divelab/Sys2Bench huggingface dataset:
Question: The total of a company's assets in 1994 was 200% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of the company's assets in 1992 was N dollars, what were the company's assets in 1994?
Options:
A)5N
B)7N
C)10N
D)15N
E)20
Rationale: In 1992, the company's assets were N.
In 1993, the company's assets were N + 4N = 5N.
In 1994, the company's assets were 5N + 10N = 15N.
The answer is D.
Answer: D
Question: Three men rent a pasture for Rs. 660. The first used it for 50 sheep for 4 months, the 2nd for 40 sheep for 3 months and the 3rd for 46 sheep for 5 months. How much should the first pay ?
Options:
A)Rs. 220
B)Rs. 235
C)Rs. 240
D)Rs. 276
E)Rs. 286
Rationale: The payment should be in ratio of 200:120:230 or 20:12:23
First person should pay 20*660/55 = 240 Rs.
ANSWER:D
Answer: D
Question: In how many ways can 5 boys and 2 girls be seated on 8 chairs so that no two girls are together?
Options:
A)5760
B)14400
C)480
D)5670
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=5670
Hence D.
Answer: D
Question: Find the average of the series : 312, 162, 132, 142 and 122?
Options:
A)178
B)172
C)128
D)107
E)174
Rationale: Average
= (312 + 162 + 132 + 142 + 122)/5
= 870/5 = 174
Answer: E
Answer: E
Question: In how many ways can the letters of the word 'LEADER' be arranged?
Options:
A)739
B)73
C)360
D)840
E)849
Rationale: The word 'LEADER' contains 6 letters, namely 1L, 2E, 1A, 1D and 1R.
Required number of ways =6!/(1!)(2!)(1!)(1!)(1!)= 360.
Answer:C
Answer: C
Question: A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?
Options:
A)100 m
B)150 m
C)190 m
D)200 m
E)None of these
Rationale: Explanation:
Relative speed of the thief and policeman = (11 – 10) km/hr = 1 km/hr
Distance covered in 6 minutes = (1/60 × 6) km = 1/10 km = 100 m
∴ Distance between the thief and policeman = (200 – 100) m = 100 m.
Answer: A
Answer: A
Question: If 21520 books need to be placed in boxes and each box can contain at most 9 books. How many books will be in the last unfilled box?
Options:
A)9 books
B)8 books
C)1 book
D)4 books
E)5 books
Rationale: The number of books that can be placed in boxes of 9 books is the first number that is divisible by 9 that occurs before 21520.
In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 21520 = 10 and 9 is divisible by 9.
Hence, we need to remove 1 to this number for it to be divisible by 9
Correct Option: C
Answer: C
Question: How many seconds will a train 120 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?
Options:
A)27 sec
B)23 sec
C)24 sec
D)25 sec
E)26 sec
Rationale: D = 120 + 150 = 270
S = 36 * 5/18 = 10 mps
T = 270/10 = 27 sec
A
Answer: A
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
Options:
A)167
B)240
C)881
D)278
E)123
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x = 240 m.
Answer: B
Answer: B
Question: 287 x 287 + 269 x 269 - 2 x 287 x 269 = ?
Options:
A)466
B)646
C)666
D)324
E)333
Rationale: Given Exp.	= a2 + b2 - 2ab, where a = 287 and b = 269
= (a - b)2 = (287 - 269)2
= (182)
= 324
Correct Option is D
Answer: D
Question: If Re.100 amounts to Rs.300 over a period of 10 years. What is the rate of simple interest?
Options:
A)20%
B)30%
C)15%
D)10%
E)12%
Rationale: 200 = (100*10*R)/100
R = 20%
Answer:A
Answer: A
Question: When N is divided by 10 the remainder is 1 and when N is divided by 3 the remainder is 2. What is the remainder G when N is divided by 30?
Options:
A)(a) 4
B)(b) 7
C)(c) 11
D)(d) 13
E)(e) 17
Rationale: N ends in the digit 1 because when N is divided by 10, the remainder is 1. Since N ends in 1, the remainder G when N is divided by 30 also ends in a 1. 11 is the only choice which ends in a 1.C
Answer: C
Question: A recycling facility is staffed by 12 floor workers and one manager. All of the floor workers are paid equal wages, but the manager is paid n times as much as a floor worker. If the manager’s wages account for 1/11 of all wages paid at the facility, what is the value of n?
Options:
A)1.1
B)2.1
C)2.2
D)2.3
E)2.4
Rationale: Say each floor worker is paid $x, then the manager is paid $xn.
Total salary would be 12x+xn and we are told that it equals to 11xn:
11x+xn=11xn --> reduce by x: 11+n=11n -->10n=11
n = 11/10 = 1.1
Answer: A
Answer: A
Question: 8th Dec 2007 was Saturday, what day of the week was it on 8th Dec, 2006?
Options:
A)Sunday
B)Tuesday
C)Friday
D)Tuesday
E)Monday
Rationale: Given that 8th Dec 2007 was Saturday
Number of days from 8th Dec, 2006 to 7th Dec 2007 = 365 days
365 days = 1 odd day
Hence 8th Dec 2006 was = (Saturday - 1 odd day) = Friday
Correct answer is Friday
Answer: C
Question: Rahul went to a shop and bought things worth Rs. 27, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Options:
A)19.7
B)20
C)22
D)20.4
E)21.7
Rationale: Total cost of the items he purchased = Rs.27
Given that out of this Rs.27, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (27−30/100−x)6/100 = 30/100
⇒ 6(27 −0.3 −x) = 30
⇒ (27 − 0.3 − x) = 5
⇒ x = 27 − 0.3 − 5 = 21.7
E
Answer: E
Question: In a school with 5 classes, each class has 2 students less than the previous class. How many students are there in the largest class if the total number of students at school is 115?
Options:
A)25
B)26
C)27
D)28
E)29
Rationale: Let x be the number of students in the largest class.
Then x + (x-2) + (x-4) + (x-6) + (x-8) = 115
5x - 20 = 115
5x = 135
x = 27
The answer is C.
Answer: C
Question: In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
Options:
A)44
B)58
C)74
D)12
E)23
Rationale: Explanation:
Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 8 = 4/9(T - 8)
10T = 792 - 352 => T = 44.
Answer:A
Answer: A
Question: Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 4 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
Options:
A)1:2
B)1:3
C)3:1
D)1:5
E)1:4
Rationale: Quantity of alcohol in vessel P = 62.5/100 * 4 = 5/2 litres
Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres
Quantity of alcohol in the mixture formed = 5/2 + 7/2 = 6 litres
As 8 litres of mixture is formed, ratio of alcohol and water in the mixture formed = 6 : 2 = 3:1.
Answer:C
Answer: C
Question: If the digits 35 in the decimal 0.00035 repeat indefinitely, what is the value of (10^5-10^3)(0.00035)?
Options:
A)37
B)41
C)3.5e-05
D)35
E)3.5e-07
Rationale: 99*0.35=34.65 approx. 35
Answer : B
Answer: B
Question: Coins are to be put into 10 pockets so that each pocket contains at least one coin. At most 6 of the pockets are to contain the same number of coins, and no two of the remaining pockets are to contain an equal number of coins. What is the least possible number of coins needed for the pockets?
Options:
A)7
B)13
C)20
D)22
E)28
Rationale: Since at most 6 of the pockets are to contain the same number of coins then minimize # of coins in each, so let each contain just 1 coin;
Next, we are told that no two of the remaining 4 pockets should contain an equal number of coins, so they should contain 2, 3, 4, and 5 coins each (also minimum possible);
Total: 1+1+1+1+1+1+2+3+4+5=20
Answer: C.
Answer: C
Question: A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
Options:
A)1
B)2
C)3
D)7
E)5
Rationale: DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph Answer:A
Answer: A
Question: If a = 2, what is the value of –(a^2 + a^3 + a^4 + a^5)?
Options:
A)-14
B)-60
C)0
D)4
E)14
Rationale: if a = -1, then putting values in equation
= -[ (2)^2 + (2)^3 + (2^4) + (2^5) ]
= -[ 4 + 8 + 16 + 32 ]
= -60
Answer = B = -60
Answer: B
Question: Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are black or both are queen?
Options:
A)55/119
B)55/221
C)55/223
D)55/227
E)56
Rationale: We have n(s) = \inline {\color{Black}52C_{2}} = = 1326.
Let A = event of getting both black cards
B = event of getting both queens
A∩B = event of getting queen of black cards
n(A) = \inline {\color{Black}26C_{2}} = = 325, n(B)= \inline {\color{Black}4C_{2}} = = 6 and n(A∩B) = \inline {\color{Black}2C_{2}} = 1
P(A) = n(A)/n(S) = 325/1326;
P(B) = n(B)/n(S) = 6/1326 and
P(A∩B) = n(A∩B)/n(S) = 1/1326
P(A∪B) = P(A) + P(B) - P(A∩B) = (325+6-1) / 1326 = 330/1326 =
B
Answer: B
Question: When the price of an article was reduced by 15% its sale increased by 80%. What was the net effect on the sale?
Options:
A)44% increase
B)44% decrease
C)53% increase
D)66% increase
E)66% decrease
Rationale: if n items are sold for $p each, revenue is $np. If we reduce the price by 15%, the new price is 0.85p. If we increase the number sold by 80%, the new number sold is 1.8n. So the new revenue is (0.85p)(1.8n) = 1.53np, which is 1.53 times the old revenue, so is 53% greater.
ANSWER:C
Answer: C
Question: Which number comes next in the series
5 12 24 36 ?
Options:
A)52
B)55
C)60
D)120
E)23
Rationale: A
52
sum of consecutive prime numbers
(2+3 , 5+7 , 11+13 , 17+19 , 23+29)
Answer: A
Question: How many ways are there to lay four balls, colored red, black, blue and green in a row?
Options:
A)11
B)33
C)44
D)23
E)77
Rationale: Answer:B
Answer: B
Question: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
Options:
A)25200
B)210
C)120
D)1000
E)20000
Rationale: Required selection = select 3 consonants from 7 and 2 vowels frm 4
= 7C3 * 4C2
= 210
As we have to form 5 letter word the above combination of consonants and vowels can be done in 5! = 120 different ways
Required no. of ways = 210 * 120
= 25200
Ans - A
Answer: A
Question: X, Y, and Z are three different Prime numbers, the product XYZ is divisible by how many different positive numbers?
Options:
A)4
B)6
C)8
D)9
E)12
Rationale: PRIME # is the # that has only 2 factors: One is 1 and another is the # itself.
infer that
FOR any given # 1 and the # itself are the definite factors.
Knowing above concepts:
product of X,Y, and Z = XYZ
divisible by 1, xyz, x, y, z, xy,yz,xz ==> total 8
ANSWER "C"
Answer: C
Question: Jane and Ashley take 10 days and 40 days respectively to complete a project when they work on it alone. They thought if they worked on the project together, they would take fewer days to complete it. During the period that they were working together, Jane took an eight day leave from work. This led to Jane's working for four extra days on her own to complete the project. How long did it take to finish the project ?
Options:
A)10.2 Days
B)15.2 Days
C)16.2 Days
D)18 Days
E)20 Days
Rationale: Let us assume that the work is laying 40 bricks.
Jane = 4 bricks per day
Ashley = 1 brick per day
Together = 5 bricks per day
Let's say first 8 days Ashley works alone,
No of bricks = 8
Last 4 days Jane works alone,
No. of bricks = 16
Remaining bricks = 40 - 24= 16
So together, they would take 16/5 = 3.2
Total no. of days = 8 + 4 + 3.2 = 15.2
Answer is B
Answer: B
Question: Evaluate 35 / .07
Options:
A)400
B)500
C)505
D)None of these
E)506
Rationale: Explanation:
35/.07 = 3500/7 = 500
Option B
Answer: B
Question: The number N is 7,6H4, where H represents the ten's digit. If N is divisible by 9, what is the value of H?
Options:
A)1
B)3
C)5
D)7
E)9
Rationale: Integer is divisible by 9 - Sum of digits is divisible by 9
Answer: A
Answer: A
Question: Rs.585 is divided amongst A, B, C so that 4 times A's share, 6 times B's share and 3 times C's share are all equal. Find C's share?
Options:
A)260
B)150
C)817
D)716
E)616
Rationale: A+B+C = 5854A = 6B = 3C = xA:B:C = 1/4:1/6:1/3= 3:2:44/9 * 585= Rs.260Answer: A
Answer: A
Question: a = 2^15 - 625^3 and a/x is an integer, where x is a positive integer greater than 1, such that it does NOT have a factor p such that 1 < p < x, then how many different values for x are possible?
Options:
A)None
B)One
C)Two
D)Three
E)Four
Rationale: This is a tricky worded question and I think the answer is should be D not C...
Here is my reason :
The stem says that x is a positive integer such that has no factor grater than 2 and less than x itself . The stem wants to say that X is a PRIME NUMBER . because any prime
Number has no factor grater than 1 and Itself .
On the other hand the stem says that X COULD get how many different number NOT MUST get different number ( this is very important issue )
AS our friends say, if we simplify Numerator more we can obtain : 5^12 ( 5^3-1) = 5^12 (124) = 5^12 (31*2*2) divided by x and we are told that this fraction is
An integer . so, X COULD Be ( not Must be) 5 , 31 ,or 2 !!! so , X could get 1 different values and answer is B....
Answer: B
Question: A train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 16 seconds. What is the length of the platform in meters?
Options:
A)240 meters
B)360 meters
C)280 meters
D)600 meters
E)Cannot be determined
Rationale: Speed of the train in metres/sec = 72000/3600 = 20
Distance travelled by train to cross the platform = 30 * 20 = 600 = Length of train + Length of platform
Distance travelled by train to cross the man = 16 * 20 = 320 = Length of train
Length of platform = 600 - 320 = 280
Answer: C
Answer: C
Question: IN Common Wealth Games an athlete runs 400 meters in 24 seconds. Hisspeed is ?
Options:
A)25 km/hr
B)27 km/hr
C)60.60 km/hr
D)32 km/hr
E)None of these
Rationale: Explanation :
(400/1000)/(24/3600)=60.60 km/hr
Answer : C
Answer: C
Question: If 2^2n + 2^2n + 2^2n + 2^2n = 4^28, then n =
Options:
A)3
B)6
C)12
D)27
E)24
Rationale: 2^2n + 2^2n + 2^2n + 2^2n = 4^28
=> 4 x 2^2n = 4^28 = 2^56
=> 2^2 x 2^2n = 2^56
=> 2^(2n+2) = 2^56
=> 2n+2 = 56=> n =27
So. Answer will be D.
Answer: D
Question: It takes Jim N minutes to prepare one omelet. It takes Cole N/2 minutes to prepare one omelet. It takes Mitch N/2 minutes to prepare 2 omelets. If Jim, Cole and Mitch together prepare a total of 30 omelets in 40 minutes, then how many minutes would it take Mitch alone to prepare 30 omelets?
Options:
A)70
B)120
C)140
D)160
E)280
Rationale: Cole is twice as fast as Jim and Mitch is 4 times as fast as Jim (it takes Mitch N/2 minutes to prepare 2 omelets, thus N/4 minutes to prepare one omelet).
Say the rate of Jim is x omelet/minute, the rate of Cole 2x omelet/minute, and the rate of Mitch 4x omelet/minute.
Then, from (time)(rate) = (job done):
(40 minutes)(x + 2x + 4x) = (30 omelets);
(40 minutes)(7x) = (30 omelets);
Since it takes 40 minutes to prepare 30 omelets at the rate of 7x omelet/minute, then it would take 40*7/4 = 70 minutes to prepare the same 30 omelets at the rate of 7x*4/7 = 4x omelet/minute (the rate of Mitch).
Or:
(40 minutes)(7x) = (30 omelets);
(40*7/4 minutes)(7x*4/7) = (30 omelets);
(70 minutes)(4x) = (30 omelets);
Answer: A.
Answer: A
Question: The dimensions of a field are 10 m by 10 m. A pit 5 m long, 5 m wide and 3 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field. What will be the rise in the height of field as a result of this operation ?
Options:
A)2m
B)2.5m
C)1.5m
D)1.25m
E)1m
Rationale: The volume of the earth removed is 5*5*3 = 75 m^3.
The remaining area of the field is 10*10 - 5*5 = 75 m^2.
75 m^3 of the earth evenly spread over the area of 75 m^2 will rise the height by (height) = (volume)/(area) = 75/75 = 1 m.
Answer: E
Answer: E
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)a)82
B)b)84
C)c)85
D)d)87
E)e)90
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: B)
84=8^2+4^2+2^2
Answer: B.
Answer: B
Question: A bag contains 8 red and 5 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
Options:
A)4/7
B)2/3
C)5/8
D)1/4
E)5/7
Rationale: Total number of balls = 8+6 = 14
number of white balls = 8
Probability = 8/14 = 4/7
Answer is A
Answer: A
Question: A farmer planned to plough a field by doing 120 hectares a day. After two days of work he increased his daily productivity by 25% and he finished the job two days ahead of schedule. What is the area of the field?
Options:
A)1420
B)1430
C)1450
D)1440
E)1460
Rationale: First of all we will find the new daily productivity of the farmer in hectares per day: 25% of 120 hectares is 25100⋅120=30 hectares, therefore 120+30=150 hectares is the new daily productivity. Lets x be the planned number of days allotted for the job. Then the farm is 120⋅x hectares. On the other hand, we get the same area if we add 120⋅2 hectares to 150(x−4) hectares. Then we get the equation
120x=120⋅2+150(x−4)
x=12
So, the job was initially supposed to take 12 days, but actually the field was ploughed in 12 - 2 =10 days. The field's area is 120⋅12=1440 hectares.
Answer is D.
Answer: D
Question: The average temperature for Monday, Tuesday, Wednesday and Thursday was 48 degrees and for Tuesday, Wednesday, Thursday and Friday was 46 degrees. If the temperature on Monday was 42 degrees. Find the temperature on Friday?
Options:
A)28
B)27
C)22
D)34
E)20
Rationale: M + Tu + W + Th = 4 * 48 = 192
Tu + W + Th + F = 4 * 46 = 184
M = 42
Tu + W + Th = 192 -42 = 150
F = 184 – 150 = 34
Answer:D
Answer: D
Question: A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 7 employees to 2 different offices?
Options:
A)215
B)310
C)343
D)243
E)123
Rationale: Each of three employee can be assigned to either of offices, meaning that each has 2 choices --> 7*7*7=7^3=343.
Answer: C.
Answer: C
Question: If x is an integer and x + x^2 + x^3 is odd, which of the following must be even?
Options:
A)x
B)x^2
C)x^3
D)3x
E)x + x^2
Rationale: x + x^2 + x^3 = odd
Since each is a power of x, x has to be odd
On checking the options, only
x + x^2 = odd + odd = even
Correct option: E
Answer: E
Question: If it would take one machine 15 minutes to fill a large production order and another machine 25 minutes to fill the same order, how many minutes would it take both machines working together, at their respective rates, to fill the order?
Options:
A)4 1/60
B)5
C)5 5/11
D)5 1/2
E)9 3/8
Rationale: Since , Machine 1-M1 take 15 mins to fill the order
The work done by M1 in a min = 1/15
Machine 2- M2 take 25 mins to fill the same order
and work done by M2 in a min = 1/25
Total work done by M1 and M2 in a min = 1/15 + 1/25 = 8/75
Time needed for M1 and M2 to complete the order = 75/8 = 9 3/8
Answer E
Answer: E
Question: 12 buckets of water fill a tank when the capacity of each tank is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres?
Options:
A)8
B)15
C)16
D)18
E)19
Rationale: Capacity of the tank = (12 x 13.5) liters = 162 liters.
Capacity of each bucket = 9 liters.
Numbers of buckets needed = (162/9) = 18
ANSWER:D
Answer: D
Question: Which of the following number will completely divide (36^9)-1?
Options:
A)5
B)6
C)7
D)9
E)4
Rationale: x^n - 1 will be divisible by x+1 only when n is even.
36^9 - 1 = (6^2)^9 - 1 = 6^18 - 1 which is divisible by 6+1 i.e. 7
Answer is C
Answer: C
Question: If x is a positive number and 1/3 the square root of x is equal to 3x, then x =
Options:
A)1/3
B)1/9
C)1/81
D)1
E)81
Rationale: 1/3 of sqrt(x) = 3x, which means that sqrt(x) = 9x
or x = 81x^2 -> divide by x
1=81x
x=1/81
C.
Answer: C
Question: In a software company 4/10 of people know C++, 2/4 of them know java, 2/8 of them know neither,find the total possibility to know C++?
Options:
A)1/4
B)1/3
C)1/2
D)2/3
E)3/4
Rationale: Assume 100 persons in a company
person knows c++=4/10=100*4/100=20 persons
person knows java=2/4=100*2/4=50 persons
neither=2/8=100*2/8=25 persons
according to our assumption 100 person=20+50+25=95 person covered(5 remaining)
so,total possibility=20 person(c++)+5(remaining)=25 persons
which is 25/100=1/4
ANSWER:A
Answer: A
Question: Percentage of profit earned by selling a book for $1380 is equal to the percentage loss incurred by selling the same book for $1020. What price should the book be sold to make 20% profit?
Options:
A)$1260
B)$1440
C)$1500
D)$1680
E)$2000
Rationale: Let C.P. be Rs. x.
Then, (1380 - x)	x 100 =(x - 1020) x 100
1380 - x = x - 1020
2x = 2400
x = 1200
Required S.P. = 120% of 1200 = 1.20 x 1200 = $1440
Answer : B
Answer: B
Question: In how many ways can five boys and three girls sit in a row such that all girls sit together?
Options:
A)A)1972
B)B)9022
C)C)2880
D)D)1097
E)E)4320
Rationale: Treat all girls as one unit. Now there are six students and they can be arranged in 6! ways. Again three girls can be arranged among themselves in 3! ways.
Required number of arrangements
= 6! * 3! = 720* 6
= 4320.
Answer:E
Answer: E
Question: If (2^x)(3^y) = 216, where x and y are positive integers, then (2^x-1)(3^y-2) equals:
Options:
A)12
B)24
C)48
D)96
E)144
Rationale: So I would start attacking this problem by quickly performing the prime factorization of 288. With that it is easy to count the 5 twos and the 2 threes that are the prime factors. So x=3, y=3. now quickly 2^2(3^1)=12. Than answer should be number 1.
A
Answer: A
Question: John walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house?
Options:
A)2 1/5 Km
B)3 1/5 Km
C)3 2/5 Km
D)3 3/5 Km
E)4 1/5 Km
Rationale: Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 16/6
= 24/2 * 16/60
= 8 * 2/5
= 16/5 = 3 1/5 Km
B
Answer: B
Question: Village A’s population is 300 greater than Village B's population. If Village B’s population were reduced by 600 people, then Village A’s population would be 4 times as large as Village B's population. What is Village B's current population?
Options:
A)900
B)1000
C)1100
D)1200
E)1300
Rationale: A = B+300.
A=4(B-600).
4(B-600)=B+300.
3B=2700.
B=900.
The answer is A.
Answer: A
Question: A business executive and his client are charging their dinner tab on the executive's expense account.The company will only allow them to spend a total of 50$ for the meal.Assuming that they will pay 7% in sales tax for the meal and leave a 15% tip,what is the most their food can cost?
Options:
A)39.55$
B)40.63$
C)41.63$
D)42.15$
E)43.15$
Rationale: Let x be the amount the most their food can cost.
x + 0.07x + 0. 15x = 50
Solving for x, x = 40.98$, this is the maximum amount that can be used for food.
Hence 40.63$ is the maximum value less than 40.98$
Hence Option B
Answer: B