divelab/Sys2Bench huggingface dataset:
Question: In how many ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women?
Options:
A)266
B)86400
C)11760
D)5040
E)None of these
Rationale: Here, 5 men out of 8 men and 6 women out of 10 women can be chosen in
8C5 × 10C6 ways, i.e., 11760 ways.
Answer C
Answer: C
Question: Excluding stoppages, the speed of a train is 55 kmph and including stoppages it is 30 kmph. Of how many minutes does the train stop per hour?
Options:
A)82
B)27
C)12
D)82
E)18
Rationale: Explanation:
T = 25/55 * 60 = 27
Answer: Option B
Answer: B
Question: Find the remainder when 32^33^34 is divided by 11
Options:
A)22
B)10
C)99
D)76
E)28
Rationale: So 32103210 gives remainder 1.
Now we have to write 32^33^34 in this format. So we have to find the remainder 33^34 when divided by 10. The remainder is nothig but unit digit of the number. Click here to learn this concept
33^34 gives unit digit of 9.
So 33^34 = 10 K + 9
323334=32(10K+9)=(3210)K.329323334=32(10K+9)=(3210)K.329
Now this expression when divided by 11 leaves a remainder of 329329 which inturn is equal to (−1)9=−1=10
Answer:B
Answer: B
Question: In a game of 100 points, A can give B 20 points and C 28 points. Then, B can give C is
Options:
A)33
B)10
C)88
D)37
E)32
Rationale: 10 points
Answer: B
Answer: B
Question: Johnson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.6. The probability that vice-president Baker will approve the proposal is 0.5. The probability that vice-president Corfu will approve the proposal is 0.4. The approvals of the three VPs are entirely independent of one another.
Suppose the Johnson must get VP Adam’s approval, as well as the approval of at least one of the other VPs, Baker or Corfu, to win funding. What is the probability that Johnson’s proposal is funded?
Options:
A)0.49
B)0.42
C)0.45
D)0.48
E)0.5
Rationale: probability of adams approval = 0.6
baker approval =0.5
corfu approval=0.4
proabability of approval is must adam approval and atleast one approval
= adam approval*baker approval*corfu approval(approval of both remaining)+adam approval*baker approval*corfu not approval(atleast one remaining approval)+
adam approval*baker not approval*coffu approval( atleast one remaining approval
= 0.6*0.5*0.4+0.6*0.5*0.6+0.6*0.5*0.4
=0.12+0.18+0.12
=0.42
B
Answer: B
Question: What is the place value of 3 in the numeral 2734?
Options:
A)45
B)30
C)43
D)56
E)40
Rationale: Option 'B'
3 * 10 = 30
Answer: B
Question: A alone can complete a work in 16 days and B alone can do in 12 days. Starting with A, they work on alternate days. The total work will be completed in
Options:
A)13 1/4
B)13 1/2
C)13 3/4
D)13 4/4
E)13 2/3
Rationale: Explanation:
A's 1 day work = 1/16
B's 1 day work = 1/12
As they are working on alternate day's
So their 2 days work = (1/16)+(1/12)
= 7/48
[here is a small technique, Total work done will be 1, right, then multiply numerator till denominator, as 7*6 = 42, 7*7 = 49, as 7*7 is more than 48, so we will consider 7*6, means 6 pairs ]
Work done in 6 pairs = 6*(7/48) = 7/8
Remaining work = 1-7/8 = 1/8
On 13th day it will A turn,
then remaining work = (1/8)-(1/16) = 1/16
On 14th day it is B turn,
1/12 work done by B in 1 day
1/16 work will be done in (12*1/16) = 3/4 day
So total days =
13 3/4
Option C
Answer: C
Question: Find the average of all prime numbers between 30 and 50
Options:
A)15
B)42
C)45
D)34
E)26
Rationale: Prime numbers between 30 and 50 are 37, 41, 43, 47
Required average = (37+ 41+ 43+ 47)/4 = 168/4 = 42
Answer is B
Answer: B
Question: For 6-digit integer 46x,y12, when x and y are drawn at random from {3,5,8}, what is the probability Q that the integer drawn is divisible by 8?
* A solution will be posted in two days.
Options:
A)1/6
B)1/3
C)1/2
D)2/3
E)5/6
Rationale: In general, the remainder divided by integer n is the same as the remainder that up to tens of n is divided by 8.
Thus, in order for 46,x,y12 to be divided by 8, y12 should be divided by 8.
Amongst 3,5,8, 3 and 5 can be divided by 8.
Therefore, Q=two out of three can be divided and the answer is D.
Answer: D
Question: A certain roller coaster has 4 cars, and a passenger is equally likely to ride in any 1 of the 4 cars each time that passenger rides the roller coaster. If a certain passenger is to ride the roller coaster 4 times, what is the probability that the passenger will ride in each of the 4 cars?
Options:
A)0
B)1/9
C)2/9
D)3/32
E)1
Rationale: If he is to ride 4 times and since he can choose any of the 4 cars each time, total number of ways is
= 4 * 4 * 4 * 4
= 256
Now the number of ways if he is to choose a different car each time is
= 4* 3 * 2 * 1
= 24
So the probability is
= 24/256 =6/64=3/32
= 3/32
Answer : D
Answer: D
Question: A cycle is bought for Rs.900 and sold for Rs.1440, find the gain percent?
Options:
A)27%
B)20%
C)80%
D)30%
E)60%
Rationale: 900 ---- 540
100 ---- ? => 60%
Answer: E
Answer: E
Question: A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?
Options:
A)33 1/6
B)33 1/0
C)33 1/3
D)33 1/5
E)33 1/2
Rationale: The total number of mangoes bought by the shopkeeper be 12.
If he buys 4 a rupee, his CP = 3
He selling at 3 a rupee, his SP = 4
Profit = SP - CP = 4 - 3 = 1
Profit Percent = 1/3 * 100 = 33 1/3 %.Answer:C
Answer: C
Question: In year Y imported machine tools accounted for 25 percent of total machine - tool sales in the United States, and Japanese imports accounted for 45 percent of the sales of imported machine tools. If the total sales of machine tools imported Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?
Options:
A)9X/80
B)13X/20
C)80/9X
D)20X/13
E)80X/9
Rationale: IMT = 0.25T
JI = 0.45 IMT
0.45 IMT = $x b
IMT = $x/(0.45) b
T = 4*IMT = 4x/0.45 = 4x*100/45 = 80x/9
Ans: "E"
Answer: E
Question: In an office in Singapore there are 60% female employees. 50 % of all the male employees are computer literate. If there are total 62% employees computer literate out of total 1200 employees, then the no. of female employees who are computer literate ?
Options:
A)504
B)674
C)672
D)960
E)None
Rationale: Solution: Total employees,
= 1200
Female employees, 60% of 1200.
= (60 *1200) /100 = 720.
Then male employees,
= 480
50 % of male are computer literate,
= 240 male computer literate.
62 % of total employees are computer literate,
= (62 *1200) /100 = 744 computer literate.
Thus, Female computer literate = 744 - 240
= 504.
Answer: Option A
Answer: A
Question: 10 liters are drawn from a cask full of wine and is then filled with water. This operation is performed one more time . The ratio of the quantity of wine now left in cask to that of the water is 4:5. How much wine did the cask hold originally?
Options:
A)10
B)20
C)30
D)45
E)60
Rationale: Let the quantity of wine in the cask originally be x liters
quantity of wine left in cask after 2 operations = x(1 - 10/x)^2 liters
x(1 - 10/x)^2 /x = 4/9
(1-10/x)^2 = (2/3)^2
x = 30
Answer is C
Answer: C
Question: A guy was asked to specify his age in years. He said, “Take my age 6 years hence, multiply it by six and subtract six of my age 6 years ago and you will know my age.” What was the age of that guy?
Options:
A)18
B)35
C)53
D)69
E)72
Rationale: Current age of the guy = A years.
Then, 6 (A + 6) – 6 (A – 6) = A
(6A + 36) – (6A – 36) = A
A = 72
E
Answer: E
Question: What is the units digit of (493) (915) (381) (756) (28)
Options:
A)0
B)1
C)4
D)5
E)6
Rationale: Just multiply the digits in the units place for each term and you will get the answer. It should be 0. you got a 5 as a unit digit and an even number term. so the multiplication of this will definitely yield a 0. Answer has to be 0.
I also tried it using the calculator and the answer is 1.
IMO B.
Answer: B
Question: Look at this series: 25000,5000,1000, ... What number should come next?
Options:
A)17
B)10
C)15
D)200
E)8
Rationale: 200
This is a simple division series. Each number is divided by 5.
ANSWER D
Answer: D
Question: How much time will a train of length 380 m moving at a speed of 72 kmph take to cross another train of length 540 m, moving at 36 kmph in the same direction?
Options:
A)50
B)99
C)88
D)92
E)12
Rationale: The distance to be covered = Sum of their lengths = 380 + 540 = 920 m.
Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps.
Time required = d/s = 920/10 = 92 sec.
Answer:D
Answer: D
Question: A work could be completed in 100days by x workers. However, due to the absence of 10workers, it was completed in 110days. The original no.of workers was:
Options:
A)90
B)100
C)110
D)130
E)140
Rationale: sax Letlheo g alnumberofworkers hex
x workers can do the wor - 100 days
(x — 10) workers can do the work in 110 days
4 100x 1u1x— 10)
1100 Q x 110
C
Answer: C
Question: An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 16-meter platform and caught it after it had traveled 45 meters. How many times did the ball bounce?
Options:
A)5
B)4
C)7
D)8
E)9
Rationale: Going down = 16 m
Going Up = 8 --> Total = 24
Going down = 8 --> Total = 32
Going Up = 4 --> Total = 36
Going down = 4 --> Total = 40
Going up = 2 --> Total = 42
Going down = 2 --> Total = 44
Going up = 1 --> Total = 45 (Caught)
No of bounce = 4
Answer : B
Answer: B
Question: Statement : Until our country achieves economic equality, political freedom and democracy would be meaningless.
Conclusions :
I. Political freedom and democracy go hand in hand.
II. Economic equality leads to real political freedom and democracy.
Options:
A) I only
B) II only
C) I and II only
D) I and III only
E) II and III only
Rationale: Explanation:
Nothing about first conclusion is stated in statement.
Only II conclusion follows.
(B) II only
Answer: B
Question: What is the value of 28^2 + 29^2 + 30^2 + 31^2 + 32^2 ?
Options:
A)4298
B)4508
C)4510
D)4528
E)4538
Rationale: This is what I did, all the nos are close to 30, and squared, so 30^2 plus there are 5 numbers, so (30)^2 x 5 =4500,
now squaring the last digits of each no individually comes up to (4+1+0+1+4) = 10.
when you add the 2 up it gives you a (4500+10) =4510,
Answer is C.
Answer: C
Question: If three numbers are added in pairs, the sums equal 10, 19 and 21. Find the numbers
Options:
A)6, 4, 15
B)7, 8, 6
C)5, 15, 45
D)12, 8, 13
E)10, 15, 20
Rationale: Let the numbers be x, y and z. Then,
x+ y = 10 ...(i) y + z = 19 ...(ii) x + z = 21 …(iii)
Adding (i) ,(ii) and (iii), we get: 2(x + y + z ) = 50 or (x + y + z) = 25.
Thus, x= (25 - 19) = 6; y = (25 - 21) = 4; z = (25 - 10) = 15.
Hence, the required numbers are 6, 4 and 15.
Answer A)6, 4, 15
Answer: A
Question: If d=1/(2^3*5^6) is expressed as a terminating decimal, how many nonzero digits will d have?
Options:
A)One
B)Two
C)Three
D)Seven
E)Ten
Rationale: Another way to do it is :
We know x^a*y^a=(X*Y)^a
given = 1/(2^3*5^6)
= Multiply and divide by 2^3
=2^3/(2^3*2^3*5^6)
=2^3/10^6
=> non zero digits are 8 => Ans A
Answer: A
Question: Three cows work to fill a tub at at different rate. Hose A and B, working together, can fill the tub in 3/5 of an hour. Hoses A and C can fill it in 1/2 an hour. Houses B and C can fill it in 2 hours. How long does it take all 3 cows, working together, to fill the tub?
Options:
A)3/10
B)2/5
C)6/11
D)1
E)6/5
Rationale: We have ,in 1 hourwhen two hose working together can fill the tub as follow:
1/a + 1/b = 1/3/5 of the work
1/a + 1/c = 1/1/2 of the work
1/b + 1/c = 1/2 of the work
=>Get total both sides we got : 2(1/a +1/b +1/c) = 10+30+15/30 of the work
or 1/a +1/b +1/c = 55/30=11/6 of the work
Calculate total amount of time taken when three hoses work together 11/6 = 6/11
C
Answer: C
Question: How many of the positive factors of 24 , 16 and how many common factors are there in numbers?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: factors of 24 - 1, 2, 3, 4, 8, 12 and 24
factors of 16 - 1 , 2, 4, 8 and 16
Comparing both, we have three common factors of 45,16-4
Answer D
Answer: D
Question: Which of the following is between 27/37 and 29/35?
Options:
A)1/3
B)3/8
C)1/2
D)5/8
E)7/9
Rationale: I see this as a POE (Process of Elimination) and Ballparking (Estimation) question. Not sure if this is the most efficient, but it worked:
1) I estimate 27/37 to be ~3/4+ (approximately slightly greater than 3/4)
2) I estimate 29/35 to be ~4/5+ (approximately slightly greater than 4/5)
3) So now I'm looking for an answer choice that is .75 < x < .80
It should be pretty easy to identify which answer choices are less than .75 (or 3/4) if you have had practice with fractions.
A) clearly wrong - it's less than 3/4
B) also clearly wrong - it's less than 3/4
C) also clearly wrong - it's less than 3/4
D) also clearly wrong - it's less than 3/4
I would just stop here and select E. But to verify:
E) 7/9 ~ .77 which is greater than .75 and less than .80
Answer: E
Question: a, b, c, d, and e are five consecutive integers in increasing order of size. Which one of the following
expressions is not odd?
Options:
A)a + b + c
B)ab + c
C)ab + d
D)ac + d
E)ac + e
Rationale: lets see the choices..
(A) a + b + c
a+a+1+a+2=3a+2..
if a is even, it is EVEN..
if a is odd, it is ODD..
(B) ab + c
a(a+1)+a+2=a^2+2a+2..
a(a+2)+2...
This will be O/E if a is O/E..
(C) ab + d
a(a+1)+a+3=a^2+2a+3..
a(a+2)+3...
This will be opposite of a.
.
(D) ac + d
a(a+2)+a+3=a^2+3a+3..
a(a+3)+3...
This will always be odd, as a(a+3) will always be even
(E) ac + e
a(a+2)+a+3=a^2+3a+3..
a(a+3)+4...
This will always be even, as a(a+3) will always be even
E must be the correct answer.
Answer: E
Question: If {x} is the product of all even integers from 1 to x inclusive, what is the greatest prime factor of {22} + {20}?
Options:
A)23
B)20
C)11
D)5
E)2
Rationale: Soln:
{22} + {20} = 22*{20} +{20} = 23*{20}
ANSWER:A
Answer: A
Question: The total car population in a Mumbai is 2,94,00 out of which 1,50,00 are made by Honda. Out of every 100 Honda cars, 98 are red in color, but only 53% of the total car population is red. Find the % of non-Honda cars that are red
Options:
A)5%
B)6%
C)6.125%
D)7.12%
E)8.13%
Rationale: Total Car.29.10 i.e., Honda +non Honda = 29400 Given: Whim. tractor .150W
Now,5346 of 2..00 = Honda +Red Non-Honda 29400 .:4 =15582 Thus...El Mall... 1.0 Now Honda 15582 flow, Non-. Honda =15582 - 15.582-14700=8B2 96 non-Honda =1=1.100 = 6.125%
C
Answer: C
Question: Jack and Christina are standing 150 feet apart on a level surface. Their dog, Lindy, is standing next to Christina. At the same time, they all begin moving toward each other. Jack walks in a straight line toward Christina at a constant speed of 7 feet per second and Christina walks in a straight line toward Jack at a constant speed of 8 feet per second. Lindy runs at a constant speed of 10 feet per second from Christina to Jack, back to Christina, back to Jack, and so forth. What is the total distance, in feet, that Lindy has traveled when the three meet at one place?
Options:
A)40
B)60
C)80
D)100
E)120
Rationale: The relative speed of Jack and Christina is 7 + 8 = 15 feet per second.
The distance between them is 210 feet, hence they will meet in (time) = (distance)/(relative speed) = 150/15 = 10 seconds.
For all this time Lindy was running back and forth, so it covered (distance) = (speed)*(time) = 10*10 = 100 feet.
Answer: D.
Answer: D
Question: Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $216 per week. How much does she earn in dollars per hour?
Options:
A)11
B)10
C)9
D)8
E)6
Rationale: Let Sheila earn x dollars per hour
So, on Monday, Wednesday and Friday , she earns 8x each
And, on Tuesday and Thursday, she earns 6x each
In total , over the week she should earn, 3(8x) + 2(6x) = 36x
She earns $216 per week
36x =216
x =6
Correct Option : E
Answer: E
Question: A money lender finds that due to a fall in the annual rate of interest from 8% to 7 3/4 % his yearly income diminishes by Rs. 61.50, his capital is?
Options:
A)24,602
B)28,888
C)24,600
D)24,628
E)24,6012
Rationale: Let the capital be Rs. x. Then,
(x * 8 * 1)/100 - (x * 31/4 * 1/100) = 61.50
32x - 31x = 6150 * 4
x = 24,600.
Answer: C
Answer: C
Question: A large box contains 21 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box?
Options:
A)250
B)350
C)450
D)550
E)525
Rationale: The number of chocolate bars is equal to
21 * 25 = 525
correct answer E
Answer: E
Question: A glass was filled with 12 ounces of water, and 0.03 ounce of the water evaporated each day during a 22-day period. What percent of the original amount of water evaporated during this period?
Options:
A)5.002%
B)5.5%
C)0.5%
D)5%
E)20%
Rationale: In 22 days 22*0.03=0.66 ounces of water evaporated, which is 0.66/12âˆ—100=5.5 of the original amount of water.
Answer: B.
Answer: B
Question: A, B, and C working alone can finish constructing a house in 4, 8, and 12 hours respectively. A starts alone and works for 1 hour. He is then joined by B and they work together for 1 hour. Finally C joins them and they all work together to finish the work. If they start working at 9 am, at what time will they finish?
Options:
A)11:12 am
B)11:32 am
C)11:49 am
D)12:07 pm
E)12:35 pm
Rationale: A completes 1/4 of the job each hour.
B completes 1/8 of the work each hour.
C completes 1/12 of the work each hour.
A completes 1/4 of the work in the first hour.
Working together, A and B complete another 3/8 for a total of 5/8.
Working together, A, B, and C can complete 11/24 of the work each hour.
To complete 3/8, the time required is (3/8) / (11/24) = 9/11 hours.
The work will be completed at 11:00 plus 9*60/11 minutes which is about 11:49 am.
The answer is C.
Answer: C
Question: 331, 482, 551, 263, 383, 242, 111
Options:
A)263
B)383
C)242
D)111
E)None of these
Rationale: Solution
In each number except 383,the product of first and third digits is the middle one. Answer B
Answer: B
Question: An alloy of zinc and copper contains the metals in the ratio 5 : 3. The quantity of zinc to be added to 6 kg of the alloy so that the ratio of the metal may be 3 : 1 is:
Options:
A)2
B)9
C)8
D)7
E)4
Rationale: Explanation:
In sixteen kg of alloy 10 kg of zinc and 6 kg copper is present
To make the ratio 3:1 we must add 8 kg of zinc to make it 18 kg of zinc and 6 kg copper
So answer is 8.
Answer: C
Answer: C
Question: I. a3 - 988 = 740,
II. b2 - 72 = 72 to solve both the equations to find the values of a and b?
Options:
A)a > b
B)a ≥ b
C)a < b
D)a ≤ b
E)a = b or the relationship between a and b cannot be established.
Rationale: a3 = 1728 => a = 12
b2 = 144 => b = ± 12
a ≥ b
ANSWER:B
Answer: B
Question: If # is an operation which results in adding the digits of integer until a single digit is left, what is the probability B that a number picked up in first 90 positive integers will have the result of # as an odd digit ?
Options:
A)(a) 4/10
B)(b) 4/9
C)(c) 1/2
D)(d) 6/10
E)(e) 5/9
Rationale: Here is how I did it. Probably there may be better way to do it.
First of all let us find out what is the maximum sum we will get by adding digits of numbers from 1 to 90.
That will be 17 (8+9+17) Why did I calculate this? I will come to that in a moment.
So to get an odd digit by carrying out the operation #, the sum of the digits of the integer should be 1, 3, 5, 7, 9, 10, 12, 14, and 16 (Why not 18? Because we know the maximum sum can be 17)
Number of integers, whose digits add to 1: 1 and 10 = 2
Number of integers, whose digits add to 3: 3, 12, 21, 30 = 4
Number of integers, whose digits add to 5: 5, 14, 23, 32, 41, 50 = 6
Number of integers, whose digits add to 7: 7, 16, 25, 34, 43, 52, 61, 70 = 8
Number of integers, whose digits add to 9: 10 multiples of 9 up to 90 = 10
Number of integers, whose digits add to 10: 19, 28, 37, 46, 55, 64, 73, 82 = 8
Number of integers, whose digits add to 12: 39, 48, 57, 66, 75, 84 = 6
Number of integers, whose digits add to 14: 59, 68, 77, 86 = 4
Number of integers, whose digits add to 16: 79, 88 = 2
So in total there are 2+4+6+8+10+8+6+4+2 = 50 such numbers
Probability B= 50/90 = 5/9
Correct answer E
Answer: E
Question: If 3a – 3b – 2c = 32 and √3a-√(2b+2c)=4, what is the value of a + b + c?
Options:
A)3
B)9
C)10
D)12
E)14
Rationale: when we look at the two equations, we can relize some similarity, so lets work on it..
3a – 2b – 2c = 32 can be written as √3a^2-√(2b+2c)^2=32
{√3a-√(2b+2c)}{√3a+√(2b+2c)}=32..
or 4*√3a+√(2b+2c)=32..
or √3a+√(2b+2c)=8..
now lets work on these two equations
1)√3a-√(2b+2c)=4..
2)√3a+√(2b+2c)=8..
A) add the two eq..
√3a+√(2b+2c)+√3a-√(2b+2c)=12..
2√3a=12..
or √3a=6..
3a=36..
a=12.
B) subtract 1 from 2..
√3a+√(2b+2c)-√3a+√(2b+2c)=4..
2√(2b+2c)=4..
√(2b+2c)=2..
2b+2c=4..
or b+c=2..
from A and B a+b+c=12+2=14..
C
Answer: C
Question: The price of an item is discounted 10 percent on day 1 of a sale. On day 2, the item is discounted another 10 percent, and on day 3, it is discounted an additional 5 percent. The price of the item on day 3 is what percentage of the sale price on day 1?
Options:
A)28%
B)40%
C)85.5%
D)70%
E)72%
Rationale: original price = 100
day 1 discount = 10%,price = 100-10 =90
day 2 discount = 10%,price = 90-9=81
day 3 discount = 5%,price = 81-4.05= 76.95
which is 76.95/90 *100 of the sale price on day 1= ~8
Answer C
Answer: C
Question: The average monthly income of P and Q is Rs. 6050. The average monthly income of Q and R is Rs. 7050 and the average monthly income of P and R is Rs. 8000. The monthly income of P+Q+R is:
Options:
A)41100
B)42000
C)21100
D)42200
E)21000
Rationale: Explanation:
Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (6050 x 2) = 12100 .... (i)
Q + R = (7050 x 2) = 14100 .... (ii)
P + R = (8000 x 2) = 16000 .... (iii)
Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 42200 or P + Q + R = 21100 .... (iv)
(P+Q+R)'s monthly income = Rs. 21100.
Answer: C
Answer: C
Question: $600 will become $720 in 4 years find the rate of interest?
Options:
A)10%
B)15%
C)5%
D)7%
E)20%
Rationale: SI = simple interest = A-P = 720-600 = $120
R = 100SI/PT = 100*120/600*4 =5%
Answer is C
Answer: C
Question: Hardy and Andy start a two-length swimming race at the same moment but from opposite ends of the pool. They swim in lanes at uniform speeds, but Hardy is faster than Andy. They 1st pass at a point 18.5m from the deep end and having completed one length each 1 is allowed to rest on the edge for exactly 50 sec. After setting off on the return length, the swimmers pass for the 2nd time just 10.5m from the shallow end. How long is the pool?
Options:
A)65
B)25
C)35
D)45
E)55
Rationale: let x=length of pool
at first meeting, combined distance=x
at second meeting, combined distance=3x
if andy swims 18.5 m of x, then he will swim 3*18.5=55.5 m of 3x
andy's total distance to second meeting=x+10.5 m
x+10.5=55.5 m
x=45 m
D
Answer: D
Question: A train covers a certain distance at a speed of 280kmph in 4 hours. To cover the same distance in 2 hours, it must travel at a speed of
Options:
A)500km/hr
B)540km/hr
C)560km/hr
D)600km/hr
E)650km/hr
Rationale: Explanation:
Distance = 280×4 = 1120km
Required speed = (1120/2) = 560km/hr
Answer: Option C
Answer: C
Question: If the units digit of n^27 is 7, which of the following could be the value of n?
I. n = 41
II. n = 43
III. n = 47
Options:
A)Only I
B)Only II
C)Only III
D)I and II
E)II and III
Rationale: I tried in this way.
Given n^27 units digit is 7.
If at all we have to get 7 as units digits only 3 and 7 series has 7
3^! = 3 , 3^2 = 9 , 3^3 = 27 , 3^4 = 81
7^1 = 7, 7^2 = 49 , 7^3 = 3 (units ) , 7^4 = 1 (units)
We have n^27 - then divide 27 by 4 = reminder 3.
Then we have for only 7^3 - we have units digit as 3.
Hence 47^27 = 7 (units).
Option B is correct answer , and with 41^27 we always get 1 as units digit and 43^27 - we get units as 3.
Answer: B
Question: Sound is said to travel in air at about 1100 feet per second. A man hears the axe striking the tree, 11/5 seconds after he sees it strike the tree. How far is the man from the wood chopper?
Options:
A)2197 feet
B)2420 feet
C)2500 feet
D)2629 feet
E)None of these
Rationale: Distance =(1100*11/5)feet=2420 feet.
Correct Option: B
Answer: B