divelab/Sys2Bench huggingface dataset:
Question: Last year, a certain public transportation system sold an average (arithmetic mean) of 41,000 tickets per day on weekdays (Monday through Friday) and an average of 22,000 tickets per day on Saturday and Sunday. Which of the following is closest to the total number of tickets sold last year?
Options:
A)1 million
B)1.25 million
C)10 million
D)12.9 million
E)125 million
Rationale: If you type that into the calculator, it results in 13.0 mil
[D], 12.9 mil, is the correct answer... see 2 posts above for quick approx method
Answer: D
Question: If x is an odd integer, which of the following must also be odd?
Options:
A)2x + 4
B)x + x
C)3x + 3
D)2x + x
E)x^2 + 1
Rationale: Odd + odd = even
Odd + even = odd
Odd*odd = odd
Odd*even = even
On checking each option
A. 2x + 4
2x = even, 2 x + 4 = even + even = even.
B. x + x
Odd + odd = even. This will be even
C. 3x + 3
3x = odd, 3x + 3 = odd + odd = even
D. 2x + x
2x = even, 2x + x = even + odd = odd
E. x^2 + 1
x^2 = odd, x^2 + 1 = odd + odd = even
Correct option: D
Answer: D
Question: If x = (y)(y + 1) and y is a prime number less than 11, which of the following could not be the product of 2 consecutive integers?
Options:
A)5x
B)11x
C)13x
D)23x
E)57x
Rationale: Given y is a prime number less than 7
so y can be 2 3 5 7
x=y*(y+1)
so x can be 6 12 30 56
So from options
A. 5x can be (5*6)
B. 11x can be (11*12)
C. 13x can be (13*12)
D. 23x cannot be
E. 57x can be (56*57)
So answer option D.
Answer: D
Question: A person want to give his money of $600 to his 3 children A,B,C in the ratio 1:2:3. What is the B+C share?
Options:
A)$200
B)$300
C)$150
D)$450
E)$500
Rationale: B's share = 600*2/6 = $200
C's share = 600*3/6 = $300
B+C = $500
Answer is E
Answer: E
Question: What is the remainder when 1003 * 1005 * 1007 is divided by 15
Options:
A)3
B)17
C)14
D)0
E)7
Rationale: 1003/15==> Remainder=13
1005/15==> Remainder=0
1007/15==> Remainder=2
13*0*2=0/15==> Remainder=0
Answer:D
Answer: D
Question: What approximate value should come in place of (x) in the following question?
139.25 + 223.94 / 4.002 = x
Options:
A)250
B)203
C)200
D)195
E)185
Rationale: Explanation:
Given: 139.25 + 223.94 / 4.002 = x
Approximate 139.25 as 140, 223.94 as 224, 4.002 as 4,
we get, x = 140 + 224 / 4 = 140 + 56 = 196 =>195
ANSWER D
Answer: D
Question: A thief is noticed by a policeman from a distance of 500 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 12 km per hour respectively. What is the distance between them after 6 minutes?
Options:
A)150 m
B)200 m
C)300 m
D)100 m
E)250 m
Rationale: Relative speed of the thief and policeman = 12 - 10 = 2 km/hr.
Distance covered in 6 minutes = 2/60 * 6 = 1/5 km = 200 m.
Distance between the thief and policeman = 500 - 200 = 300 m
C
Answer: C
Question: Sum of even numbers between 15 and 25 is
Options:
A)70
B)80
C)130
D)100
E)None
Rationale: Explanation: 16 + 18 + .......24.
Taking 2 common we get = 2 ( 8 + 9 + 10 +.....+ 12)
Sum of n natural numbers upto 12
8 + 9 + 10 +.....+ 12 = (1 + 2 + 3 + ......+ 12) - ( 1 + 2 + 3 + ....+ 7)
By applying the formula for the first n natural numbers sum n(n+1)/2 we get, 12(12+1)/2−7(7+1)/2=50
So 16 + 18 + .......24 = 2 × 50 = 100
Correct Option: D
Answer: D
Question: If 25% of x is 5 less than 10% of 500, then x is?
Options:
A)188
B)180
C)156
D)840
E)121
Rationale: 25% of x = x/4 ; 10% of 500 = 10/100 * 500 = 50
Given that, x/4 = 50 - 5 => x/4 = 45 => x = 180.
Answer: B
Answer: B
Question: A certain plant was 11 feet long on the day it was plantedthe length grows by a constant amount everyday(inc. the first day it was planted).
if this plant grew by 30% b/w the 4th day and 10 th day after it was planted ,how many feet per day does the plant grow
Options:
A)a) 2
B)b) 4.5
C)c) 0.69
D)d) 5.5
E)e) 3
Rationale: If the plant is 11 feet tall when it is planted, it will be 11 + k feet tall at the end of the day (where k is the constant length it grows by every day).
Similarly, at the end of the 4th day the plant must be 11 + 4k feet tall and at the end of the 10th day it must be 11 + 10k feet tall.
Therefore 6k = 0.3 (11 + 4k)
=> k = 0.69
Therefore the plant grows by 0.69 feet every day.
Option (C)
Answer: C
Question: A straight fence is to be constructed from posts 6 inches wide and separated by lengths of chain 8 feet long. If a certain fence begins and ends with a post, which of the following could not be the length of the fence in feet? (12 inches = 1 foot)
Options:
A)26
B)32
C)43
D)60
E)77
Rationale: There is one post for each length of chain, plus one final post at the end.
The length of the fence in feet is 8.5x + 0.5, where each is the number of chain lengths.
The length of the fence is an integer when x = 1,3,5,7,...
The length of the fence could be 9, 26, 43, 60, 77,...
The answer is B.
Answer: B
Question: A mathematics teacher tabulated the marks secured by 35 students of 8th class. The average of their marks was 72. If the marks secured by Reema was written as 35 instead of 99 then find the correct average marks up to two decimal places.
Options:
A)73.41
B)74.31
C)72.43
D)73.43
E)73.82
Rationale: Total marks = 35 x 72 =2520
Corrected total marks = 2520 - 35 + 99 =2584
Correct Average = 2584/35 = 73.82
Answer : E
Answer: E
Question: Presently the ratio between the ages of David and James is 3:2. after 8 years David will be 29. What is the present age of James?
Options:
A)24
B)23
C)14
D)21
E)25
Rationale: Let the present ages of David and James be 3x years and 2x years respectively
3x+8 = 29
3x = 21
x = 7
James's age = 2x =14 years
Answer is C
Answer: C
Question: A bookseller has two display windows. She plans to display 3 new fiction books in the left window, and 3 new non-fiction books in the right window. Assuming she can put the four fiction books in any order, and separately, the three non-fiction books in any order, how many total configurations will there be for the two display windows?
Options:
A)24
B)72
C)144
D)36
E)420
Rationale: The left window will have permutations of the 3 fiction books, so the number of possibilities for that window is
permutations = 3! = (3)(2)(1) = 6
The right window will have permutations of the 3 non-fiction books, so the number of possibilities for that window is
permutations = 3! = (3)(2)(1) = 6
Any of the 24 displays of the left window could be combined with any of the 6 displays of the right window, so the total number of configurations is 6*6 = 36
Answer: D.
Answer: D
Question: Jim wishes to buy 3 gifts that cost 27 dollars, 9 dollars, and 12 dollars. He has 1/4 of the money
he needs. How much more money must he earn in order to buy the gifts?
Options:
A)$57
B)$36
C)$7
D)$17
E)$27
Rationale: $27 + $9 + $12 = $48 needed
1/4 x $48 = $12 on hand
$48 - $12 = $36 to earn
correct answer B
Answer: B
Question: John goes to his office by car at a speed of 40kmph and reaches 8 minutes earlier. If he goes at a speed of 30kmph , he reaches 4mins late. What is the distance from his house to office?
Options:
A)18 km
B)20 km
C)22 km
D)24 km
E)30 km
Rationale: Let his office time be 10 a.m. He reaches office at 8 minutes earlier when he travels at 40 kmph => He reaches at 9:52 a.m
He reaches his office 4 minutes late when travels at 30 kmph speed=> He reaches at 10.04 a.m
The time difference is (10.04 – 9.52) = 12 minutes
Let the distance be D and time=
Distance
Speed
T1 – T2 = 12 minutes = 12/60
hours = 1/5hours
D/30– D/40= 1/5
(4D-3D)/120= 1/5
D= 24 km
Answer: D
Question: In how many ways can seven members be selected from a group of fifteen members?
Options:
A)10C6
B)15C7
C)10C4
D)10C3
E)10C1
Rationale: seven members can be selected from fifteen members in
15C7
= 15c7 ways.
Answer: B
Answer: B
Question: At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present ?
Options:
A)12 years
B)15 years
C)19 and half
D)21 years
E)23 years
Rationale: Let the present ages of Arun and Deepak be 4x years and 3x years respectively. Then,
4x + 6 = 26
4x = 20
x = 5.
Deepak's age = 3x = 15 years.
Answer: Option B
Answer: B
Question: The sum of digits of a two digit number is 12,The difference between the digits is 4. Find the number
Options:
A)84
B)94
C)83
D)72
E)None
Rationale: Description :
=> x+y=12, x-y=4
Adding these 2x =16
=> x=8, y=4.
Thus the number is 84
Answer A
Answer: A
Question: X starts a business with Rs.45000. Y joins in the business after 6 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?
Options:
A)1:2
B)2:1
C)3:1
D)2:3
E)5:3
Rationale: Ratio in which they should share the profit
= Ratio of the investments multiplied by the time period
=45000×12:30000×6
=45×12:30×6
=3×12:2×6
=3:1
Answer is C
Answer: C
Question: A rectangular window is twice as long as it is wide. If its perimeter is 16 feet, then what are its dimensions in feet?
Options:
A)3/2 by 7/2
B)8/3 by 16/3
C)2 by 4
D)3 by 6
E)10/3 by 20/3
Rationale: Let x be the width of the window. Then the length is 2x.
x+2x+x+2x = 16
6x = 16
x = 16/6 = 8/3
The width is 8/3 and the length is 16/3.
The answer is B.
Answer: B
Question: A cistern is filled by a tap in 3 1/2 hours. Due to leak in the bottom of the cistern, it takes half an hour longer to fill the cistern. If the cistern is full how long will it take the leak to empty it?
Options:
A)11
B)12
C)29
D)28
E)29
Rationale: 2/7 - 1/x = 1/4
x = 28
Answer:D
Answer: D
Question: If the annual increase in the population of a town is 4% and the present number of people is 15625, what will the population be in 3 years?
Options:
A)15265
B)16458
C)25600
D)17576
E)14785
Rationale: The required population is = 15625 (1 + 4/100)^3
= 15625 * 26/25 * 26/25 * 26/25
= 17576
Answer is D
Answer: D
Question: Raviraj invested an amount of 10,000 at compound interest rate of 10 pcpa for a period of three years. How much amount will Raviraj get after three years?
Options:
A)12,310
B)13,210
C)13,320
D)13,120
E)None of these
Rationale: Amount = 10000(1 + 10⁄100)3
= 10000 × 11⁄10 × 11⁄10 × 11⁄10
= 13310
Answer E
Answer: E
Question: The ratio of three numbers is 1:2:5 and the sum of their squares is 4320. The sum of the numbers is?
Options:
A)A)10
B)B)12
C)C)15
D)D)14
E)E)9
Rationale: Let the numbers be x,2x,5x
then, x^2+4x^2+25x^2 = 4320
30x^2 = 4320
x^2 = 144
x=12
Answer is B
Answer: B
Question: A and B can do a piece of work in 10 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?
Options:
A)40 days
B)20 days
C)10 days
D)60 days
E)40 days
Rationale: C
10 days
C = 1/5 – 1/10 = 1/10 => 10 days
Answer: C
Question: Sum of three numbers 308, If the first number be twice then second and third number be one third of the first, then the second number is
Options:
A)A)70
B)B)71
C)C)72
D)D)83
E)E)84
Rationale: Explanation:
Let the second number is x, then first is 2x, and third is 1/3(2x)
=>2x+x+2x/3=308
<=>11x/3=308
=>x=84
Answer: Option E
Answer: E
Question: There are several bags of same weight. A bag is 6 kgs plus three fourth of the weight of an other bag. What is the weight of a bag?
Options:
A)22
B)88
C)70
D)27
E)24
Rationale: Let the bags weight is x
Then 6 + 3434 x = x,
Solving we get x = 24
Answer:E
Answer: E
Question: If a store adds 60 chairs to its current inventory, the total number of chairs will be the same as three-halves the current inventory of chairs. If the manager wants to increase the current inventory by 30%, what will the new inventory of chairs be?
Options:
A)40
B)60
C)100
D)156
E)160
Rationale: Explanation:
Letâ€™s say t = total current inventory of chairs. The first sentence states that 60 + t = (3/2)t. First solve for the current inventory:
60 + t = (3/2)t
60 = (3/2)t âˆ’ t
60 = (1/2)t
120 = t
The manager wants to increase this by 30%.
30% of 120 is 36, so the new inventory will be 120+36=156
Answer: (D).
Answer: D
Question: Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 3:5, find his marks in Science?
Options:
A)18
B)66
C)77
D)55
E)34
Rationale: S:E = 1:3
E:M = 3:5
------------
S:E:M = 3:9:15
3/27 * 162 = 18
Answer: A
Answer: A
Question: At 15:00 there were 22 students in the computer lab. At 15:03 and every three minutes after that, 3 students entered the lab. If at 15:10 and every ten minutes after that 8 students left the lab, how many students were in the computer lab at 15:44 ?
Options:
A)7
B)14
C)25
D)27
E)32
Rationale: Initial no of students + 3 * (1 + No of possible 3 minute intervals between 15:03 and 15:44) -
8 *(1 + No of possible 10 minute intervals between 15:10 and 15:44)
20 + 3*14 -8 * 4 = 32
E
Answer: E
Question: Pipe A can fill a tank in 16 minutes and pipe B cam empty it in 24 minutes. If both the pipes are opened together after how many minutes should pipe B be closed, so that the tank is filled in 30 minutes?
Options:
A)18
B)27
C)98
D)27
E)21
Rationale: Let the pipe B be closed after x minutes.
30/16 - x/24 = 1 => x/24 = 30/16 - 1 = 14/16
=> x = 14/16 * 24
= 21.
Answer:E
Answer: E
Question: A motorist covers a distance of 39km in 45min by moving at a speed of x kmph for the first 15min, then moving at double the speed for the next 20 min, and then again moving at his original speed for the rest of the journey. Find x.
Options:
A)29 kmph
B)27 kmph
C)55 kmph
D)36 kmph
E)29 kmph
Rationale: D
36 kmph
Total distance = 39 km
Total time = 45 min
D = S*T
x * 15/60 + 2x * 20/60 + x * 10/60 = 39 km
x = 36 kmph
Answer: D
Question: A sum of money on compound interest amounts to Rs. 8240 in 2 years and Rs. 9888 in 3 years. The rate of interest is
Options:
A)10%
B)25%
C)20%
D)12%
E)24%
Rationale: Explanation: Let the sum be P and rate of interest be R% per annum.
Amount after 2 year = 8240
P(1+R/100)T = 8240
P(1+R/100)2 = 8240 --- ( 1)
Amount after 3 year = 9888
P(1+R/100)T = 9888
P(1+R/100)3 = 9888 --- (2)
(2) ÷ (1) => [P(1 + R/100)3]/[P(1+R/100)2 = 9888/8240
1+R100 = 9888/8240
R/100 = (9888/8240 − 1 )= 1648/8240 = 15
R = 100/5 = 20%
Solution 2
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If a certain sum of money at compound interest amounts to Rs.x in t1 years and Rs.y in t2 years, then the rate of interest per annum can be given by
R = [(y/x)<sup>1/(t2−t1)</sup> − 1] × 100%
R = [(y/x)<sup>1/(t2−t1)</sup> − 1] × 100 = [(9888/8240)<sup>1/(3−2)</sup> − 1] × 100 = [(9888/8240) − 1] × 100
= (1648/8240) × 100 = (15) × 100 = 20%
Answer: Option C
Answer: C
Question: Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:
Options:
A)9
B)10
C)12
D)13
E)15
Rationale: Let the three integers be x, x + 2 and x + 4.
Then, 3x = 2(x + 4) + 3
x = 11.
Third integer = x + 4 = 15.
Answer:E
Answer: E
Question: A, B and C invested Rs. 27000/-, Rs. 35000/- and Rs. 14000/- respectively in a business. At theend of year, they earn a profit of Rs 5320/-. B’s share of profit is:
Options:
A)Rs. 2540/-
B)Rs. 2450/-
C)Rs. 2045/-
D)Rs. 2504/-
E)None of these
Rationale: Explanation:
A : B : C = 27000 : 35000 : 14000 = 27 : 35 : 14
B’s Share = Rs. (5320 * 35/76)
= Rs. (140 * 35/2)
= Rs. (70 * 35) = Rs 2450/-
Answer: Option B
Answer: B
Question: Rajeev purchased six calculators at the cost of Rs.690. How many calculators can he purchase for Rs.920?
Options:
A)8
B)9
C)11
D)12
E)14
Rationale: Explanation:
Price of one calculator = Rs.690/6 = Rs.115
1. The No. of calculators which can be bought for Rs.920 = 920/115 = 8 Nos.
Answer: Option A
Answer: A
Question: Working alone, Mary can pave a driveway in 5 hours and Hillary can pave the same driveway in 2 hours. When they work together, Mary thrives on teamwork so her rate increases by 33.33%, but Hillary becomes distracted and her rate decreases by 50%. If they both work together, how many hours will it take to pave the driveway?
Options:
A)2 hours
B)4 hours
C)5 hours
D)6 hours
E)7 hours
Rationale: Initial working rates:
Mary = 1/5 per hour
Hillary = 1/2 per hour
Rate when working together:
Mary = 1/5 + (1/3*1/5) = 1/4 per hour
Hillary = 1/2 - (1/2*1/2) = 1/4 per hour
Together they work 1/4 + 1/4 = 1/2 per hour
So they will need 2 hours to complete the driveway. The correct answer is A.
Answer: A
Question: Which of the following equations describes a line that is perpendicular to y=x+5?
Options:
A)y = x − 5
B)y = −1 − x
C)y = 5x
D)y = 5x+1
E)y = 1/x + 5
Rationale: Two perpendicular lines have slopes that are inverse reciprocals of each other.
The slope of y=x+5 is 1 so the slope of a perpendicular line will be -1.
The answer is B.
Answer: B
Question: If c= (a-1)(a+2), then what is the least possible value of c?
Options:
A)1/2
B)2
C)-9/4
D)1
E)-2
Rationale: Answer : C
Answer: C
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
Options:
A)80%
B)80%
C)40%
D)48%
E)10%
Rationale: The total CP = Rs. 16000 + Rs. 6250
= Rs. 22250 and SP = Rs. 31150
Profit(%) = (31150 - 22250)/22250 * 100
= 40%
Answer: C
Answer: C
Question: (100 x 60) + (138 x 400) = ? x 60
Options:
A)880
B)550
C)1100
D)1020
E)600
Rationale: Explanation :
? = (100 x 60) + (138 x 400)/60
= 6000 + 55200/60 = 1020
Answer : Option D
Answer: D
Question: Yearly subscription to professional magazines cost a company $940.00. To Make a 25% cut in the magazine budget, how much less must be spent?
Options:
A)705
B)655
C)656
D)657
E)658
Rationale: total cost 940
940*25/100=235
so the cut in amount is 235
the less amount to be spend is 940-235=705
ANSWER:A
Answer: A
Question: The population of a city increases by 9% per year but due to migration it decrease by 1% per years. What will be the percentage increase in population in 3 years?
Options:
A)9%
B)9.27%
C)25.97%
D)12%
E)None of these
Rationale: Actual increase in population=8%
Let, earlier population=100 then the population after 3 years
=100(1+8/100)^3=125.97
∴Required percentage=25.97%
ANSWER:C
Answer: C
Question: A wizard named Nepo says "I am only three times my son's age. My father is 40 years more than twice my age. Together the three of us are a mere 1240 years old." How old is Nepo?
Options:
A)340 yr
B)330 yr
C)350 yr
D)360 yr
E)370 yr
Rationale: nepo's age=x yr
nepo's son's age=x/3 yr
nepo's father's age=2x+40 yr
total age=1240
x+x/3+2x+40=1240
3x+x+6x+120=1240*3
10x=3720-120
x=360
Hence nepo's age is 360 yr
ANSWER:D
Answer: D
Question: Smita was making 1 design (again some nonsense) size of larger cube to be made is 5*5*5 using smaller cubes of 1*1*1. She created solid larger cube .Then she decided to make hollow cube of same size. Then how many 1*1*1 cubes required to make hollow larger cube.
Options:
A)95 cubes
B)96 cubes
C)97 cubes
D)99 cubes
E)98 cubes
Rationale: For making a solid cube you require 5*5*5=125 cubes;
now for a hollow one, you have to remove a 3*3*3=27 cubes from the core of solid cobe. therefore required cubes for hollow one is 125-27=98 cubes
ANSWER:E
Answer: E
Question: 4,6,10,14,22,34,38,46 ? what is next term in the series.
Options:
A)50
B)52
C)56
D)58
E)60
Rationale: 4,6,10,14,22,26,34,38,46,?
this is right question .
It satisfy prime number like(2,3,5,7,11,13,17,19,23,29,31.....)
2*2=4
2*3=6
2*5=10
2*7=14
2*11=22
2*13=26
2*17=34
2*19=38
2*23=46
2*29=58
ANSWER:D
Answer: D
Question: In one hour, a boat goes 11km along the stream and 5 km against it. Find the speed of the boat in still
water
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: Explanation:
We know we can calculate it by 1/2(a+b)
=> 1/2(11+5) = 1/2(16) = 8 km/hr
Answer: C
Answer: C
Question: A batsman makes a score of 87 runs in the 17th match and thus increases his average by 3. Find his average after 17th match
Options:
A)36
B)37
C)38
D)39
E)35
Rationale: Explanation:
Let the average after 17th match is x
then the average before 17th match is x-3
so 16(x-3) + 87 = 17x
=> x = 87 - 48 = 39
Option D
Answer: D
Question: Together, Andrea and Brian weigh p pounds; Brian weighs 8 pounds more than Andrea. Brian and Andrea's dog, Cubby, weighs p/4 pounds more than Andrea. In terms of p, what is Cubby's weight in pounds?
Options:
A) p/2 - 10
B) 3p/4 - 4
C) 3p/2 - 5
D) 5p/4 - 10
E) 5p - 5
Rationale: Together, Andrea and Brian weigh p pounds --> A + B = p.
Brian weighs 10 pounds more than Andrea --> B = A + 8 --> A + (A + 8) = p --> A = (p - 8)/2 = p/2 - 4.
Brian and Andrea's dog, Cubby, weighs p/4 pounds more than Andrea --> C = A + p/4 = (p/2 - 4) + p/4 = 3p/4 -4.
Answer: B.
Answer: B
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm.
Options:
A)280
B)234
C)285
D)236
E)250
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (15) = 285 cm2
Answer: Option C
Answer: C
Question: The average age of applicants for a new job is 30, with a standard deviation of 8. The hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age. Assuming that all applicants' ages are integers and that the endpoints of the range are included, what is the maximum number of different ages of the applicants?
Options:
A)8
B)16
C)17
D)18
E)34
Rationale: Minimum age = Average - 1 Standard deviation = 30 - 8 = 22
Maximum age = average + 1 Standard deviation = 30+ 8 = 38
Maximum number of different ages of the applicants = 38 - 22 + 1 = 17
Answer C
Answer: C
Question: If m and n are the roots of the quadratic equation x^2−(2√5)x−2=0, the value of m2+n2 is:
Options:
A)18
B)20
C)22
D)24
E)32
Rationale: Product of root, MN = C/A = -2/1 = -2
Sum of root, M+N = -B/A = -(-2\sqrt{5}/1 )= 2\sqrt{5}
(M+N)^2 = M^2 + N^2 + 2MN = 4*5 = 20
2MN = -2(2) = -4
M^2 + N^2 = 20 + 4 = 24
ANSWER:D
Answer: D
Question: If x^2 + y^2 = 16 and xy = 3, then (x − y)^2 =
Options:
A)8
B)11
C)10
D)17
E)20
Rationale: but you cannot take xy+ 3 to mean xy=-3..
only if xy+3=0, it will mean xy=-3..
rest your solution is perfect and you will get your correct answer as 16-2*3=10..
Answer C
Answer: C
Question: At Veridux Corporation, there are 250 employees. Of these, 90 are female, and the rest are males. There are a total of 40 managers, and the rest of the employees are associates. If there are a total of 150 male associates, how many female managers are there?
Options:
A)15
B)20
C)25
D)30
E)35
Rationale: 250 Employees:
90 Male, 160 Female
40 Managers, 210 Associates
150 Male Associates implies 60 Female Associates which means the remaining 30 females must be Managers
D. 30
Answer: D
Question: A shopkeeper loses 15%,if an article is sold for Rs. 136. What should be the selling price of the article to gain 20%?
Options:
A)s.147
B)s.148
C)s.144
D)s.189
E)s.192
Rationale: Given that SP = Rs. 136 and loss = 15%
CP = [100(SP)]/(100 - l%) = (100 * 136)/85 = Rs. 160.
To get 20% profit, New SP = [(100 + p%)CP]/100
= (160 * 120)/100
= Rs.192
Answer:E
Answer: E
Question: Bullock likes to keep a spare tyre in his car every time. On a certain day, he travels 1, 50,000 km and just to make the most of all the tyres, he changes the tyres between his journey such that each tyre runs the same distance.
What is the distance traveled by each tyre?
Options:
A)70,000
B)60,000
C)80,000
D)90,000
E)120,000
Rationale: The distance traveled by each tyre:
4/5 * 1, 50, 000km = 120,000 km. E
Answer: E
Question: A man takes 3 hours 45 minutes to row a boat 30 km downstream of a river and 2 hours 30 minutes to cover a distance of 5 km upstream. Find the speed of the current.
Options:
A)1 km/hr
B)2 km/hr
C)3 km/hr
D)4 km/hr
E)None of these
Rationale: Explanation:
First of all, we know that
speed of current = 1/2(speed downstream - speed upstream) [important]
So we need to calculate speed downstream and speed upstream first.
Speed = Distance / Time [important]
Speed upstream =(30/3 3/4)km/hr
=8 km/hr
Speed Downstream = (5/2 1/2)km/hr
=2km/hr
So speed of current = 1/2(8−2)
=3 km/hr
Option C
Answer: C
Question: There are 7 man and 5 women sitting in a circle, find the all possible way so that two women wont sit together?
Options:
A)6!*7P5
B)6!*7P4
C)6!*7P3
D)5!*7P5
E)4!*7P5
Rationale: 7 men can sit in a circle in (7-1)!= 6! ways
no two women sit together,so woman have to sit alternate to men
there will be 7 places,in which 5 women have to sit
so women can sit in 7 places as 7P5 ways
reqd ways= 6!*7P5
ANSWER:A
Answer: A