divelab/Sys2Bench huggingface dataset:
Question: Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1305 as rent for parking his cars, what is the total rent paid by all the four agencies?
Options:
A)Rs. 4500
B)Rs. 4800
C)Rs. 5250
D)Rs. 7134
E)None of these
Rationale: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15
= 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60
Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.
The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k
It is given that A paid Rs. 1305
45k = 1305 => k = 29
246k = 246(29) = Rs. 7134
Thus the total rent paid by all the four agencies is Rs. 7134.
ANSWER:D
Answer: D
Question: The number of stamps that P and Q had were in the ratio of 9:2 respectively. After P gave Q 33 stamps, the ratio of the number of P's stamps to the number of Q's stamps was 6:5. As a result of the gift, P had how many more stamps than Q?
Options:
A)11
B)33
C)45
D)67
E)80
Rationale: P started with 9k stamps and Q started with 2k stamps.
(9k-33)/(2k+33) = 6/5
45k - 12k = 178 + 165
33k = 343
k = 11
P has 9(11) - 33 = 66 stamps and Q has 2(11)+33 = 55 stamps.
The answer is A.
Answer: A
Question: Gill drives 120 miles from Los Angeles to San Diego to fetch a package. On her way there she drives at 40 miles per hour. On her way back she drives 50% faster. What is Gill's average velocity T for the round trip?
Options:
A)24 miles per hour
B)48 miles per hour
C)50 miles per hour
D)53 1/3 miles per hour
E)68 miles per hour
Rationale: Here's an Average Speed question in which the prompt gives you almost all of the immediate numbers needed to work with.
Driving from LA to SD, we have a distance of 120 miles and a speed of 40 miles/hour.
D = (R)(T)
120 = (40)(T)
120/40 = 3 = T
3 hours to drive to SD
On the way back, she drives 50% FASTER. Gill's return speed is (1.5)(40) = 60 miles/hour.
D = (R)(T)
120 = (60)(T)
120/60 = 2 = T
2 hours to drive to SD
Total Distance = 240 miles
Total Time = 3+2 = 5 hours
Average Speed = 240/5 = 48 miles/hour
Final Answer:
B
Answer: B
Question: Harold works at a resort from the beginning of March to the end of September. During the month of August this past year, he made 6 times the average (arithmetic mean) of his monthly totals in tips for the other months. His total tips for August were what fraction of his total tips for all of the months he worked?
Options:
A)1/3
B)2/5
C)3/7
D)1/2
E)4/7
Rationale: The time from beginning of March to the end of September is 7 months.
If x is the average monthly tip for all months other than August then his August month tip will be 6*x
His total tip for the 7 months = 6*(average tip for the months other than August) + 6x
=12x
August tips as a fraction of total tips = 6x/12x =1/2. So D
Answer: D
Question: A certain sum amounts to Rs.1725 in 3 years and Rs.1875 in 5 years. Find the rate % per annum?
Options:
A)7%
B)5%
C)2%
D)1%
E)6%
Rationale: 3 --- 1725
5 --- 1875
--------------
2 --- 150
N = 1 I = 75 R = ?
P = 1725 - 225 = 1500
75 = (1500*1*R)/100
R = 5%
Answer:B
Answer: B
Question: The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 5 years hence?
Options:
A)22
B)77
C)70
D)98
E)71
Rationale: A + B = 60, A = 2B
2B + B = 60 => B = 20 then A = 40.
5 years, their ages will be 45 and 25.
Sum of their ages = 45 + 25 = 70.
Answer: C
Answer: C
Question: Raja buys 100 shares of par value Rs. 15 each, of a company, which pays an annual dividend of 12% at such a price that he gets 10% on his investment. Find the market value of a share.
Options:
A)2
B)4
C)5
D)6
E)18
Rationale: Face value of each share = Rs.15
Total dividend received by Raja= 100Ã—15Ã—12/100 = Rs.180
Let market value of 100 shares = Rs.x
xÃ—10/100=180
x =1800
ie, Market value of 100 shares = Rs.1800
Hence, Market value of each share = Rs.18
Answer is E
Answer: E
Question: Sn = n^2 + 5n + 94 and K = S6 – S5 - S4 + S3 + S2 – S1. What is the value of K?
Options:
A)12
B)50
C)45
D)41
E)36
Rationale: I used brute force for this question:
S6: 36+30+94=160
S5: 25+25+94=144
S4: 16+20+94=130
S3: 9+15+94=118
S2: 4+10+94=108
S1: 1+5+94=100
S6-S5-S4+S3+S2-S1= 16-12+8=12
Answer A
Answer: A
Question: There are 8 stores in town that had a total of 21 visitors on a particular day. However, only 12 people went shopping that day; some people visited more than one store. If 8 people visited exactly two stores each, and everyone visited at least one store, what is the largest number of stores anyone could have visited?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: 8 people visited 2 stores each for 16 visits.
To maximize the number of stores that one person visited, let's assume that 3 people visited 1 store each. The number of remaining visits is 21 - 16 - 3 = 2, which is the maximum that one person could have visited.
The answer is A.
Answer: A
Question: The content of several smaller cylinders ( 3 meter diameter and 6 meter height) were to be emptied into a larger cylinder(20 meter diameter and 10 meter height), how many smaller cylinders will fill up the larger cylinder?
Options:
A)20
B)10
C)50
D)74
E)73
Rationale: Calculate the volume of the larger cylinder and divide it by the volume of the smaller cylinder.
volume of cylinder =πr2h
larger cylinder volume=3141.59
smaller cylinder volume=42.41
therefore the number of cylinders B that can be filled to capacity=3141.59/42.41=74.1
Answer is D 74 smaller cylinders can be filled to capacity.
Answer: D
Question: Sawyer and Beth each drove from Smallville to Crown City by different routes. Sawyer drove an an average speed of 40 miles per hour and completed the trip in 30 minutes. Beth's route was 5 miles longer, and it took her 20 minutes more than Sawyer to complete the trip. How many miles per hour was Beth's average speed on this trip?
Options:
A) 24
B) 30
C) 48
D) 54
E) 75
Rationale: Speed = Distance/Time
Distance for Sawyer = Speed * Time = 40 * 1/2 = 20 miles
Distance for Beth = Distance for Sawyer +5 = 20+5 = 25 miles
Time taken by Beth = Time taken by Sawyer + (1/3 hour) = 1/2+1/3 = 5/6
Speed of Beth = D/T = 25/(5/6) = 25*6/5 = 30 miles per hour
Hence, B is the answer.
Answer: B
Question: A man has a recurring deposit of $2000 every month with a compounded monthly interest rate of 5%. How many months it will take to get an amount of $2500?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: 1 month: 2000*5/100 = 100: Total: 2100
2nd month: 2100*5/100 = 105: Total: 2100+105= 2205
3rd month: 2205*5/100 = 110: Total: 2205+110= 2315
4th month: 2315*5/100 = 116: Total: 2315+116= 2431
5th month : 2431*5/100 = 122: Total: 2431+122= 2553 >2500
;4 years;
ANSWER:B
Answer: B
Question: Dan can do a job alone in 12 hours. Annie, working alone, can do the same job in just 9 hours. If Dan works alone for 4 hours and then stops, how many hours will it take Annie, working alone, to complete the job?
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: Dan can complete 1/12 of the job per hour.
In 4 hours, Dan completes 4(1/12) = 1/3 of the job.
Annie can complete 1/9 of the job per hour.
To complete the job, Annie will take 2/3 / 1/9 = 6 hours.
The answer is C.
Answer: C
Question: The owner of a furniture shop charges his customer 10% more than the cost price. If a customer paid Rs. 2200 for a computer table, then what was the cost price of the computer table?
Options:
A)2299
B)2000
C)2670
D)6725
E)2601
Rationale: CP = SP * (100/(100 + profit%))
= 2200(100/110) = Rs. 2000
Answer:B
Answer: B
Question: In a college, the ratio of the number of boys to girls is 6 : 5. If there are 200 girls, the total number of students in the college is
Options:
A)440
B)520
C)620
D)720
E)820
Rationale: Explanation:
Let the boy are 6x and Girls are 5x
=> 5x = 200
=> x = 40
Total students = 6x+5x = 11x = 11(40) = 440
Option A
Answer: A
Question: If population of certain city increases at the rate of 5%. If population in 1981 was 231525, then population in 1978 was?
Options:
A)120000
B)120029
C)187899
D)178968
E)200000
Rationale: X * (105/100) * (105/100) * (105/100) = 231525
X = 231525/1.157625
X = 200000
Answer:E
Answer: E
Question: Calculate the value of e from the below equation: e^3âˆ’25e+8=74
Options:
A)5
B)3
C)4
D)6
E)2
Rationale: Use elimination method to find the correct option. you find that of all the options 6 is the correct value for e
Answer: D
Answer: D
Question: If the wheel is 56 cm then the number of revolutions to cover a distance of 1056 cm is?
Options:
A)10
B)12
C)3
D)11
E)9
Rationale: 2 * 22/7 * 56 * x = 1056
=> x = 3
Answer: C
Answer: C
Question: How many integers between 300 and 1000 are there such that their unit digit is odd?
Options:
A)200
B)250
C)350
D)400
E)450
Rationale: There are 700 numbers from 301 to 1000 (inclusive).
Half of the numbers are odd, so there are 350 odd numbers.
The answer is C.
Answer: C
Question: Each of the dogs in a certain kennel is a single color. Each of the dogs in the kennel either has long fur or does not. Of the 45 dogs in the kennel, 36 have long fur, 27 are brown, and 8 are neither long-furred nor brown. How many long-furred dogs are brown?
Options:
A)26
B)19
C)11
D)8
E)6
Rationale: No of dogs=45
Long fur=36
Brown=27
Neither long fur nor brown=8
Therefore, either long fur or brown=45-8=37
37=36+27-Both
Both=26
Answer A
Answer: A
Question: In a office work is distribute between p persons. If 1/5 members are absent then work increased for each person is?
Options:
A)13.28%
B)14.28%
C)15.28%
D)16.28%
E)25%
Rationale: let total % of work is 100%
total person=p
1/5 person are absent of total person . so absent person is 1/5p ie p/5.
left person is, p-p/5=4p/5.
p person do the work 100%
1 person do the work 100*p%
4p/5 person do the work (100*p*5)/4p%=125%
work increased for each person is=(125-100)%=25%
ANSWER:E
Answer: E
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red?
Options:
A)12/479
B)12/497
C)12/455
D)12/487
E)12/486
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
When three marbles are drawn, the probability that one is yellow and two are red
= (²C₁)(⁴C₂)/¹⁵C₃
= (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13)
= 12/455
Answer: C
Answer: C
Question: Richard receives an increment in his salary. His salary presently forms 30% of the total income of his family. Before the increment his salary used to form 20% of the total income of his family. By how many percentage points did the salary of Richard as a percentage of his family's total income increase?
Options:
A)14(2/7)
B)16(2/3)
C)10
D)8
E)13(3/7)
Rationale: The salary of Richard as a percentage of his family's total income was 20%
The salary of Richard as a percentage of his family's total income now is 30%
The percentage points that have increased is 10 (from 20% to 30%).
Answer (C)
Answer: C
Question: The 323rd term of the series a, b , b, c, c, c, d, d, d, d, e, e, e, e, e, .... is
Options:
A)u
B)v
C)w
D)y
E)z
Rationale: a is one time, b,2 times so on...
so 323=n(n+1)/2..
0r n(n+1)= 646... now 25*26=650...24*25<646 so n= 25. and 25th alphabet is Y. ans D
Answer: D
Question: John, Karen, and Luke collected cans of vegetables for a food drive. The number of cans that John collected was 1/2 the number of cans that Karen collected and 1/5 the number of cans that Luke collected. The number of cans that Luke collected was what fraction of the total number of cans that John, Karen, and Luke collected?
Options:
A) 1/5
B) 1/3
C) 2/5
D) 1/2
E) 2/3
Rationale: John = (1/2)Karen --> Karen = 2(John)
John = 1/5(Luke) --> Luke = 5(John)
Total = 10(John)
Luke/Total = 2/10 = 1/5
Answer: A
Answer: A
Question: A train 210 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
A)22 sec
B)16 sec
C)17 sec
D)18 sec
E)12 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 210 * 2/35 = 18 sec
Answer:D
Answer: D
Question: A number x is 5 times another number y. The percentage that y is less than x is
Options:
A)12.5%
B)80%
C)88%
D)11%
E)1%
Rationale: Say y=1 and x=5.
Then y=1 is less than x=5 by (5-1)/5*100=4/5*100=80%.
Answer: B.
Answer: B
Question: If n = 4^11 – 4, what is the units digit of n?
Options:
A)0
B)1
C)4
D)6
E)8
Rationale: Always divide the power (incase 11) by 4 and use the remainder as the new power. The question now becomes 4^3 - 4. Now 4^3 has last digit 4. , we subtract 4 from 4 = 0 is the answer. Option A
Answer: A
Question: On the first of the year, James invested x dollars at Proudstar bank in an account that yields 1.5% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year?
Options:
A)11.04%
B)6.12%
C)8%
D)7.25%
E)10%
Rationale: Per quarter, interest = 1.5% So for a year, interest = 6% Due to quarter cumulation, effective yield (YTM) would be slight higher than 6% Answer = 6.12% =ANSWER:B
Answer: B
Question: If 288 is divided into four parts proportional to 5, 7, 4, 8 then the smallest part is :
Options:
A)46
B)44
C)20
D)48
E)42
Rationale: Given ratio = 5 : 7 : 4 : 8 , sum of ratio = 24
:. The smallest part = (288 *4/24) = 48
ANSWER:D
Answer: D
Question: x, a, z, and b are single digit positive integers. x = 1/6 a. z = 1/6 b. (10a + b) – (10x + z) could NOT equal
Options:
A)35
B)30
C)43
D)60
E)65
Rationale: a=6x , b =6z therefore(6x.10+6z) - (10x +z) = (6-1) (10x+z) =5.(10x+Z)
number should be divisible by 5
C
Answer: C
Question: If the a radio is sold for rs 490 and sold for rs 465.50.find loss percentage.
Options:
A)3
B)5
C)7
D)9
E)None of them
Rationale: cost price=rs 490,selling price= 465.50.
loss=rs(490-465.50)=rs 24.50.
loss%=[(24.50/490)*100]%=5%
Answer is B
Answer: B
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)None of these
Rationale: Explanation:
WC = 3:1
WT = 1:3
x 3x
1/x â€“ 1/3x = 1/10
x = 20/3
3/20 + 1/20 = 1/5 => 5 days
ANSWER IS D
Answer: D
Question: The price of a book is increased from $300 to $390. What is the % of increase in its price?
Options:
A)10%
B)20%
C)30%
D)35%
E)45%
Rationale: Explanation: Change in the price = Rs 390 – Rs 300
= Rs 90
Percentage of increase = Change in the price Initial Price
* 100.
Percentage increase in price =( 90 / 300
) *100 = 30%
C
Answer: C
Question: Machine A and machine B are each used to manufacture 440 sprockets. It takes machine A 10 hours longer to produce 440 sprockets than machine B. Machine B produces 10% more sprockets per hour than machine A. How many sprockets per hour does machineAproduce?
Options:
A)6
B)6.6
C)60
D)4.4
E)110
Rationale: time taken by B = t
time taken by A = t+10
qty produced by A = q
qty produced by B = 1.1 q
for B: t(1.1q) =440
qt=400
for A: (t+10)(q) = 440
qt+10q=440
400+10q=440
q=4
so A can produce 4/hour.
then B can produce = 4(1.1)=4.4/hour.
D
Answer: D
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train?
Options:
A)150 meter
B)166 meter
C)154 meter
D)146 meter
E)141 meter
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9 = 150 meter
Answer: A
Answer: A
Question: If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value F of z - x?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: x<y<z
To find the least possible value for z-x; we need to find the values for z and x that can be closest to each other. If x is some even number, then what could be minimum possible odd z.
If x is some even number
y-x>5; y>x+5; minimum value for y=x+5+2=x+7[Note: x+5 is as even+odd=odd and nearest odd greater than x+5 is x+5+2]
Minimum value for z=y+2=x+7+2=x+9 [Note: z=y+2 because both z and y are odd. Difference between two odd numbers is 2]
F=z-x = x+9-x= 9
Ans:D
Answer: D
Question: If a, b and c are even integers, which of the following could be the value of a^2 + b^2 + c^2?
Options:
A)166
B)168
C)182
D)22
E)200
Rationale: a, b and c are even integers which means that, supposing that x, y and z are integers, then a=2x, b=2y and c=2z
Therefore we have: a^2+b^2+c^2=2^2*x^2+2^2*y+2^2*z=4x^2+4y^2+4z^2=4(x^2+y^2+z^2).
Which means that the total a^2+b^2+c^2 must be divisible by 4.
The only choice which is divisible by 4 is: E)
200=14^2+2^2+0^2
Answer: E.
Answer: E
Question: The function F(n) is defined as the product of all the consecutive positive integers between 4 and n^2, inclusive, whereas the function G(n) is defined as the product of the squares of all the consecutive positive integers between 1 and n, inclusive. The exponent on 2 in the prime factorization of F(3)/G(3) is
Options:
A)	1
B)	2
C)	3
D)	4
E)	5
Rationale: F(3)/G(3)
=product(1 to 3 ^2) / 1.2^2.3^2
=1.2.3.4.5.6.7.8.9/1.4.9
=1.2.3.(2^2).5.(2.3).7.(2^3).9/1.(2^2).9
=1.(2^7).3.5.7.9/1.(2^2).9
Loof for 2^7/2^2=2^5 ----Exponent 4
Answer: D
Answer: D
Question: To fill an art exhibit, the peoples in an art course are assigned to create one piece of artwork each in the following distribution: 1/3 are sculptures, 1/8 are oil paintings, 1/2 are watercolors, and the remaining 10 pieces are mosaics. How many peoples are in the art class?
Options:
A)80
B)120
C)240
D)320
E)400
Rationale: Let the total number of peoples in the art class = s
Distribution of artwork is as
1/3 are sculptures
1/8 are oil paintings
1/2 are watercolors, and the remaining 10 pieces are mosaics
(1/3)s +(1/8)s +(1/2)s + 10 = s
Since remaining 10 pieces are mosaics , (1/24)s = 10
s = 240
Answer C
Answer: C
Question: In a single throw of a die what is the probability of getting a number greater than 4 ?
Options:
A)1/2
B)1/4
C)1/3
D)2/5
E)1/6
Rationale: when a die is thrown S={1,2,3,4,5,6}
E = event of getting a number greater than 4 = {5,6}
P(E) = n(E)/n(S) = 2/6 = 1/3
Answer is C
Answer: C
Question: Divide Rs. 3364 between A and B, so that A's Share at the end of 5 years may equal to B's share at the end of 7 years, compound interest being at 5 percent.
Options:
A)Rs. 1764 and Rs.1600
B)Rs. 1756 and Rs.1608
C)Rs. 1722 and Rs.1642
D)Rs. 1755 and Rs.1600
E)None of these
Rationale: Explanation: A's share after 5 years = B's share after 7 years
(A's present share)(1+5100)5 = (B's present share)(1+5100)7
=>(A's present share)/(B's present share) = (1+5/100)7/(1+5/100)5 = (1+5/100)(7âˆ’5) = (1+5/100)2 =(21/20)2 =441/400
i.e, A's present share : B's present share = 441 : 400
Since the total present amount is Rs.3364, A's share = 3364 Ã— 441/(441 + 400)
= (3364 Ã— 441)/841 = 4 Ã— 441 = Rs. 1764
B's present share = 3364 - 1764 = Rs.1600
ANSWER IS A
Answer: A
Question: In how many ways can 5 boys and 1 girls be seated on 8 chairs so that no two girls are together?
Options:
A)5760
B)14400
C)480
D)56
E)40320
Rationale: Let us take opposite of the constraint.
2 girls sitting together:	:
1 case is GGBGBBBB.
Total number of ways=3!*5!*5 with just shifting the rightmost girl.
Then the 2 leftmost girls can shift one position , and using the above reasoning, the total number of ways = 3!*5!*4 and so on till the rightmost girl has 1 position.
So total number of ways = 3!*5!(5+4+3+2+1)=120*90=10800
Similarly another case is:
GBGGBBBB.
Using the above reasoning, the total number of cases is: 3!*5!*(15) =10800
Let us take 3 girls sitting together
GGGBBBBB
There are 3! *5! Ways. The 3 leftmost girls can shift 6 positions. So there are a total of 3!*5!*6=4320 ways
So total is 2*10800 + 4320=25920
The total number of possibilities = 8! Ways =40,320
Answer is 40320-25920=480
Hence C.
Answer: C
Question: Mangala completes a piece of work in 10 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is?
Options:
A)8 days
B)10 days
C)12 days
D)14 days
E)16 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 10 × 40/50 = 8 days
A)
Answer: A
Question: In a bag there are a certain number of yellow balls and blue balls. The probability of picking up exactly 1 blue ball when 2 balls are randomly drawn, is 1/2. Which of the following is the ratio of the number of yellow balls to blue balls in the bag
Options:
A)3:1
B)1:3
C)1:5
D)1:1
E)3:1
Rationale: since the probability of drawing a blue ball out of two picks is 1/2.
the ratio of the blue ball to yellow balls should be 1:1
Answer : D
Answer: D
Question: A train running at the speed of 50 km/hr crosses a pole in 9 sec. What is the length of the train?
Options:
A)125 m
B)786 m
C)566 m
D)546 m
E)445 m
Rationale: Speed = 50 * 5/18 = 125/9 m/sec
Length of the train = speed * time = 125/9 * 9
= 125 m
Answer: A
Answer: A
Question: Jack has $1.60 in pennies, nickels and dimes. The number of each kind of coin is the same. What is the total number of coins that Jack has?
Options:
A)40
B)35
C)30
D)25
E)20
Rationale: Let the number of each type of coin be a. Then 0.01a + 0.05a + 0.10a = 1.600.16a = 1.60a = 10So the total number of coins = 3a = 30Answer: C
Answer: C
Question: Length of a rectangular plot is 30 mtr more than its breadth. If the cost of fencin g the plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
Options:
A)46 m
B)60 m
C)65 m
D)78 m
E)80 m
Rationale: Let breadth = x metres.
Then, length = (x + 30) metres.
Perimeter = 5300/26.5 m = 200 m.
2[(x + 30) + x] = 200
2x + 30 = 100
2x = 70
x = 35.
Hence, length = x + 30 = 65 m
C
Answer: C
Question: . A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
Options:
A)28
B)108
C)297
D)27
E)28
Rationale: Explanation:
The boy can select one trouser in nine ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 12 = 108 ways.
Answer: Option D
Answer: D
Question: If f(x)=5x and g(y)=4y-8 then g(f(x))
Options:
A)87x-7
B)98x-8
C)58x-9
D)20x-8
E)96x-7
Rationale: g(f(x))=4(5x)-8 = 20x-8
Answer is D
Answer: D
Question: If b is a positive integer, which of the following could NOT be the square of b?
Options:
A) 5,008,644
B) 5,004,169
C) 4,999,696
D) 4,995,225
E) 4,990,752
Rationale: A number ending with 2 can never be a perfect square.
Units digit of a perfect square must be:
1,4,9,6,5
Answer E)
Answer: E
Question: In T.Nagar the building were numbered from 1 to 100.Then how many 4's will be present in the numbers?
Options:
A)18
B)19
C)20
D)21
E)22
Rationale: just count the number of 4's from 1 to 100
(4,14,24,34,40,41,42,43,44,45,46,47,48,49,54,64,74,84,94)
totally there are 20
ANSWER:C
Answer: C
Question: If Susan takes 13 seconds to run y yards, how many minutes will it take her to run x yards at the same rate?
Options:
A)13x/(60y)
B)xy/13
C)60xy/13
D)xy/780
E)780x/y
Rationale: The answer is A.
She runs x yards in 13x/y seconds =13x/60y minutes.
Answer: A
Question: In a meeting of 4 representatives from each of 6 different companies, each person shook hands with every person not from his or her own company. If the representatives did not shake hands with people from their own company, how many handshakes took place?
Options:
A)250
B)260
C)240
D)270
E)280
Rationale: In fact, all 24 people will shake hands with 20 others.
So, it SEEMS like the TOTAL number of handshakes = (24)(20)
HOWEVER, we need to keep in mind that we have counted each handshake TWICE.
To account for this DUPLICATION, we must divide (24)(20) by 2.
So, the TOTAL # of handshakes = (24)(20)/2 = 240
Answer : C
Answer: C