divelab/Sys2Bench huggingface dataset:
Question: Place a number in each of the following empty
boxes so that the sum of the numbers in any 3
consecutive boxes is 2015. What is the number
that should go in the box with the question
mark?
Options:
A)684
B)567
C)892
D)431
E)999
Rationale: To help illustrate the problem, we will label a few boxes as shown below.
Since the sum of the numbers in any 3 consecutive boxes is the same,
607 + A + B = A + B + C.
After taking away both A and B from the above equation we get 607 = C
Therefore, the number in box C should be 607.
Since the sum of the numbers in any 3 consecutive boxes is 2015,
C + 724 +? = 607 + 724 +? = 2015
Therefore, ? = 684
correct answer A
Answer: A
Question: Nirmala gains 10% by selling her bicycle for a certain price. If she sells it at 2 times the price, the percentage of profit will be :
Options:
A)130%
B)140%
C)160%
D)120%
E)None of these
Rationale: Explanation :
Solution: Let C.P =Rs. x. then, S.P. = Rs. (110% of x) = Rs. 11x/10.
New S.P. = Rs. (2*11x/10) =Rs. 22x/10. profit = Rs. (22x/10 - x) = Rs. 6x/5.
.'. Profit% = (6x/5 *1/x * 100) = 120%.
Answer : D
Answer: D
Question: A question paper has 2 parts, A & B, each containing 8 questions. If a student has to choose 8 from part A &4 from part B, in how many ways can he choose the questions?
Options:
A)110
B)70
C)120
D)130
E)140
Rationale: There 8 questions in part A out of which 8 question can be chosen as = 8C8.
Similarly,4 questions can be chosen from 8 questions of Part B as = 8C4.
Hence, total number of ways,
=8C8*8C4
=[8!/(0!8!)]*[8!/(4!*4!)]
= {1}*{8*7*6*5/(4!)}
= 70.
B
Answer: B
Question: In what ratio P:Q should the Mixture P of milk and water in the ratio of 5:4 be mixed with another Mixture Q of milk and water in the ratio 2:7 so that the resultant mixture contains equal quantities of milk and water?
Options:
A)3:2
B)2:1
C)4:3
D)4:1
E)5:1
Rationale: (5/9)*P +(2/9)*Q = (4/9)*P+(7/9)*Q
P=5Q
P/Q = 5/1
The answer is E.
Answer: E
Question: If 36x = 216^y, which of the following expresses x in terms of y?
Options:
A)6^(3y-2)
B)6^3y
C)6^(3y-1)
D)6^(y-36)
E)6^(2y/216)
Rationale: By exponential simplification. 36 = 6^2 and 216=6^3 therefore (6^2)x=(6^3)^y gives x=(6^3y)/(6^2) further simplified to x=(6^3y)(6^-2) which gives x=6^(3y-2) (because exponential is additive in multiplication. i.e. a^b*a^c=a^(b+c). Answer: A
Answer: A
Question: Two pipes A and B can fill a cistern in 37 1/2 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the pipe B is turned off after?
Options:
A)7
B)6
C)9
D)7
E)2
Rationale: Let B be turned off after x minutes. Then, part filled by (A + B) in x min + part filled by A in (30 - x) min = 1.
x(2/75 + 1/45) + (30- x) 2/75 = 1
11x + 180 - 6x = 225 => x = 9
Answer: B
Answer: B
Question: What will the ratio of simple interest earned by certain amount at the same rate of interest for 5 years and that for 11 years.
Options:
A)1:2
B)2:3
C)2:7
D)5:3
E)None of these
Rationale: Explanation:
Let the principal be P and rate be R
then
ratio = [(P∗R∗6/100) /(P∗R∗9/100)]
=5PR /11PR=5:11
OptionE
Answer: E
Question: 2, 3, 6, 0, 10, -3, 14, (...)
Options:
A)6
B)2
C)-2
D)-6
E)0
Rationale: Explanation :
There are two series
2, 6, 10, 14, ... (Adding 4)
3, 0, -3, ... (Subtracting 3)
Hence, next term is -3 - 3 = -6
Answer : Option D
Answer: D
Question: Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 6 meters, and the interior of tank B has a height of 6 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?
Options:
A)60%
B)80%
C)100%
D)120%
E)125%
Rationale: The radius of tank A is 6/(2*pi).
The capacity of tank A is 10*pi*36 / (4*pi^2) = 180 / (2*pi)
The radius of tank B is 10 / (2*pi).
The capacity of tank B is 6*pi*100 / (4*pi^2) = 300 / (2*pi)
Tank A / Tank B = 180/300 = 6/10 = 60%
The answer is A.
Answer: A
Question: At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?
Options:
A)8%
B)3%
C)4%
D)2%
E)1%
Rationale: 150 = (750*5*R)/100
R = 4%
Answer:C
Answer: C
Question: On decreasing the price of a Air Conditioner by 20%, its sale is increased by 40%. The effect on the revenue is?
Options:
A)8 % decrease
B)4 % increase
C)16% decrease
D)12 % increase
E)none of these
Rationale: Net% change in revenue
= ( x + y + xy/100) %
= [-20 + 40 + ( -20 x 40)/100]% or 12%
ANSWER:D
Answer: D
Question: Three workers have a productivity ratio of 1 to 2 to 3. All three workers are working on a job for 5 hours. At the beginning of the 6th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 9th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest?
Options:
A)42 to 1
B)30 to 7
C)5 to 1
D)1 to 6
E)1 to 5
Rationale: The fastest worker who does 3 units of job worked for all 10 hours, so he did 3*10=30 units of job;
The slowest worker who does 1 unit of job worked for only 5+2=7 hours (first 5 hours and last 2 hours), so he did 1*7=7 units of job;
The ratio thus is 30 to 7.
Answer: B.
Answer: B
Question: Jennifer had $150 to spend on herself. She spent 1/5 of the money on a sandwich, 1/6 for a ticket to a museum, and 1/2 of it on a book. How much money does Jennifer have left over?
Options:
A)$4
B)$14
C)$5
D)$15
E)$20
Rationale: 1/5 x $150 = $30 for sandwich
1/6 x $150 = $25 for museum
1/2 x $150 = $75 for book
$30 + $25 + $75 = $130 spent
$150 - $130 = $20 left over
correct answer E
Answer: E
Question: The cost price of 16 articles is equal to the selling price of 11 articles. Find the profit percent?
Options:
A)18 2/15
B)45 5/11
C)36 2/14
D)18 2/16
E)45 2/12
Rationale: 16 CP = 11 SP
11 --- 2 CP
100 --- ? =>45 5/11%.Answer: B
Answer: B
Question: For a party 240 guests were invited.Contracted have gained 12.5% profit but 30 guest were absent.He charged same cost , lost 100 rs. what is the meal cost?
Options:
A)20/3
B)80/3
C)10/3
D)40/3
E)50/3
Rationale: Let Cost of one meal be x.
Hence, C.P. of 240 meals = 240 x.
Since contractor gains 12.5 % profit therefore
total selling price = 240x + 240*12.5/100 x
= 270x.
Now 30 guest were absent.
Therefore C.P will remain same = 240x
And new S.P for 210 guest = (270/240 ) *
210 x
In this case he incurrs a loss of Rs 100.
240x - (9/8) x * 210 = 100
x=80/3.
So, cost of one meal is Rs. 80/3.
ANSWER:B
Answer: B
Question: A certain basketball team that has played 2/3 of its games has a record of 16 wins and 4 losses. What is the greatest number of the remaining games that the team can lose and still win at least 3/4 of all of its games?
Options:
A) 7
B) 6
C) 5
D) 4
E) 3
Rationale: 16 wins, 4 losses - total 20 games played.
The team has played 2/3rd of all games so total number of games = 30
3/4th of 30 is 22.5 so the team must win 23 games and can afford to lose at most 7 total games. It has already lost 4 games so it can lose another 3 at most.
Answer (E)
Answer: E
Question: Present ages of Sameer and Anand are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Anand's present age in years?
Options:
A)24
B)25
C)26
D)27
E)28
Rationale: Let the present ages of Sameer and Anand be 5x and 4x years respectively.
Then, (5x + 3)/(4x + 3) = 11/9
9(5x + 3) = 11(4x + 3) => x = 6
Anand's present age = 4x = 24 years.
ANSWER:A
Answer: A
Question: The owner of a furniture shop charges his customer 20% more than the cost price. If a customer paid Rs. 8337 for a computer table, then what was the cost price of the computer table?
Options:
A)Rs.6725
B)Rs.6727
C)Rs.6908
D)Rs.6725
E)Rs.6947.5
Rationale: CP = SP * (100/(100 + profit%))
= 8337(100/120) = Rs.6947.5
Answer: E
Answer: E
Question: A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 10 per metre of cloth. What is the cost price of one metre of cloth?
Options:
A)26
B)95
C)90
D)42
E)22
Rationale: SP of 1m of cloth = 8925/85 = Rs. 105
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 105 - Rs. 10 = Rs. 95
Answer:B
Answer: B
Question: The sum of the numbers is 550. If the first number be twice the second and third number be one-third of the first, then the second number is:
Options:
A)48
B)150
C)72
D)84
E)27
Rationale: Let the second number be x. Then, first number = 2x and third number = 2x/3.
2x + x + 2x/3 = 550
11x/3 = 550
x = 150
ANSWER:B
Answer: B
Question: In how many ways can a committee consisting of three men and four women be formed from a group of six men and seven women?
Options:
A)⁶C₄ ⁷C₃
B)⁶C₃ ⁷C₅
C)⁷C₄ ⁶C₃
D)⁶C₃ ⁷C₃
E)⁷C₅ ⁶C₄
Rationale: The group contain six men and seven women
Three men can be selected from six men in ⁶C₃ ways.
Four women can be selected from seven women in ⁷C₄ ways.
Total number of ways = (⁷C₄)(⁶C₃).
Answer:C
Answer: C
Question: Find the number which is nearest to 3105 and is exactly divisible by 21?
Options:
A)3100
B)2500
C)2545
D)5800
E)3108
Rationale: On dividing 3105 by 21, we get 18 as remainder.
Number to be added to 3105 = (21 - 18) - 3.
Hence, required number = 3105 + 3 = 3108.
Answer E
Answer: E
Question: A Sum of Rs.2600, is lent out in 2 parts SI at 10% for 5yrs is equal to SI on 2nd part at 9% rate for 6 yrs. find the ratio of parts.
Options:
A)13:15
B)27:25
C)15:17
D)17:19
E)21:23
Rationale: Solution :
Given SI1 = SI 2
P1 : P2 = 1/R1T1 : 1/R2T2
= 1/(10*5) : 1/(9:6)
27:25
B
Answer: B
Question: If 102y = 25, then 10-y equals:
Options:
A)3
B)2
C)6
D)9
E)1/5
Rationale: 102y = 25
(10y)2 = 52
10y = 5
1/10y = 1/5
10-y = 1/5
Answer :E
Answer: E
Question: Anand and Deepak started a business investing Rs. 4,500 and Rs. 8,000 respectively. Out of a total profit of Rs. 3,000. Deepak's share is?
Options:
A)s. 1600
B)s. 1500
C)s. 2450
D)s. 1920
E)s. 1400
Rationale: Ratio of their shares = 4500 : 8000 = 9 : 16
Deepak's share = Rs. (3000 * 16/25) = Rs. 1920 ANSWER "D
Answer: D
Question: What will be the difference in simple and compound interest on 7000 after three years at the rate of 10 percent per annum?
Options:
A)160
B)42
C)62
D)217
E)None of these
Rationale: For 3 years:
Diff.=Sum×(rate)2(300+rate)/(100)3
= 7000×10×10×310/100×100×100 = 217
Answer D
Answer: D
Question: 16 men went to a restaurant. Fifteen of them paid Rs.80 each and the sixteenth man paid Rs.75 more than the average of all the 16 men. What is the total bill?
Options:
A)1360
B)1560
C)1660
D)1760
E)1460
Rationale: 15 paid Rs.80 each = 15*80 = 1200
total = x
then 16th man would have paid = x-1200
that is = 75+(x/16)
((x/16)=average)
equating these two
x-1200 = 75+(x/16)
x-(x/16)= 1275
15/16x = 1275
x = 1275*16/15
x = 1360
ANSWER:A
Answer: A
Question: A is thrice as efficient as B and is, therefore, able to finish a piece of work 10 days earlier than B. In how many days A and B will finish it together?
Options:
A)3 1/2 days
B)3 4/5 days
C)3 days
D)5 days
E)6 days
Rationale: Explanation:
WC = 3:1
WT = 1:3
x 3x
1/x – 1/3x = 1/10
x = 20/3
3/20 + 1/20 = 1/5 => 5 days
Answer: D
Answer: D
Question: A book store bought copies of a new book by a popular author, in anticipation of robust sales. The store bought 400 copies from their supplier, each copy at wholesale price x. The store sold the first 150 copies in the first week at 80% more than x, and then over the next month, sold a 100 more at 20% more than x. Finally, to clear shelf space, the store sold the remaining copies to a bargain retailer at 40% less than x. What was the bookstore’s net percent profit or loss on the entire lot of 400 books?
Options:
A) 30% loss
B) 10% loss
C) 10% profit
D) 20% profit
E) 60% profit
Rationale: [[x(150)(1.8)+x(100)(1.2)+x(150)(0.6)]/400x] - 1
[50[(3)(1.8) + (2)(1.2) + (3)(0.6)] / (50)(8)] - 1
[(5.4 + 2.4 + 1.8)/8] - [8/8]
+1.6/8
+20%
answer is D
Answer: D
Question: A dice is rolled 3times & sum of 3 no.'sappearing on the uppermost face is 15. The chance that the first roll was four is?
Options:
A)2/113
B)3/114
C)1/108
D)2/119
E)3/117
Rationale: Sol. Total number of favorable outcomes n(S) . e . 216 Combinations of outcomes for getting sum of 15 on uppermost face = (4, 5, 6) (5, 4, 6) (6, 5, 4) (5, 6, 4), (4, 6, 5), (6, 4, 5), (5, 5, 5), (6, 6, 3), (6, 3, 6) (3, 6, 6) Now outcomes on which first roll was a four, n(E) = (4, 5, 6), (4, 6, 5) P(E) n(E) 2 1 Pt') = n(S) = 216 = 1/108
C
Answer: C
Question: Two persons start running simultaneously around a circular track of length 300 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
Options:
A)16 seconds
B)17 seconds
C)19 seconds
D)27 seconds
E)87 seconds
Rationale: Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 300 / (15 + 25)5/18 = 300* 18 / 40 * 5
= 27 seconds.
Answer: D
Answer: D
Question: The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years
Options:
A)A)3:4
B)of these
C)C)4:3
D)inadequate
E)B)3:5
Rationale: Let P's age and Q's age be 6x and 7x years respectively.
Then, 7x - 6x = 4 => x = 4
Required ratio = (6x + 4) : (7x + 4)
28 : 32 = 7:8
ANSWER:B
Answer: B
Question: If x is equal to the sum of the integers from 50 to 70, inclusive, and y is the number of even integers from 50 to 70, inclusive, what is the value of x + y?
Options:
A)1211
B)1231
C)1251
D)1271
E)1291
Rationale: x = 50 + 51 +...+ 70 = 21(60) = 1260
y = 11
x+y = 1271
The answer is D.
Answer: D
Question: Jordan took a bus from home to market, that travels at 20 kmph. While walking back at 2 kmph,
halfway through, he suddenly realized he was getting late and he cycled back the remaining distance in 10 kmph. Find the average speed.
Options:
A)2.9 kmph
B)4.3 kmph
C)5.1 kmph
D)1.8 kmph
E)none of these
Rationale: Let the distance be 2x(one way)
Time taken by bus = 2x/20, by walking =x/2, by cycling = x/10 hours
:. Average speed = Total Distance/Total time
= 2x / x/10 + x/2 + x/10
= 2 *60 / 6+30+6
= 2.9
ANSWER:A
Answer: A
Question: A is twice as good a workman as B and together they finish a piece of work in 18 days. In how many days will A alone finish the work?
Options:
A)27 days.
B)32 days.
C)18 days.
D)33 days.
E)29 days.
Rationale: A
27 days.
If A takes x days to do a work then B takes 2x days to do the same work.
--> 1/x+1/2x = 1/18
--> 3/2x = 1/18
--> x = 27 days.
Hence, A alone can finish the work in 27 days.
Answer: A
Question: What is the lowest positive integer that is divisible by each of the integers 1 through 9 inclusive?
Options:
A)420
B)840
C)1260
D)2520
E)5020
Rationale: We have to find the LCM of 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, and 3^2.
The LCM is 1*2^3*3^2*5*7= 2520
The answer is D.
Answer: D
Question: At a recent small town election for mayor a total of 963 votes were cast for the four candidates, the winner exceding his opponents by 53, 79 and 105 votes, respectively. How many votes were cast for each candidate?
Options:
A)134
B)178
C)195
D)166
E)194
Rationale: C
195
The number of votes the winning candidate received was
963 + 53 + 79 + 105	/4= 300.
The second received 300 – 53 = 247,
The third received 300 – 105 = 195.
Answer: C
Question: A palindrome is a number that reads the same forward and backward, such as 242. How many even three-digit numbers are palindromes?
Options:
A)40
B)400
C)500
D)5,000
E)100,000
Rationale: if the palindrome must be even, it must begin and end in 2,4 6 and 8 ( 4 ways) e.g 212,414.
The middle number in the three-digit could be 0-9 ( 10 ways), e.g 252, 282
we thus have, 4 *10 = 40.
A
Answer: A
Question: A sum of money deposited at compound interest (compounded yearly) amounts to $1210 in 2 years and to $1452 in 3 years. What is the interest rate?
Options:
A)20%
B)10%
C)60%
D)70%
E)30%
Rationale: 1452 - 1210 = 242
242 / 1210 = 0.2 = 20%
The answer is A.
Answer: A
Question: Convert the following into a fraction: 0.3%
Options:
A)1/3
B)2/3
C)3/10
D)1/6
E)None of the Above
Rationale: 0.3 =3/10
Answer is C.
Answer: C
Question: In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?
Options:
A)33
B)67
C)25
D)66
E)81
Rationale: A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75.
In a game of 100 points, B gives (100 - 75) = 25 points to C.
Answer: C
Answer: C
Question: The value of 48 ÷ 12 x (9/8 of 4/3 ÷ 3/4 of 2/3) is ?
Options:
A)1 1/3
B)5 1/3
C)3
D)12
E)None
Rationale: Answer
Given expression = 48/12 x (3/2 ÷ 1/2)
= 4 x (3/2) x 2
= 12
Option: D
Answer: D
Question: There are a lot of houses such that the numbers of their doorplates are odd numbers and the first number of the doorplates is 685, the last number of the doorplates is 705. How many houses are there?
Options:
A)12
B)11
C)13
D)9
E)10
Rationale: So it starts from 685 and goes like 687, 689,...... 705. and both first and last number are inclusive. Since every other number is odd, it's just 1/2 of the numbers and since it starts with an odd and ends with an odd inclusive add one to the result.
i.e., ([705-685][/2]+1 = 11
Ans B
Answer: B
Question: A and B starts a business investing Rs.85000 and Rs.15000 respectively. Find out the ratio in which the profits should be shared.
Options:
A)3:17
B)17:3
C)10:3
D)3:10
E)5:12
Rationale: Here A's and B's capitals are there for equal time. Hence
A : B = 85000 : 15000
= 85 : 15
= 17 : 3
Answer is B.
Answer: B
Question: What is the lowest positive integer that is divisible by each of the odd integers between 15 and 23, inclusive?
Options:
A)3×17×19×21
B)5×17×19×23
C)7*15*17*19*21
D)7×15×19×21
E)7*15*17*19*23.
Rationale: We should find the LCM of 15 = 3*5, 17, 19, and 21 = 3*7,23 --> LCM = 3*5*7*17*19*23 = 7*15*17*19*23.
Answer: E
Answer: E
Question: A jar is filled with red, white, and blue tokens that are equivalent except for their color. The chance of randomly selecting a red token, replacing it, then randomly selecting a white token is the same as the chance of randomly selecting a blue token. If the number of tokens of every color is a multiple of 5, what is the smallest possible total number of tokens in the jar?
Options:
A) 9
B) 12
C) 15
D) 18
E) 21
Rationale: (Red / Total Coins)*(White / Total Coins) = (Blue / Total Coins)
i.e. Red*White = Blue*Total Coins
Let, Red = 3a
White = 3b
Blue = 3c
Total Coins = 3(a+b+c)
i.e. 3a * 3b = 3c*3(a+b+c)
i.e. a*b = c*(a+b+c)
For smallest values of a, b and c
2*3 = 1*(1+2+3)
i.e. Minimum Total Coins = 3*(1+2+3) = 12
Answer: Option B
Answer: B
Question: Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 200 m, in what time will they cross other travelling in opposite direction?
Options:
A)17 sec
B)12 sec
C)16 sec
D)15 sec
E)20 sec
Rationale: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/5 = 8 m/sec.
Relative speed = 12 + 8 = 20 m/sec.
Required time = (200 + 200)/20 = 20 sec.
Answer:E
Answer: E
Question: What is the least number to be subtracted from 800 to make it a perfect square?
Options:
A)1
B)16
C)20
D)71
E)60
Rationale: The numbers less than 800 and are squares of certain number is 784.
The least number that should be subtracted from 800 to make it perfect square = 800 - 784 = 16.
ANSWER:B
Answer: B
Question: Working alone at a constant rate, Alan can paint a house in a hours. Working alone at a constant rate, Bob can point 1/4 of the same house in b hours. Working together, Alan and Bob can paint 1/3 of the house in c hours. What is the value of b in terms of a and c?
Options:
A)(3ac)/(a+c)
B)(4a-12c)/(3ac)
C)(3ac)/(4a-12c)
D)(ac)/(a+2c)
E)(ac)/(a+c)
Rationale: work time
A 1 a
B 1/4 b
A+B 1/3 c
A's rate = 1/a
B's rate = 1/4b
when they are working together , their combined rate is 1/a + 1/(4b) = (1/3)/c
1/(4b) = 1/(3c) - 1/a
=> b = 3ac /(4a-12c)
Answer is C.
Answer: C
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 25 hours respectively. The ratio of their speeds is?
Options:
A)4:5
B)5:3
C)4:4
D)4:9
E)4:2
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √25 : √9 = 5:3
Answer:B
Answer: B
Question: What is the smallest positive integer that can be multiplied by 605 to make it a perfect square?
Options:
A)2
B)3
C)5
D)7
E)11
Rationale: 605 is multiplied by 5 gives 3025
Its a square root of 55
Answer is 5 -Option C
Answer: C
Question: If 45-[28-{37-(15-*)}]= 54, then * is equal to:
Options:
A)-29
B)-19
C)15
D)29
E)39
Rationale: 45-[28-{37-(15-*)}]= 54 => 45-[28-{37-15+*}]=54
45-[28-37+15-*]=54 => 45[43-37-*]=54
45-[6-*]=54 => 45-6+*=54
39+*=54 => *=54-39
= 19
ANSWER:C
Answer: C
Question: WINK, Inc. follows a certain procedure that requires two tasks to be finished independently in order for a job to be done. On any given day, there is a 5/8 probability that task 1 will be completed on time, and a 3/5 probability that task 2 will be completed on time. On a certain day, what is the probability that task 1 will be completed on time, but task 2 will not?
Options:
A)1/4
B)3/40
C)13/40
D)7/20
E)13/22
Rationale: P(1 and not 2)=5/8*(1-3/5)=1/4
Answer: A.
Answer: A
Question: Kim purchased n items from a catalog for $8 each. Postage and handling charges consisted of $3 for the first item and $1 for each additional item. Which of the following gives the total dollar amount for Kim’s purchase, including postage and handling, in terms of n ?
Options:
A)8n + 2
B)8n + 4
C)9n + 2
D)9n + 3
E)9n + 4
Rationale: n items for $8 each
total price $8n
postage and handling of $3 for 1st item and $1 for the rest
total postage and handling = $ [3+ (n-1)]
= $ n+2
total cost
8n+n+2 = 9n+2	;
ANSWER:C
Answer: C
Question: |8 - 3| - |4 - 6| = ?
Options:
A)3
B)2
C)1
D)0
E)4
Rationale: |8 - 3| - |4 - 6| = | 5 | - | -2 | = 5 - 2 = 3
correct answer A
Answer: A
Question: When m is divided by 9, the remainder is 8. When m is divided by 13, the remainder is 5. If 1 < m < 200, what is the greatest possible value of m?
Options:
A)47
B)65
C)103
D)117
E)161
Rationale: Looking at the choices, options BD can be eliminated as they are divisible by 13
Starting from the highest number 164;
161 = 153 + 8 (153 divisible by 9)
161 = 156 + 5 (156 divisible by 13)
it fits the result
Answer = E
Answer: E
Question: In a certain year, the population of a certain town was 9000. If in the next year the population of males increases by 4% and that of the females by 9% and the total population increases to 9600, then what was the ratio of population of males and females in that given year?
Options:
A)7 : 8
B)5 : 4
C)2 : 3
D)Data inadequate
E)None of these
Rationale: Let the population of males = x; then the population of females = 9000 – x
Now, 4% of x + 9% of (9000 – x)
= (9600 – 9000 ) = 600
or 0.04x + 720 – 0.09x = 600
or 720 – 600 = 0.09x – 0.04x
or, 120 = 0.05x
x = 4200
Reqd ratio of population of males and females
4200/9000−4200=4200/4800=7:8
Answer A
Answer: A
Question: A library has an average of 540 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:
Options:
A)300
B)276
C)290
D)285
E)None
Rationale: Since the month begins with sunday,to there will be five sundays in the month
Average required = (540x5 + 240x25) /30) = 290
Answer: Option C
Answer: C
Question: Nil and Ethan are brothers. They left their home
at the same time and drove to the same beach.
Nil drove at a speed of 60 miles per hour. Ethan
drove at a speed of 20 miles per hour. Nil
arrived at the beach 0.5 hour earlier than Ethan.
What is the distance between their home and the
beach?
Options:
A)50 miles
B)60 miles
C)70 miles
D)80 miles
E)90 miles
Rationale: Every hour, Nil gets ahead of Ethan 60 - 20 =
40 miles. When Nil arrived at the beach, Ethan
is only 20 × 0.5 = 10 miles behind. That tells us
they only drove 1 hour when Nil arrived at the
beach.
The distance between their home and the beach
is
Nil’s speed × Nil’s time
= 60 × 1 = 60 miles.
correct answer B
Answer: B