cloud, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction of the total distance did he cover while the sun was shining on him?
Options:
A)1/8
B)1/6
C)1/7
D)1/5
E)1/4
Rationale: If s is an integer and we know that the average speed is 2.8, s must be = 2. That meanss+1= 3. This implies that the ratio of time for s=2 is 1/4 of the total time. The formula for distance/rate is D=Rt...so the distance travelled when s=2 is 2t. The distance travelled for s+1=3 is 3*4t or 12t. Therefore, total distance covered while the sun was shining over him is 2/14 = 1/7. Answer: C
Answer: C
Question: The average age of 35 students in a class is 16 years. The average age of 21 students is 14. What is the average age of remaining 38 students?
Options:
A)14 years
B)7 years
C)19 years
D)21 years
E)None
Rationale: Solution
Sum of the ages of 14 students	= (16 x 35) - (14 x 21)
= 560 - 294.
= 266.
∴ Required average	= 266 / 38
= 7 years.
Answer B
Answer: B
Question: Find the average marks of all the students in 2 separate classes, if the average marks of students in the first class of 58 students is 67 and that of another class of 52 students is 82.
Options:
A)74.1
B)56.3
C)67.8
D)79.7
E)19.4
Rationale: Sum of the marks for the class of 58 students = 58 * 67 = 3886
Sum of the marks for the class of 52 students = 52 * 82 = 4264
Sum of the marks for the class of 110 students =
3886 + 4262 = 8150
Average marks of all the students = 4200/80
= 74.1
Answer:A
Answer: A
Question: The average of first six prime numbers:
Options:
A)5.6
B)11.2
C)12.9
D)6.83
E)7.4
Rationale: Explanation:
The first six prime numbers is 2, 3, 5, 7, 11, 13
Average =41 /6 = 6.83
Answer: Option D
Answer: D
Question: A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half. The number of pupils in the class is
Options:
A)36
B)40
C)99
D)13
E)12
Rationale: Let there be x pupils in the class.
Total increase in marks = (x * 1/2) = x/2.
x/2 = (83 - 63) => x/2 = 20 => x = 40.
Answer: B
Answer: B
Question: In an electric circuit, two resistors with resistances G and H are connected in parallel. In this case, if I is the combined resistance of these two resistors, then the reciprocal of I is equal to the sum of the reciprocals of G and H. What is I in terms of G and H?
Options:
A)(GH)
B)(G+H)
C)GH/(G + H)
D)(G-H)
E)NONE OF THESE
Rationale: The wording is a bit confusing, though basically we are told that 1/I= 1/G + 1/H, from which it follows that I=GH/(G + H).
Answer: C
Answer: C
Question: What is the sum of the different positive prime factors of 960?
Options:
A)5
B)10
C)15
D)17
E)21
Rationale: Prime factorization of 960
=96 * 10
=16*6 * 10
=4*4 * 2*3 * 2*5
=2*2 * 2*2 * 2* 3 * 2*5
=2^6 * 3 * 5
Sum of the different positive prime factors of 960 = 2+3+5
=10
Answer B
Answer: B
Question: There are 38 people in a party. If everyone is to shake hands with one another, how many hand shakes are possible?
Options:
A)435
B)367
C)703
D)997
E)261
Rationale: Explanation:
Total number of persons = n = 38
Shake hands involve only 2 persons = r = 2
Number of shake hands = nCr = 38C2
38C2 = (38 * 37) /(2 * 1) = 703
ANSWER:C
Answer: C
Question: If x=−a^4, which of the following must be true?
I. x is negative.
II.If a is negative then x is negative.
III. a is non-negative.
Options:
A)I and II only
B)I only
C)II only
D)III only
E)II and III only
Rationale: I. x is negative --> not necessarily true
II. x is non-negative. m can take ANY value: positive, negative, zero. We don't have any restrictions on its value;
III. If a is negative then x is negative.
Answer: C (II only).
Answer: C