divelab/Sys2Bench huggingface dataset:
Question: Amit and Ian paint a wall in alternating shifts. First Amit paints alone, then Ian paints alone, then Amit paints alone, etc. During each of his shifts, Amit paints 1/2 of the remaining unpainted area of the wall, while Ian paints 1/3 of the remaining unpainted area of the wall during each of his shifts. If Amit goes first, what fraction of the wall's area will remain unpainted after Amit has completed his 6th shift?
Options:
A)1/27
B)1/54
C)1/81
D)1/162
E)1/486
Rationale: Fraction of area unpainted after FIRST shift of Amit = 1-(1/2) = 1/2
Fraction of area unpainted after FIRST shift of Ian = (1/2)-(1/3)(1/2) = (2/3)(1/2)
Fraction of area unpainted after SECOND shift of Amit = (1/2)(2/3)(1/2)
Fraction of area unpainted after SECOND shift of Ian = (2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after THIRD shift of Amit = (1/2)(2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after THIRD shift of Ian = (2/3)(1/2)(2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after FORTH shift of Amit = (1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after FORTH shift of Ian = (2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after FIFTH shift of Amit = (1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after FIFTH shift of Ian = (2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after SIXTH shift of Amit = (1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)=486
Answer: option E
Answer: E
Question: Find the area of the quadrilateral of one of its diagonals is 28 cm and its off sets 8 cm and 2 cm?
Options:
A)140 cm2
B)150 cm2
C)168 cm2
D)182 cm2
E)200 cm2
Rationale: 1/2 * 28(8 + 2)
= 140 cm2
Answer: A
Answer: A
Question: Two representatives must be selected from each of two groups of students. One group consists of four men and one woman, and the other group consists of two women and one man. What is the probability that 2 men and 2 women will be selected ?
Options:
A)1/6
B)1/4
C)2/7
D)7/15
E)1/2
Rationale: Group 1: 4 Men and 1 Woman
Group 2: 1 Men and 2 Woman
Need: 2 Men and 2 women
Case 1: 2 Men from Group 1 and 2 women from group 2 - 4C2*2C2 = 6 ways
Case 2: 1 Men and 1 Woman from Group 1 and 1 Man and 1 women from group 2 - 4*1*1*2 = 8 ways
Total Favorable cases = 6+8 = 14
Total Possible ways of selecting students 2 from each group = 5C2*3C2 = 10*3 = 30
Probability = 14/30 = 7/15
Answer : Option D
Answer: D
Question: A can do a piece of work in 40 days; B can do the same in 30 days. A started alone but left the work after 10 days, then B worked at it for 10 days. C finished the remaining work in 10 days. C alone can do the whole work in?
Options:
A)24 days
B)30 days
C)44 days
D)17 1/2 days
E)60 days
Rationale: Explanation:
10/40 + 10/30 + 10/x = 1
x = 24 days
Answer: A
Answer: A
Question: P is a prime number. If 6p is between 15 and 95, which of the following E can be a value of 7p + 2?
Options:
A)E.15
B)E.79
C)121
D)65
E)21
Rationale: [3,5,7,11,13] are prime numbers that fits this equation 15< 6X <95. Afterwards subtract 2 from all the answer n see if it's divisible by 7. Therefore A and E are out. Leaves out with B C D.
B =11
C =17
D = 9
Only 11 is the set of prime numbers that fit between 15 and 95. Therefore 79 is the answer.B
Answer: B
Question: here are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period?
Options:
A)4561
B)3564
C)1542
D)1800
E)2451
Rationale: 5 subjects can be arranged in 6 periods in 6P5 ways.
Any of the 5 subjects can be organized in the remaining period (5C1 ways).
Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.
Total number of arrangements
= 6P5× 5C1 /2!=1800
Ans: D
Answer: D
Question: If money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. If Pat's parents invested $ 5000 in a long term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of investment 18 years later, when Pat is ready for college?
Options:
A)20000 dollars
B)$15000
C)$12000
D)$10000
E)$9000
Rationale: Since investment doubles in 70/r years then for r=8 it'll double in 70/8=~9 years (we are not asked about the exact amount so such an approximation will do). Thus in 18 years investment will double twice and become ($5,000*2)*2=$20,000 (after 9 years investment will become $5,000*2=$10,000 and in another 9 years it'll become $10,000*2=$20,000).
Answer: A.
Answer: A
Question: If (x-12)(x-3) < 0, which of the following must be true?
Options:
A)x^2 + 5x + 6 < 0
B)x^2 + 5x + 6 > 0
C)12 - x > 0
D)x - 5 < 0
E)11 - x > 0
Rationale: (x-12)(x-3)<0 can be written as (12-x)(x-3)>0
So,to inequality hold true multiple of (12-x) and (x-3) must be positive and if I let both elements positive/negative then the range becomes 3<x<12
Answer Choice E matched which says 12-x>0 or x<12,which must be true (I started to look from E to A for making easy decision first)
Correct Answer C
Answer: C
Question: Two trains of length 120 m and 280 m are running towards each other on parallel lines at 32 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
Options:
A)33 1/5 sec
B)23 1/5 sec
C)24 1/5 sec
D)23 3/5 sec
E)20 1/5 sec
Rationale: Relative speed = (32 + 30) * 5/18 = 4 * 5 = 17.22 mps.
Distance covered in passing each other = 120 + 280 = 400 m.
The time required = d/s = 400/20 = 23 1/5 sec.
ANSWER:B
Answer: B
Question: The 201st term of the series a, b , b, c, c, c, d, d, d, d, e, e, e, e, e, .... is
Options:
A)r
B)s
C)t
D)u
E)v
Rationale: a is one time, b,2 times so on...
so 201=n(n+1)/2..
0r n(n+1)= 402 ... now 19*20=380...20*21<402 so x= 20.. and 20th alphabet is T ans D
Answer: D
Question: If the average (arithmetic mean) of the four numbers K, 3K + 3, 3K – 4 and 5K + 1 is 60, what is the value of K?
Options:
A) 11
B) 15 3/4
C) 20
D) 23
E) 25 3/10
Rationale: K + 3K +3 + 3K - 4 + 5K +1 = 12K
(12K)/4 = 60
12K = 60 * 4 = 240
K = 240/ 12 = 20.
Answer C.
Answer: C
Question: Will must choose a 3-character computer password, consisting of 3 letter from the alphabet , in any order.From how many different passwords can Will choose?
Options:
A)390
B)2,340
C)93,600
D)7,020
E)14,040
Rationale: 26C1*25C1*24C1 = 15600
=> 2340 * 3 ! = 93,600.
Option E is correct answer...but OA is C.
Answer: C
Question: John's Ice Cream Shop sells ice cream at m cents a scoop. For an additional n cents, a customer can add 2 toppings to his or her sundae. How much would a sundae with 2 scoops and 2 toppings cost, in terms of m and n?
Options:
A)2m+2n
B)2m+n
C)3m+n
D)4m+n
E)5m+n
Rationale: Answer B 2m+n
Answer: B
Question: From a pack of 52 cards, one card is drawn. What is the probability that the card drawn is a face card (Jack, Queen and King only)?
Options:
A)1/13
B)3/13
C)13/13
D)8/13
E)6/13
Rationale: Answer:	Solution
Let S be the sample space. Then,
n(S) = 52C1	= 52.
Let E = event of getting 1 face card.
n(E) = number of ways of choosing 1 face card out of 12
=12C1 = 12
P(E) = n(E) / n(S)	= 12 / 52
= 3/13.
Answer B
Answer: B
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
Options:
A)Rs.4329
B)Rs.4529
C)Rs.4520
D)Rs.4530
E)Rs.4523
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 5
= Rs. 4530
Answer:D
Answer: D
Question: The least number which should be added to 9422 so that the sum is exactly divisible by 5, 6, 4 and 3 is?
Options:
A)59
B)58
C)48
D)38
E)28
Rationale: L.C.M. of 5, 6, 4 and 3 = 60.
On dividing 9422 by 60, the remainder is 2.
Number to be added = (60 - 2) = 58
B)
Answer: B
Question: A man rows his boat 90 km downstream and 55 km upstream, taking 3 hours each time. Find the speed of the stream?
Options:
A)76 kmph
B)6 kmph
C)14 kmph
D)8 kmph
E)4 kmph
Rationale: Speed downstream = d/t = 90/(3)
= 30 kmph
Speed upstream = d/t = 55/(3)
= 18 kmph
The speed of the stream = (30 - 18)/2
= 6 kmph
Answer:B
Answer: B
Question: If grapes are 90% water and raisins are 17% water, then how many kilograms did a quantity of raisins, which currently weighs 14 kilograms, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.)
Options:
A)108.6
B)110.4
C)112.6
D)114.8
E)116.2
Rationale: Let x be the original weight of the grapes.
The weight of the grape pulp was 0.1x.
Since the grape pulp is 83% of the raisins, 0.1x = 0.83(14 kg).
Then x = 8.3*14 = 116.2 kg.
The answer is E.
Answer: E
Question: Chris age after 13years will be 5 times his age 5years back. what is the present age of Chris?
Options:
A)A)20
B)B)25
C)C)15
D)D)22
E)E)12
Rationale: Chris present age= x
after 13years = x+13
5years back = x-5
x+13= 5(x-5)
x=12
Answer is E
Answer: E
Question: 3 candidates in an election and received 4136, 7636 and 11628 votes respectively. What % of the total votes did the winning candidate got in that election?
Options:
A)45%
B)49%
C)50%
D)59%
E)61%
Rationale: Total number of votes polled = (4136 + 7636 + 11628) = 23400
So, Required percentage = 11628/23400 * 100 = 50%
C
Answer: C
Question: Line m lies in the xy-plane. The y-intercept of line m is -2, and line m passes through the midpoint of the line segment whose endpoints are (2, 8) and (10,0). What is the slope of line m?
Options:
A)-1
B)0
C)1
D)2
E)3
Rationale: The midpoint of (2,8) and (10,0) is (6,4).
The slope of a line through (0,-2) and (6,4) is (4-(-2))/(6-0) = 6/6 = 1
The answer is C.
Answer: C
Question: Anup was asked to find the value of 7/12 of a sum of money E. Instead of multiplying the same by 7/12,he divided it by 7/12 and his answer exceeded the correct answer by 95. The correct answer is:
Options:
A) 48
B) 89
C) 84
D) 69
E) 49
Rationale: E=12/7*x-7/12*x=95 --> x=84 --> 7/12*x=49.
So if bythe correct answerquestion means 7/12 of the amount then the answer should be E.
Answer: E
Question: If x and y are positive integers such that x/y = 2.18, which of the following numbers could be y?
Options:
A)50
B)5
C)150
D)2
E)100
Rationale: With the given information, we are trying to find the value of y.
To achieve this we must convert the given decimal to a fraction and reduce it to it's lowest integer form.
Take the decimal x/y = 2.18 and because it's in the hundreds decimal place, put the given value (x/y = 2.18/1) and multiply it by 100.
Take the resulting fraction (x/y = 218/100) and reduce it to it's lowest form.
Both of the numbers are divisible by 2.
The result is x/y = 109/50.
Thus y = 50.
The correct answer is A.
Answer: A
Question: All of the citizens of a country have a four-character or five-character national identification code that is created using the 26 letters of the alphabet and the 10 digits from 0 to 9. What is the maximum number of citizens who can be designated with these codes?
Options:
A)37(36^4)
B)36^9
C)35(36^5)
D)37(36^5)
E)35(36^9)
Rationale: The number of possible 4-digit codes is 36^4.
The number of possible 5-digit codes is 36^5.
The total sum is 36^4 + 36^5 = 36^4(1+36) = 37(36^4)
The answer is A.
Answer: A
Question: When 1/20% of 4,000 is subtracted from 1/20 of 4,000, the difference is
Options:
A)50
B)198
C)380
D)398
E)400
Rationale: 1/20 % of 4000 = 2
1/20 of 4000 = 200
200-2 = 198
Ans:B
Answer: B
Question: Twelve telegenic contestants with a variety of personality disorders are to be divided into two “tribes” of five members each, tribe A and tribe B, for a competition. How many distinct groupings of two tribes are possible?
Options:
A)120
B)126
C)792
D)1200
E)1260
Rationale: My ans is 12C5 = 792
C
Answer: C
Question: If the number is decreased by 5 and divided by 7 the result is 7. What would be the result if 24 is subtracted and divided by 10?
Options:
A)4
B)7
C)8
D)5
E)3
Rationale: Explanation:
Let the number be x. Then,
(x - 5)/7 = 7 => x - 5 = 49
x = 54
.: (x - 24)/10 = (54 - 24)/10 = 3
Answer: Option E
Answer: E
Question: The average age of a class of 40 students is 15 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher
Options:
A)30 Years
B)56 Years
C)32 Years
D)34 Years
E)49 Years
Rationale: Total age of students is 40X15 = 600 Years
Total age inclusive of teacher = 41X (15+1) = 656
So, Teacher's age is 656-600 = 56 Yrs
There is a shortcut for these type of problems
Teacher's age is 15+(41X1) = 56 Years
B
Answer: B
Question: There is a sequence such that each term is positive integer and each digit of the terms in the sequence has 3 to be ordered, what is the value F of 100th term?
Options:
A)126
B)192
C)232
D)252
E)342
Rationale: (1~99) 19, (100~199)  19, (200~299) 19. The 100th term should be 100-(19+19+19)=43th number. Hence, the correct answer F is 342. The correct answer is E.
Answer: E
Question: What should come in place of the question mark (?) in the following number series?
11 17 25 35 47 ?
Options:
A)53
B)55
C)57
D)59
E)61
Rationale: The numbers increase by 6, 8, 10, 12,...
The next number should be 47+14 = 61
The answer is E.
Answer: E
Question: Roberto has three children: two girls and a boy. All were born on the same date in different years. The sum of the ages of the two girls today is smaller than the age of the boy today, but a year from now the sum of the ages of the girls will equal the age of the boy. Five years from today, the difference between the age of the boy and the combined ages of the girls will be
Options:
A)1
B)2
C)3
D)–4
E)–1
Rationale: Approach I (Plugin's)
Girl I ............... Girl II ................ Boy
1 ....................... 1 ........................ 3 (Assume the current ages)
1 + 1 < 3 .......... (Satisfies the given condition)
1 Year later there ages are
2 ....................... 2 ......................... 4
2 + 2 = 4 ............ (Satisfies the given condition)
After 5 years there ages are
6 ....................... 6 ............................ 8
Difference = 8 - (6+6) = 8 - 12 = -4
Answer = D
Answer: D
Question: Cars emerging from a motorway arrive at a junction that splits the road into two separate lanes. The number of cars per hour that continue in either lane is constant. If 490 cars per hour were diverted from the left lane to the right lane, the number of cars entering the right lane per hour would be twice as big as the number of cars entering the left lane per hour. Alternatively, if 490 cars per hour were diverted from the right lane to the left lane, the number of cars entering the left lane per hour would be four times as great as the number of cars entering the right lane per hour. How many cars enter the left lane per hour?
Options:
A)1190
B)1200
C)1400
D)700
E)900
Rationale: as per question 490 cars diverted from left lane to right lane. Thus we get equation R+490=2(L-490)
as per question 490 cars diverted from right lane to left lane .thus we get equation L+490=4(R-490)
by solving two equation i.e R +490 =2L-980 OR. R =2L -1470 AND L+490= 4R -1960 OR L= 4R -2450
BY SOLVING WE GET L= 4( 2L -1470) -2450 OR L= 8L -5880-2450 OR 8330 =7L THUS L =1190
A
Answer: A
Question: A certain company reported that the revenue on sales increased 30 % from 2000 to 2003, and increased 80 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005?
Options:
A)50 %
B)40 %
C)35 %
D)32 %
E)39 %
Rationale: Assume the revenue in 2000 to be 100. Then in 2003 it would be 130 and and in 2005 180, so from 2003 to 2005 it increased by (180-130)/130=50/130= 39%
Answer: E.
Answer: E
Question: A certain rectangular window is three times as long as it is wide. If its perimeter is 32 feet, what are its dimensions in terms of length by width?
Options:
A)12 by 2
B)11 by 3
C)10.5 by 3.5
D)12 by 4
E)9 by 3
Rationale: 2x+2y=32
x+y=16
x+3x=16
4x=16
x=4
Answer D
Answer: D
Question: For what value of “k” will the equation (2kx2 + 5kx+2)=0 have equal roots?
Options:
A)2/7
B)9/4
C)16/25
D)7/1
E)7/2
Rationale: For a 2nd degree equation ax2+bx_c=0 has equal roots the condition is b2-4ac=0
in the given equation
(5k)^2-4*2k*2=0
by solving this equation
we get k=0, k=16/25
ANSWER:C
Answer: C
Question: From (1, 2, 3, 4, 5, 6), one number is picked out and replaced and one number is picked out again. If the sum of the 2 numbers is 5, what is the probability that the 2 numbers included the number 3?
Options:
A)1/5
B)1/2
C)3/10
D)3/5
E)1/4
Rationale: We know that the sum of two numbers picked was 8. So, there could be the following cases:
(1, 4);
(4, 1);
(2, 3);
(3, 2);
Total of 4 cases out of which 2 have 3, thus the probability is 2/4=1/2.
Ans B
Answer: B
Question: Mandrake has to choose from 4 from 12 people. There are 3 girls, 5 boys , 4 children. What is total probability that he will choose 1G , 2B , 1C?
Options:
A)1/7
B)2/7
C)3/7
D)4/7
E)8/33
Rationale: (3C1 * 5C2 * 4C1)/ 12C4 = 3*10*4/495 = 120/495=8/33
ANSWER:E
Answer: E
Question: Two trains from opposite directions are to cross each other. The length of two trains are 100 meter and 200 meter respectively. The speed of first train is 100 km/hour and second train 200 km/hour. In how much time will they cross each other?
Options:
A)2 second
B)3.6 second
C)5 second
D)5.5 second
E)6 second
Rationale: The crossing moment starts when the head of first compartment of two trains meet or touch. The process of crossing each other continues till 100 + 200 meter = 300 meter is covered. The speed will be 100km/hour + 200 km/hour = 300 km/hour. 300x1000 meter covered in 3600 seconds. So, 300 meter covered in 3.6 seconds.
Answer: B.
Answer: B
Question: Which expression is the greatest
Options:
A)3252/3257
B)3456/3461
C)3593/3598
D)3346/3351
E)3453/3458
Rationale: Options can be re-written as (x-5)x => 1-(5/x)
A) 1- (5/3257)
B) 1- (5/3461)
C) 1- (5/3598)
D) 1- (5/3351)
E) 1- (5/3458)
To get the largest among these second half should be the least and so denominator to be largest. Hence 'C'.
Answer: C
Question: The sequence {A(n)} is defined by A(1) = 2 and A(n+1)=A(n)+2*n what is the value of A(100)?
Options:
A)9902
B)9900
C)10100
D)9904
E)9906
Rationale: n=1, A(1)=2
n=2, A(2)=A(1+1)=A(1)+2*1=2+2=4
n=3, A(3)=A(2+1)=A(2)+2*2=4+4=8
n=4, A(4)=A(3+1)=A(3)+2*3=8+6=14
if n=1, A(1)=2
if n=2, A(2)=4, i.e 2*2-0=4
if n=3, A(3)=8, i.e 3*3-1=8
if n=4, A(4)=14 i.e 4*4-2=14
..........
if n=100, A(100)=100*100-98=10000-98=9902
ANSWER:A
Answer: A
Question: A certain sum amounts to Rs.640 in 4 years and Rs.760 in 6 years. Find the rate % per annum?
Options:
A)9%
B)5%
C)3%
D)1%
E)8%
Rationale: 4 --- 640
6 --- 760
--------------
2 --- 120
N = 1 I = 60 R = ?
P = 640 - 240 = 400
60 = (400*1*R)/100
R = 15%
Answer: E
Answer: E
Question: Rodrick mixes a martini that has a volume of 'n' ounces having 30% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 25% Vermouth by volume. How many ounces of Gin must he add?
Options:
A)n/6
B)n/3
C)n/5
D)5n/6
E)8n/5
Rationale: total V G
1 ounce 0.3 0.6
n ounce 0.3n 0.6n -------------initial expression
lets say g ounces of gin is added to this mixture
n+g 0.3n 0.6n+g --------------final expression
given that after adding g ounces of gin , V should become 25% of the total volume.
=>Volume of V/total volume = 25/100
=> 0.3n /n+g = 1/4
=> 1.2n = n+g
=> g = n/5
Answer is C.
Note that after we add pure Gin, the volume of Vermouth will remain the same. Based on this set the equation:
0.3n=0.25(n+g) --> g=n/5
Answer: C.
Answer: C
Question: Look at this series: 15, 15, 27, 27, 39, 39,? ... What number should fill the blank?
Options:
A)51
B)39
C)23
D)15
E)None
Rationale: Explanation: In this simple addition with repetition series, each number in the series repeats itself, and then increases by 12 to arrive at the next number.
Answer: Option A
Answer: A
Question: The value of x + x(x^x) when x = 6 is
Options:
A)279942
B)245872
C)434323
D)278879
E)342333
Rationale: Solution:
x + x(x^x)
Put the value of x = 6 in the above expression we get,
6 + 6(6^6)
= 6 + 6(6 x 6 x 6 x 6 x 6 x 6)
= 6 + 6(46656)
= 6 + 279936
= 279942
Answer: (A)
Answer: A
Question: In how many ways can 5 different rings be worn in four particular fingers? (Some fingers may get more than one ring and some may get no rings.)
Can somebody explain?
Options:
A)6720
B)7720
C)7820
D)7950
E)8120
Rationale: First ring can be worn in 4 ways (on any of the four fingers);
Second ring can be worn in 5 ways (as it can go on any of four fingers - 4 ways; plus it can go below the first one - 1);
Third ring can be worn in 6 ways (the same logic as for the second ring);
Fourth ring can be worn in 7 ways;
Fifth ring can be worn in 8 ways;
Total: 4*5*6*7*8=6720. ANS:A
Answer: A
Question: If A : B = 4 : 7 and B : C = 4 : 9 then A : B : C is :
Options:
A)20 : 35 : 63
B)35 : 36 : 63
C)16 : 28 : 63
D)25 :34: 68
E)None of these
Rationale: Expl : A : B = 4 : 7
B : C = 4 :9 = 4*7/4 : 9 *7/4 = 7 : 63/4
A : B : C = 4 : 7 : 63/4 = 16 : 28 : 63
Answer: C
Answer: C
Question: A person is 24 years older than his daughter. In 2 years, the person’s age will be 2 times the age of his daughter. Then, the current age of the daughter is:
Options:
A)22
B)42
C)32
D)41
E)56
Rationale: Let the daughter’s current age be A years. Then, the person’s current age = (A +24) years.
(A + 24) + 2 = 2 (A + 2)
A + 26 = 2A + 4
A = 22
Answer: A
Question: A small company employs 3 men and 4 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?
Options:
A) 1/14
B) 1/7
C) 20/70
D) 18/70
E) 1/2
Rationale: Total ways to choose 4 employees from 8 employees = 8C4
Two women = 4C2
Two Men = 3C2
P = (5C2 * 3C2)/8C2 = 18/70 hence D.
Answer: D
Question: A certain ski shop sells pairs of gloves in 12 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)1/24
D)1/23
E)1/12
Rationale: Chance of getting a color from the 12 different colored gloves = 24/24=1
Chance of picking the same color as first sock out of the remaining 12∗2−1=23 socks = 1/23
Probability of 1st x Probability of 2nd = 1∗1/23=1/23
Answer is D
Answer: D
Question: In an office, totally there are 2200 employees and 40% of the total employees are males. 30% of the males in the office are at-least 50 years old. Find the number of males aged below 50 years?
Options:
A)661
B)600
C)620
D)616
E)None of these
Rationale: Number of male employees = 2200* 40/100 = 880
Required number of male employees who are less than 50 years old = 880* (100 - 30)%
= 880* 75/100 = 616.
ANSWER:D
Answer: D
Question: A man is 20 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is?
Options:
A)11
B)25
C)27
D)18
E)91
Rationale: Let the son's present age be x years.
Then, man's present age = (x + 20) years.
(x + 20) + 2 = 2(x + 2) x + 22 = 2x + 4 => x = 18.
Answer: D
Answer: D
Question: If 5^25 * 4^13 = 2 * 10^n, what is the value of n?
Options:
A)11
B)25
C)22
D)23
E)32
Rationale: My attempt:
5^(25) * 4^(13) = 2*10^p
5^(25) * 2 ^ (26) = 2 * (2*5)^p
5^(25) * 2 ^ (26) = 2 * 2^(p) * 5^(p)
5^(25) * 2 ^ (26) = 2^(p+1) * 5^(p)
=> (p+1) = 26
=> p = 25
Answer: 21 (B)
Answer: B
Question: The volume of a certain substance is always directly proportional to its weight. If 48 cubic inches of the substance weigh 112 ounces, what is the volume, in cubic inches, of 53 ounces of this substance?
Options:
A)27
B)36
C)42
D)22
E)147
Rationale: 112 ounces of a substance has a volume of 48 cubic inches
53 ounces of a substance has a volume of (48/112)*53 = 22 cubic inches
Answer D
Answer: D
Question: There are 750 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?
Options:
A)75
B)100
C)125
D)175
E)225
Rationale: female = x
Male = 750-x
x/2 + 750-x/4 = 1/3* (750)= 250
x= 250
x/2 = 125 is supposed to be the answer
ANSWER:C
Answer: C