divelab/Sys2Bench huggingface dataset:
Question: a certain no. of men can finish a piece f work in 10 days.If however there were 10 men less it will take 10 days more for the work to be finished.How many men were there originally
Options:
A)100
B)110
C)120
D)130
E)none of these
Rationale: 20 men will do work in 10 day
but 10 i.e. (20-10) will complete work in 20i.e. (10+10) days.
ANSWER:E
Answer: E
Question: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is ?
Options:
A)5/11
B)5/12
C)5/16
D)5/10
E)5/13
Rationale: Explanation:
Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9) = 5/12
Answer:B
Answer: B
Question: I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
Options:
A)299
B)280
C)288
D)271
E)212
Rationale: x*(85/100) = (480 - x)119/100
x = 280
Answer: B
Answer: B
Question: Cost is expressed by the formula tb^4. If b is doubled, the new cost E is what percent of the original cost?
Options:
A)E=200
B)E=600
C)E=800
D)E=1600
E)50
Rationale: Original Cost E, C1=t1*b1^4
New Cost C2= t2*b2^4....only b is doubled so t2=t1 and b2=2b1
C2=t2*(2b1)^4
=16(t1*b1^4)
=16C1
16 times C1=>1600% of C1
Ans D=1600
Answer: D
Question: Let the number which when multiplied by 16 is increased by 375.
Options:
A)14
B)20
C)26
D)25
E)30
Rationale: Solution
Let the number be x .
Then, 16x - x = 375
‹=›15x = 375
x ‹=› 25.
Answer D
Answer: D
Question: How many two-element subsets of <1, 2,3,4,5,6,7> are there that do not contain the pair of elements 2 and 4?
Options:
A)11
B)12
C)14
D)15
E)20
Rationale: 7C2 - 1 = 20 Answer is E
Answer: E
Question: If E=x^4 + y^4 = 100, then the greatest possible value of x is between
Options:
A)0 and 3
B)3 and 6
C)6 and 9
D)9 and 12
E)12 and 15
Rationale: My attempt:
If E=x^4+y^4=100, then the greatest possible value of x would be when y is minimum.
Let y^4 be 0. Now x^4 = 100. x should be definitely greater than 3 but less than 4. The only option that fits this range is B
Hence answer is --
b) 3 and 6.
Answer: B
Question: What should come in place of the question mark (?) in the following number series?
3 7 19 55 163 ?
Options:
A)467
B)487
C)475
D)485
E)None of these
Rationale: Explanation:
3
7=3+4
19=7+4*3
55=19+12*3
163=55+36*3
487=163+108*3
Answer: B
Answer: B
Question: If the number 517*324 is completely divisible by 9, then the smallest whole number in the place of * will be:
Options:
A)3
B)1
C)5
D)4
E)2
Rationale: Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 9.
x = 5.
C
Answer: C
Question: Rahul's Mathematics test had 70 problems, 10 arithmetic, 30 algebra, 35 geometry problems.
Although he answered 70% of arithmetic, 40% of arithmetic and 60% of geometry problems correctly,
still he got less than 60% problems right. How many more questions he would have to answer more to get
passed
Options:
A)5
B)6
C)2
D)8
E)9
Rationale: Explanation:
Number of questions attempted correctly = (70% of 10 + 40% of 30 + 60% of 35)
= 7 + 12 + 21 = 40.
Questions to be answered correctly for 60% = 60% of total quations
= 60 % of 70 = 45.
He would have to answer 42 - 40 = 2
Answer: Option C
Answer: C
Question: The manager of a theater noted that for every 10 admissions tickets sold, the theater sells 3 bags of popcorn at 2.25 $ each, 4 sodas at 1.70 $ each and 2 candy bars at 1.00$ each. To the nearest cent, what is the average (arithmetic mean) amount of these snacks sales per ticket sold?
Options:
A)1.48$
B)1.56$
C)1.60$
D)1.64$
E)1.70$
Rationale: For every 10 tickets amount of snacks sold is 3*2.25+4*1.7+2*1=$15.55, hence amount of the snacks sales per ticket is $15.55/10=~$1.56.
Answer: B.
Answer: B
Question: If x+y=20, x-y=36, for integers of x and y, x=?
Options:
A)20
B)25
C)28
D)20
E)42
Rationale: x+y = 20
x-y = 36
2x =56
x = 28
Answer is C
Answer: C
Question: When the number 72y6139 is exactly divisible by 11, then the smallest whole number that can replace y is?
Options:
A)1
B)3
C)5
D)6
E)9
Rationale: The given number =72y6139
Sum of the odd places =9+1+y+7
Sum of the even places = 3+6+2=11
(Sum of the odd places)- (Sum of even places) = Number (exactly divisible by 11)
(16+y)-(11) = divisible by 11
y � 5 = divisible by 11.
Y must be 6, to make given number divisible by 11.
D
Answer: D
Question: List F consists of 12 consecutive integers. If -4 is the least integer in list F, what is the range of positive integers in list F?
Options:
A)5
B)6
C)7
D)11
E)12
Rationale: Since -4 is the least integer in list F, then 7 is the largest integer in that list. Thus the range of the positive integers in the list is 7-1=6.
Answer: B.
Answer: B
Question: A car covers a distance of 624 km in 8 hours. Find its speed?
Options:
A)78
B)277
C)298
D)269
E)213
Rationale: 624/8 = 78 kmph
Answer:A
Answer: A
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
Options:
A)217
B)444
C)728
D)278
E)268
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 16 + 21 = 37
T = 12
D = 37 * 12 = 444
Answer: B
Answer: B
Question: A speed of 11 metres per second is the same as :
Options:
A)50.4 km/hr
B)55 km/hr
C)60 km/hr
D)68.5 km/hr
E)39.6 km/hr
Rationale: Sol.
11 m/sec = [11 * 18/5] km/hr = 39.6 km/hr.
Answer E
Answer: E
Question: A, B and C have Rs.700 between them, A and C together have Rs.300 and B and C Rs.600. How much does C have?
Options:
A)200
B)250
C)300
D)350
E)400
Rationale: A+B+C = 700
A+C = 300
B+C =600
--------------
A+B+2C = 900
A+B+C = 700
----------------
C = 200
ANSWER:A
Answer: A
Question: If the average of e, b, c, 14 and 15 is 12. What is the average value of e, b, c and 29
Options:
A)12
B)13
C)14
D)15
E)16
Rationale: e+b+c+14+15 = 12*5 = 60
=>e+b+c = 60-29 = 31
e+b+c+29 = 31+29= 60
Average = 60/4 = 15
Answer D
Answer: D
Question: The diagonals of a rhombus are 30 cm and 12 cm. Find its area?
Options:
A)176
B)190
C)180
D)278
E)292
Rationale: 1/2 * 30 * 12
= 180
Answer:C
Answer: C
Question: Three years ago the average age of a class of six members was 22 years. A boy have been added, the average age of the class is the same today. What is the age of the boy?
Options:
A)A)1
B)B)2
C)C)3
D)D)4
E)E)5
Rationale: 6 * 25 = 150
7 * 22 = 154
`4
D
Answer: D
Question: Consider a lady took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years she had to pay Rs. 5400 interest only for the period. The principal amount borrowed by her was
Options:
A)Rs. 2000
B)Rs. 10000
C)Rs. 15000
D)Rs. 20000
E)None of these
Rationale: Explanation :
Principal = Rs. (100×5400 / 12×3)
=> Rs. 15,000.
Answer : C
Answer: C
Question: A, B and C enter into a partnership. They invest Rs. 1,20,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years ?
Options:
A)9 : 4 : 8
B)9 : 4 : 7
C)3 : 4 : 2
D)3 : 4 : 1
E)9 : 4 : 5
Rationale: A : B : C = (120000 x 36) : (80000 x 12 + 40000 x 24) : (120000 x 24 + 40000 x 12)
= 432 : 192 : 336
= 9 : 4 : 7.
Answer: B
Answer: B
Question: If w is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
Options:
A)√n + 1
B)n + 1
C)n^2 + 1
D)w + 2√w + 1
E)n^2 + 2n + 1
Rationale: If w is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
w = (x)^2 where x is a positive integer
To calculate -
(x+1)^2 = x^2 + 2x + 1
root(w) = x
Ans - w + 2 root(w) + 1
This should beD
Answer: D
Question: Apple costs X rupees per kilogram for first 30 kgs and Y rupees per kilogram for each additional kilogram. If the price of 40 kilograms is 420 and for 50 kgs of Apples is 540 then the cost of first 10 kgs of Apples is
Options:
A)100
B)3.66
C)3.6
D)3.62
E)3.61
Rationale: Ans: By framing equations we get
30X+10Y=420
30X+20Y=540
Eliminate Q by multiplying the first equation by 2 and subtracting second equation from the first
60x+20y = 840 -
30x+20y = 540
=> 30x = 300 => x = 10
Then we get X = 10
Cost of 10 kgs of apples = 10x 10 = 100
Answer:A
Answer: A
Question: There are 50 employees in the office of ABC Company. Of these, 22 have taken an accounting course, 14 have taken a course in finance and 15 have taken a marketing course. Nine of the employees have taken exactly two of the courses and 3 employee has taken all three of the courses. How many of the 50 employees have taken none of the courses?
Options:
A)4
B)9
C)8
D)5
E)14
Rationale: 50 Employees. Counting every different attendand to the courses we have:
Accounting: 22
Finance: 14
Marketing: 15
Which would add up to 51 different attendands, which is not possible.
Now 9 have taken exactly 2 courses, which means that there are 9 less different attendands. Say that 9 of the Finance attentands also attended Accounting.
51-9= 42
3 Person has taken all three courses. As above, we subtract him from the number of different attendands. Since this time the person took all three courses, we have to substract him two times.
42-6= 36.
Answer : E
Answer: E
Question: A cricket player whose bowling average was 24.85 runs per wicket, takes 5 wicket for 52 runs in a match. Due to this his average decreases by 0.85. What will be the number of wickets taken by him till the last match?
Options:
A)64
B)72
C)85
D)96
E)108
Rationale: Average = Total Runs / Total wickets
Total runs after last match = 24.85w + 52
Total wickets after last match = w + 5
(24.85w + 52) / (w + 5) = 24.85 - 0.85 = 24
w = 80
so total wickets aftr last match = w+5 = 85
ANSWER:C
Answer: C
Question: A box contains ten bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that at least one bulb is good?
Options:
A)1/6
B)16/625
C)609/625
D)5/6
E)18/263
Rationale: Required probability
= 1 - 16/625
= 609/625
Answer: C
Answer: C
Question: A bag contains 10 balls numbered from 0 to 9. the balls are such that the person picking a ball out of the bag is equally likely to pick anyone of them. A person picked a ball and replaced it in the bag after noting its number. He repeated this process 2 more times. What is the probability that the ball picked first is numbered higher than the ball picked second and the ball picked second is numbered higher than the ball picked third?
Options:
A)72/100
B)3/25
C)4/5
D)1/6
E)1/9
Rationale: Explanation :
Let, the number of the ball picked first =a, second =b and third =c and these three numbers a, b and c are distinct.
Three distinct ball can be picked in (10×9×8) ways.
The order of a, b and c can be as follows:-
(i) a>b>c.
(ii) a>c>b.
(iii) b>c>a.
(iv) b>a>c.
(v) c>a>b.
(vi) c>b>a.
They will occur equal number of times. So, the number of ways in which (a>b>c) are :-
=>1/6 x 10 x 9 x 8.
=>120.
Hence, the required probability is :-
=>120 / (10x10x10).
=>3/25.
Answer : B
Answer: B
Question: In a certain pond, 100 fish were caught, tagged, and returned to the pond. A few days later, 100 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?
Options:
A) 400
B) 625
C) 1,250
D) 2,500
E) 10,000
Rationale: total fish = x
percentage of second catch = (2/100)*100 = 2%
so, x * 2% = 50
x = 2500 ans. D
Answer: D
Question: P has $21 more than what Q and R together would have had if both B and C had 1/5 of what P has. How much does P have?
Options:
A)$35
B)$36
C)$37
D)$38
E)$39
Rationale: P = (2/5)*P+21
(3/5)*P=21
P=35
The answer is A.
Answer: A
Question: A circle graph shows how the MegaTech corporation allocates its Research and Development budget: 14% microphotonics; 24% home electronics; 10% food additives; 29% genetically modified microorganisms; 8% industrial lubricants; and the remainder for basic astrophysics. If the arc of each sector of the graph is proportional to the percentage of the budget it represents, how many degrees of the circle are used to represent basic astrophysics research?
Options:
A)8°
B)10°
C)18°
D)54°
E)52°
Rationale: 14% microphotonics;
24% home electronics;
10% food additives;
29% genetically modified microorganisms;
8% industrial lubricants;
100-(14+24+10+29+8)=15% basic astrophysics.
15% of 360° is 54°.
Answer: D.
Answer: D
Question: If x = 147, which of the following numbers could be subtracted from x to create a sum that is divisible by 6?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Divisibility rule of 6: A number is divisible by 6 if it is divisible by both 2 and 3
Divisibility rule of 3: A number is divisible by 3 if the sum of the digits is divisible by 3
x = 147. We need to make this number even in order for it to be divisible by 2.
Hence we need to subtract an odd number from it.
Hence left over options are A, C, and E
147 - 1 = 146. Sum of digits = 11.
This is not divisible by 3.
147 - 3 = 144. Sum of digits = 9
This is divisible by 3.
Hence 3 should be subtracted from 147 to make the resultant a multiple of 6.
Correct Option: C
Answer: C
Question: If log 27 = 1.467, then the value of log 9 is:
Options:
A)0.978
B)0.945
C)0.954
D)0.958
E)0.998
Rationale: log 27 = 1.467
log (3cube ) = 1.467
3 log 3 = 1.467
log 3 = 0.489
log 9 = log(3square ) = 2 log 3 = (2 x 0.489) = 0.978.
Answer: Option A
Answer: A
Question: If the integer x is rounded to the nearest hundred, the result represents a 66 2/3 % increase over the value obtained when x is rounded to the nearest ten. which of the following is a possible value of x?
Options:
A)64
B)67
C)99
D)133
E)147
Rationale: 100= (x-y) + 2/3(x-y)
300=5(x-y)
x-y =60
64 rounded to nearest tenth will result in 60.
Answer A
Answer: A
Question: How many numbers between 1 and 100 are divisible by 7 ?
Options:
A)9
B)11
C)17
D)14
E)12
Rationale: No. of divisible by 7 7, 14 --------- 98, n = a + (N - 1)d
98 = 7 + (N - 1) 7, 98 = 7 + 7N - 7
98/7= N = 14
Answer:D
Answer: D
Question: A sum of money is to be divided among Ann, Bob and Chloe. First, Ann receives $4 plus one-half of what remains. Next, Bob receives $4 plus one-third of what remains. Finally, Chloe receives the remaining $32. How much money N did Bob receive?
Options:
A)20
B)22
C)24
D)26
E)52
Rationale: Notice that we need not consider Ann's portion in the solution. We can just let K = the money REMAINING after Ann has received her portion and go from there.
Our equation will use the fact that, once we remove Bob's portion, we have $32 for Chloe.
So, we getK - Bob's $ = 32
Bob received 4 dollars plus one-third of what remained
Once Bob receives $4, the amount remaining is K-4 dollars. So, Bob gets a 1/3 of that as well.
1/3 of K-4 is (K-4)/3
So ALTOGETHER, Bob receives4 + (K-4)/3
So, our equation becomes:K -[4 + (K-4)/3 ]= 32
Simplify to get: K - 4 - (K-4)/3 = 32
Multiply both sides by 3 to get: 3K - 12 - K + 4 = 96
Simplify: 2K - 8 = 96
Solve: K = 52
Plug this K-value intoK - Bob's $ = 32to get: 52 - Bob's $ = 32
So, Bob's $ N= 20
Answer:
B
Answer: B
Question: If d is a positive even integer, and n and m are consecutive integers, then (n - m)^d/(m - n)d =
Options:
A)-2
B)-1
C)0
D)1
E)2
Rationale: d= +ve even integer
Since,n and m are consecutive integers , their difference will be 1
((n-m)^d)/((m-n)d)= ((n-m)/(m-n))^d = (-1)^d
Since we are raising the difference of n and m to power d , which is even , the answer will be 1 .
Answer D
Answer: D
Question: A sum of $800 amounts to $920 in 3 years at simple interest. If the interest rate is increased by 3% it would amount to how much ?
Options:
A)$506
B)$774
C)$992
D)$854
E)$1021
Rationale: S.I = 920-800 = 120
P = $800
T = 3 years
R = 100*120 / 800*3 = 5%
New rate = 5+3 = 8%
New S.I. = 800*8*3/100 = $192
New amount = 800+192 = $992
Answer is C
Answer: C
Question: The ratio, by weight, of coffee to sugar to water in a pot of coffee is 5:2:20. The ratio is then altered so that the ratio of coffee to sugar is halved while the ratio of coffee to water is tripled. If the altered pot of coffee contains 8 grams of sugar, how many grams of water does it contain after alteration?
Options:
A)12
B)12.5
C)13
D)13.5
E)14
Rationale: The new ratio of coffee to sugar is 2.5:2
The new ratio of coffee to water is 15:20.
The new ratio of coffee to sugar to water is 15:12:20.
If there are 8 grams of sugar, then there are (21/12)*8=14 grams of water.
The answer is E.
Answer: E
Question: Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years.
Year	Item of Expenditure
Salary	Fuel and Transport	Bonus	Interest on Loans	Taxes
1998	288	98	3.00	23.4	83
1999	342	112	2.52	32.5	108
2000	324	101	3.84	41.6	74
2001	336	133	3.68	36.4	88
2002	420	142	3.96	49.4	98
Total expenditure on all these items in 1998 was approximately what percent of the total expenditure in 2002?
Options:
A)62%
B)69.45%
C)70%
D)71%
E)72%
Rationale: Required percentage
=	[	(288 + 98 + 3.00 + 23.4 + 83)	x 100	]	%
(420 + 142 + 3.96 + 49.4 + 98)
=	[	495.4	x 100	]	%
713.36
~= 69.45%.
B)
Answer: B
Question: The area of sector of a circle whose radius is 12 metro and whose angle at the center is 54Â° is?
Options:
A)52.6
B)52.9
C)67.9
D)52.1
E)52.2
Rationale: 54/360 * 22/7 * 12 * 12 = 67.9 m2
Answer: C
Answer: C
Question: What is 1! + 2! + ... + 10! ?
Options:
A)4,037,910
B)4,037,913
C)4,037,915
D)4,037,916
E)4,037,918
Rationale: All options have different Unit digit so calculating unit digit of the sum above will suffice
Unit digit of (1! + 2! + 3! + 4! + 5! + 6!+... + 10!) = 1 + 2+ 6 + 4 + 0 + 0 + 0 + 0+ 0 + 0 = Unit digit 3, Hence
every Factorial of an integer greater than 4 will have Unit digit 0 as it will be a multiple of 10
Answer: option B
Answer: B
Question: Apples are bought at 11 for a $ and an equal number more at 9 a $. If these are sold at 10 for a $, find the loss or gain percent?
Options:
A)5% loss
B)7% loss
C)3% loss
D)2% loss
E)1% loss
Rationale: E
1% loss
Answer: E
Question: There are two groups of students in the sixth grade. There are 20 students in group A, and 80 students in group B. If, on a particular day, 20% of the students in group A forget their homework, and 15% of the students in group B forget their homework, then what percentage of the sixth graders forgot their homework?
Options:
A)13%
B)14%
C)15%
D)16%
E)17%
Rationale: Number of students in group A = 20
students who forget homework in group A = 20 % of 20 = 4 students
Number of students in group B = 80
students who forget homework in group B = 15 % of 80 = 12 students
Total number of students = 20 + 80 = 100
students who forgot homework = 4 + 12 = 16 students
percentage of students who forget homework = 16/100 * 100 = 16%
Answer: D
Answer: D
Question: What is the value of (44444445*88888885*44444442+44444438)/44444444^2
Options:
A)88888883
B)88888827
C)16992677
D)88888237
E)88888182
Rationale: Ans: A
Let x = 44444444
(x+1)×(2x−3)×(x−2)+(x−6)x2(x+1)×(2x−3)×(x−2)+(x−6)x2
(x2−x−2)×(2x−3)+(x−6)x2(x2−x−2)×(2x−3)+(x−6)x2
2x3−2x2−4x−3x2+3x+6+x−6x22x3−2x2−4x−3x2+3x+6+x−6x2
2x3−5x2x2=2x−52x3−5x2x2=2x−5
Substituting the value of x in 2x - 5, we get 88888883
Answer:A
Answer: A
Question: Find average speed if a man travels at speed of 20km/hr up and 26km/hr dawn at an altitude of 240m.
Options:
A)25.8
B)26.8
C)22.6
D)28.8
E)29.8
Rationale: avg speed=2*x*y/(x+y)
=2*20*26/(20+26)=22.6
ANSWER:C
Answer: C
Question: Find the remainder Y when 12^190 is divided by 1729 ?
Options:
A)12
B)1
C)1728
D)1717
E)4
Rationale: 12^(190) can be written as. ((12^3)^63)* 12. 12^3 when divided by 1729 gives a remainder Y -1. so in the numerator we have -12. Now acccording to remainder theorm the answer will be 1729-12=1717.D
Answer: D
Question: What is the perimeter of a square with area 9p^2/36 ?
Options:
A)3p/4
B)3p^2/4
C)2p
D)3p^2
E)4p/3
Rationale: Area of square, (side)^2 = (3p/6)^2
Therefore side of the square = 3p/6
Perimeter of square = 4*side = 4* (3p/6) = 2p
Answer is C.
Answer: C
Question: Find the simple interest on Rs.500 for 9 months at 6 paisa per month?
Options:
A)238
B)270
C)987
D)167
E)121
Rationale: I = (500*9*6)/100 = 270
Answer:B
Answer: B
Question: A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%?
Options:
A)600
B)267
C)132
D)277
E)161
Rationale: Cost price = Rs.500
profit = 20% of 500 = Rs.100
Selling price = Cost price + Profit
= 500 + 100 = 600
Answer:A
Answer: A
Question: Two vessels A and B contain spirit and water in the ratio 5 : 2 and 7 : 6 respectively. Find the ratio in which these mixture be mixed to obtain a new mixture in vessel C containing spirit and water in the ration 8 : 5?
Options:
A)4 : 3
B)3 : 4
C)5 : 6
D)7 : 9
E)None
Rationale: Let the C.P. of spirit be Re. 1 litre.
Spirit in 1 litre mix. of A = 5/7 litre, C.P. of 1 litre mix. in A = Re. 5/7
Spirit in 1 litre mix. of B = 7/13 litre, C.P. of 1 litre mix. in B = Re. 7/13
Spirit in 1 litre mix. of C = 8/13 litre, Mean price = Re. 8/13.
By the rule of alligation, we have:
Required ratio = 1/13 : 9/91 = 7 : 9.
Answer D
Answer: D
Question: Three numbers are in the ratio of 2 : 3 : 4 and their L.C.M. is 240. Their H.C.F. is:
Options:
A)30
B)20
C)40
D)60
E)70
Rationale: Explanation:
Let the number be 2x, 3x and 4x
LCM of 2x, 3x and 4x = 12x
12x = 240
=> x = 240/12 = 20
HCF of 2x, 3x and 4x = x = 20
Answer: Option B
Answer: B
Question: A box contains 40 balls, numbered from 1 to 40. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd?
Options:
A)1/4
B)3/8
C)1/2
D)5/8
E)3/4
Rationale: I don't think order matters in this case, because 2 + 2 + 1 = 2 + 1 + 2
My answer is: 1/4
A
Answer: A
Question: How many even prime numbers are there less than 50?
Options:
A)15
B)1
C)2
D)16
E)17
Rationale: 2 is the only even prime number
Answer is B
Answer: B
Question: The total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year, less the age of the tree in years (rounded down to the nearest integer). During its 4th year, the plum tree grew 50 plums. If this trend continues, how many plums will it grow during its 6th year?
Options:
A)36
B)41
C)38
D)40
E)42
Rationale: 1st year : 0-1 (age), we take age = 0 (as the question says that we have to(rounded down to the nearest integer))
2ndyear : 1-2 (age), we take age = 1
3rd year : 2-3 (age), we take age = 2
4th year : 3-4 (age), we take age = 3
5th year : 4-5 (age), we take age = 4
6th year : 5-6 (age), we take age = 5
Thus for the 4th year = 50,
5th year = 50 -4 = 46
6th year = 46-5 = 41
The correct answer is B.
Answer: B
Question: The number of singles that a baseball player hit increased 18 percent from her first season to her second season, and the number of doubles that she hit in the same time period decreased by 6 percent. If the total number of singles and doubles that she hit increased 3 percent from her first season to her second season, what is the ratio of the number of singles she hit in her first season to the number of doubles she hit in her first season?
Options:
A)1:3
B)4:5
C)1:5
D)2:5
E)3:5
Rationale: Soln:-
1.18S + 0.94D = 1.03[S + d]
0.15S = 0.09D
S/D = 3/5
ANSWER:E
Answer: E
Question: Jill, who lives in City C, plans to visit 3 different cities, M, L, and S. She plans to visit each city exactly once and return to City C after the 3 visits. She can visit the cities in any order. In how many different orders can she visit the 3 cities?
Options:
A)3
B)6
C)8
D)9
E)12
Rationale: 3! = 6
M	L	S	C
M	S	L	C
L	M	S	C
L	S	M	C
S	M	L	C
S	L	M	C
She can visit the cities in any order. Number of ways of arranging the three cities is 3! = 6 ways. Hence B.
Answer: B
Question: What approximate value should come in place of the question mark (?) in the following equation?
39.05 × 14.95 – 27.99 × 10.12 = (36 + ?) × 5
Options:
A)22
B)29
C)34
D)32
E)25
Rationale: Solve using approximation
Answer E
Answer: E