divelab/Sys2Bench huggingface dataset:
Question: How many diagonals does a 59-sided convex polygon have?
Options:
A)1168
B)1652
C)2452
D)3304
E)4256
Rationale: A 59-sided convex polygon has 59 vertices.
If we examine a single vertex, we can see that we can connect it with 56 other vertices to create a diagonal. Note that we can't connect the vertex to itself and we can't connect it to its adjacent vertices, since this would not create a diagonal.
If each of the 59 vertices can be connected with 56 vertices to create a diagonal then the total number of diagonals would be (59)(56) = 3304
However, we must recognize that we have counted every diagonal twice.
To account for counting each diagonal twice, we must divide 3304 by 2 to get 1652.
The answer is B.
Answer: B
Question: An inspector rejects 0.04% of the meters as defective. How many will he examine to reject 2?
Options:
A)A)1500
B)B)2000
C)C)2500
D)D)5000
E)E)3100
Rationale: Let the number of meters to be examined be x
Then, 0.04% of x = 2
(4/100)*((1/100)*x = 2
x = 5000
Answer is D
Answer: D
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 150, the runs scored by B are?
A. 15 B. 18
Options:
A)22
B)18
C)99
D)36
E)24
Rationale: A:B = 2:3
B:C = 2:5
A:B:C = 4:6:15
6/25 * 150 = 36
Answer: D
Answer: D
Question: An bus covers a certain distance at a speed of 250 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?
Options:
A)1520 km/hr
B)1250 km/hr
C)1256 km/hr
D)1231 km/hr
E)1220 km/hr
Rationale: Distance = (250 x 5) = 1250 km.
Required speed = 1250km/hr.
B
Answer: B
Question: Number of prime numbers between 30 and 50 is
Options:
A)4
B)5
C)6
D)7
E)9
Rationale: total 5=31,37,41,43,47
ANSWER:B
Answer: B
Question: If V = {1, 7, 18, 20, 29, 33}, how much less is the mean of the numbers in V than the median of the numbers in V?
Options:
A) 1.0
B) 1.5
C) 2.0
D) 2.5
E) 3.0
Rationale: This is a good question to understand the difference between mean and median.
Mean: Average of all the numbers. (Sum of all the elements divided by the number of elements)
Median: Arrange the elements of the set in increasing order. If the number of terms is odd, the middle term is the median. If the number of terms is even, the average of middle two terms is the median
Coming to this question,
Mean = (1 + 7 + 18 + 20 + 29 + 33)/6 = 18
Median = (18 + 20)/2 = 19
Difference = 1
Option A
Answer: A
Question: The compound interest accrued on an amount of Rs.44000 at the end of two years is Rs.1193.60. What would be the simple interest accrued on the same amount at the same rate in the same period?
Options:
A)Rs.10529
B)Rs.10528
C)Rs.10560
D)Rs.10508
E)Rs.10568
Rationale: Let the rate of interest be R% p.a.
4400{[1 + R/100]2 - 1} = 11193.60
[1 + R/100]2 = (44000 + 11193.60)/44000
[1 + R/100]2 = 1 + 2544/1000 = 1 + 159/625
[1 + R/100]2 = 784/625 = (28/25)2
1 + R/100 = 28/25
R/100 = 3/25
Therefore R = 12 SI on Rs.44000 at 12% p.a. for two years = 44000(2)(12)/100
=Rs.10560
Answer:C
Answer: C
Question: A tank has an inlet and outlet pipe. The inlet pipe fills the tank completely in 2 hours when the outlet pipe is plugged. The outlet pipe empties the tank completely in 6 hours when the inlet pipe is pluggeed.
If there is a lekage also which is capable of draining out the liquid from the tank at half of the rate of outet pipe,them what is the time taken to fill the emty tank when both the pipes are opened?
Options:
A)3 hours
B)4 hours
C)5 hours
D)None of these
E)Cannot be determined
Rationale: Explanation:
Rate of leakage = 8.33% per hour
Net efficiency = 50 - (16.66 + 8.33)= 25%
Time required = 100/25 = 4 hours
Answer: B
Answer: B
Question: P & Q sitting in a circular arrangement with 10 persons. What is the probability that P & Q will sit together?
Options:
A)1/13
B)2/11
C)3/14
D)1/15
E)2/17
Rationale: n(S)= number of ways of sitting 12 persons at round table:
=(12-1)!=11!
Since two persons will be always together, then number of persons:
=10+1=11
So, 11 persons will be seated in (11-1)!=10! ways at round table and 2 particular persons will be seated in 2! ways.
n(A)= The number of ways in which two persons always sit together =10!×2
So probability = 10!*2!/11!= 2/11
B
Answer: B
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?
Options:
A)26 sec
B)76 sec
C)48 sec
D)27 sec
E)22 sec
Rationale: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.9 = 2 km
= 2000 m.
Required time = 2000 * 3/125
= 48 sec.
Answer:C
Answer: C
Question: On a certain day, Tim invested $600 at 10 percent annual interest, compounded annually, and Lana invested 800 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years?
Options:
A)$5
B)$15
C)$44
D)$100
E)$105
Rationale: Compounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly - in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc.
With respect to the problem at hand, at the end of two years, Tim would have
600(1.10)^2 = 600(1.21) = 726
and Lana would have
800(1.05)^2 = 800(1.1025) = 882
Thus, Tim earned 126 dollars, while Lana earned 82 dollars
The difference is $44 and the answer is C.
Answer: C
Question: Sakshi invests a part of Rs. 12,000 in 12% stock at Rs. 120 and the remainder in 15% stock at Rs. 125. If his total dividend per annum is Rs. 1310, how much does he invest in 12% stock at Rs. 120?
Options:
A)s. 4000
B)s. 4500
C)s. 5500
D)s. 6000
E)s. 6500
Rationale: Let investment in 12% stock be Rs. x.
Then, investment in 15% stock = Rs. (12000 - x).
12/120 * x + 15/125 * (12000- x) = 1310
x/10 + 3/25(12000-x) = 1310
5x + 72000 - 6x = 1310 x 50
x = 6500.
Answer = E
Answer: E
Question: When an amount was distributed among 14 boys, each of them got rs 80 more than the amount received by each boy when the same amount is distributed equally among 18 boys. What was the amount?
Options:
A)5000
B)5030
C)5010
D)5040
E)5020
Rationale: Let the total amount be Rs. X the,
x/14 - x/18 = 80 <=> 2x/126 = 80 <=>x/63
= 63 x 80 = 5040.
Hence the total amount is 5040
Answer is D.
Answer: D
Question: A table is bought for Rs.950/- and sold at Rs.800/- find the loss percentage
Options:
A)10% Loss
B)10% Gain
C)15% Loss
D)20% Gain
E)30% Gain
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (800 ~ 950)/950 = 15% Loss
C
Answer: C
Question: It takes eleven minutes to load a certain video on a cellphone, and fifteen seconds to load that same video on a laptop. If the two devices were connected so that they operated in concert at their respective rates, how many seconds would it take them to load the video, rounded to the nearest hundredth?
Options:
A)13.48
B)13.85
C)14.21
D)14.67
E)14.92
Rationale: The laptop can load the video at a rate of 1/15 of the video per second.
The phone can load the video at a rate of 1/(60*11) = 1/660 of the video per second.
The combined rate is 1/15 + 1/660 = 45/660 of the video per second.
The time required to load the video is 660/45 = 14.67 seconds.
The answer is D.
Answer: D
Question: A sum of money deposited at C.I. amounts to Rs.1980 in 3 years and to Rs.2492 in 4 years. Find the rate percent?
Options:
A)30%
B)10%
C)25%
D)19%
E)50%
Rationale: 1980--- 512
100 --- ? => 25%
Answer: C
Answer: C
Question: 13 different biology books and 8 different chemistry books lie on a shelf. In how many ways can a student pick 2 books of each type?
Options:
A)80
B)160
C)720
D)1100
E)2184
Rationale: No. of ways of picking 2 biology books(from 13 books) = 13c2 = (13*12)/2 = 78
No. of ways of picking 2 chemistry books(from 8 books) = 8c2 = (8*7)/2 = 28
Total ways of picking 2 books of each type = 78*28 =2184
(Option E)
Answer: E
Question: Madhu started a business and he invested in 76000, After some month, Amar came to join with him and invest 57000.The end of the year the total profit was divided among them into ratio form 2 : 1.Find after how many months Amar join?
Options:
A)5 months
B)3 months
C)7 months
D)4 months
E)8 months
Rationale: we can assume that Amar join into business after x months. So Amar money was invest into (12 – x ) months.
912000 = 114000 ( 12 – x ) = 114 ( 12 – x ) = 912Rightarrow x = 4
After 4 months amar join the business.
Answer: D
Answer: D
Question: Steve traveled the first 2 hours of his journey at 35 mph and the remaining 3 hours of his journey at 80 mph. What is his average speed for the entire journey?
Options:
A)60 mph
B)56.67 mph
C)53.33 mph
D)62 mph
E)66.67 mph
Rationale: Distance traveled in 2 hours = 2 * 35 = 70 m
Distance traveled in 3 hours = 3 * 80 = 240m
Total distance covered = 240 + 70 = 310m
Total time = 2 + 3 =5 h
Hence avg speed = total distance covered / total time taken
= 310/5 = 62 mph
Answer: D
Answer: D
Question: A train covers a distance of 12 km in 10 min. If it takes 7 sec to pass a telegraph post, then the length of the train is?
Options:
A)177 m
B)189 m
C)140 m
D)178 m
E)188 m
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec
= 20 m/sec.
Length of the train = 20 * 7
= 140 m.
Answer: C
Answer: C
Question: 96 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?
Options:
A)42
B)52
C)60
D)32
E)15
Rationale: x/7 = y/9 => x:y = 7:9
7/16 * 96 = 42
ANSWER A
Answer: A
Question: If a/x = 1/3 and a/y =1/ 5, then (x + y) =
Options:
A)A)2a
B)B)a/2
C)C)6a
D)D)7a
E)E)8a
Rationale: Ratio 1:
3a = x
Ratio 2:
5a = y
x+y = 8a
Answer is E
Answer: E
Question: A scooter costs 45,000 when it is brand new. At the end of each year, its value is only 80% of what it was at the beginning of the year. What is the value of the scooter at the end of 3 years?
Options:
A)10,000
B)23,040
C)12,800
D)12,000
E)None of these
Rationale: After first year, the value of the scooter = 36,000
After second year, the value of scooter = 28,800
After third year, the value of scooter = 23,040
Answer B
Answer: B
Question: Which of the following equivalent to (1/343)^2?
Options:
A)(0.019)^3
B)(0.020)^3
C)(0.021)^3
D)(0.022)^3
E)(0.023)^2
Rationale: (1/343)^2 = (1/7^3)^2 = (1/7)^6 = (1/49)^3 = (0.020)^3
Answer: Option B
Answer: B
Question: Company ABC imported 10,000 widgets made of either brass or aluminum. The widgets are painted blue, red or green. If 10 percent of the widgets are made of brass and of those 20 percent are painted green and 40 percent are painted red how many brass widgets painted blue were imported?
Options:
A)420
B)400
C)1050
D)1680
E)2100
Rationale: Answer A.
We are told that 10% of all imported widgets are made of brass and of those, 20% are green and 40% are red. Since we know that there are only three colors, the remaining 40% must be blue. 40% blue of 10% brass widgets leads to 4% blue brass widgets out of the total 10,550 widgets.
10,000 /100 * 4 = 400.
Answer B.
Answer: B
Question: † and ¥ represent nonzero digits, and (†¥)^2 - (¥†)^2 is a perfect square. What is that perfect square?
Options:
A)121
B)361
C)576
D)961
E)1089
Rationale: Let the digits be a and b
(ab) can be written as (10a + b)
(ba) can be written as (10b + a)
(ab)^2 - (ba)^2 = (ab + ba)(ab - ba) = (10a + b + 10b + a)(10a + b - 10b - a) = 11(a + b)*9(a - b) = 99(a^2 - b^2)
99(a^2 - b^2) is a perfect square.
So the perfect square must be divisible by 99. Only option E is divisible by 99.
Answer: E
Answer: E
Question: Today Joelle opened an interest-bearing savings account and deposited $10,000. If the annual interest rate is 5 percent compounded interest, and she neither deposits nor withdraws money for exactly 2 years, how much money will she have in the account?
Options:
A)$12025
B)$11075
C)$11025
D)$11095
E)$11015
Rationale: Interest for 1st year =10000*5/100 = 500
Interest for 2nd year = 10500 *5/100 = 525
Total =10000+500+525 = 11025
Answer : C
Answer: C
Question: Find the L.C.M of 42,88,220
Options:
A)1120
B)1320
C)1220
D)1420
E)1520
Rationale: 42=2*3*7 88=2^3*11 220=2^2*5*11
L.C.M=2^3*3*5*11=1320
Answer=(B)
Answer: B
Question: √2 percent of 2√2 =
Options:
A)5.0
B)0.05
C)1.0
D)2.0
E)4.0
Rationale: The other solutions are great, but here's one more approach.
First, we scan the answer choices to see that they are quite spread apart. This means we can also use someAPPROXIMATION
All test-takers must memorize the following approximations:
√2 ≈ 1.4
So, √2 percent of 2√2 ≈ 1.4 percent of (2)(1.4)
≈ (1.4/100)(2.8)
≈ 3.92/100
≈ 0.03
Check the answer choices to see that B is the only answer that's close.
Answer: B
Answer: B
Question: A bike covers a certain distance at the speed of 45km/h in 5 hrs. If the bike was to cover the same distance in approximately 9 hrs, at what approximate speed should the bike travel?
Options:
A)10 km/h
B)15 km/h
C)25 km/h
D)35 km/h
E)45 km/h
Rationale: Ans.(C)
Sol. Total distance = 45 × 5 = 225 km
Now speed = 225/9 = 25 km/h
Answer: C
Question: There are three numbers. 5/7th of the first number is equal to 48% of the second number. The second number is 1/9th of the third number. If the third number is 1125, then find 25% of the first number?
Options:
A)45
B)62
C)87
D)21
E)82
Rationale: Let the first number and the second number be F and S respectively.
5/2 F = 48/100 S ----> (1)
S = 1/9 * 1125 = 125
(1) => 5/7 F = 48/100 * 125
=> F = 84
25% of F = 1/4 * 84 = 21.
Answer:D
Answer: D
Question: The probability that a card drawn from 52 cards will be a diamond or a king is ?
Options:
A)4/13
B)8/57
C)8/5
D)79/8
E)78/45
Rationale: here n(s)=52
there are 13 cards of diamond and there are 3 more kings
let E be the event getting diamond or king
then n(E)=13+3=16
p(E)=n(E)/n(s)=16/52=4/13
Answer is (A)
Answer: A
Question: A and B start a business with Rs.2000 and Rs.4000 respectively. Hoe should they share their profits at the end of one year?
Options:
A)3:5
B)3:4
C)3:9
D)3:1
E)1:2
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
2000 : 4000=> 1:2,Answer: E
Answer: E
Question: How many kgs. of wheat costing Rs. 5 per kg must be mixed with 45 kg of rice costing Rs. 6.40 per kg so that 20% gain may be obtained by selling the mixture at Rs. 7.20 per kg ?
Options:
A)18
B)99
C)77
D)26
E)11
Rationale: If the selling price of the mixture is Rs.7.2 when sold at 20% profit then
CP ×120100×120100 = 7.2 ⇒⇒ CP = Rs.6
Now by applying weighted average formula = K×5+45×6.4K+45=6K×5+45×6.4K+45=6
⇒⇒ K = 18 kgs
Answer:A
Answer: A
Question: One-third less than 25% of 180 is equal to:
Options:
A)15
B)30
C)35
D)40
E)45
Rationale: Lots of ways to tackle this.
25% of 180 = 45
1/3 of 45 = 15
So, 1/3 less than 45 is equal to 45 - 15 = 30
Answer: B
Answer: B
Question: An article is bought for Rs.600 and sold for Rs.500, find the loss percent?
Options:
A)16 2/8%
B)16 3/3%
C)19 2/3%
D)16 2/3%
E)16 8/3%
Rationale: 600 ---- 100
100 ---- ? => 16 2/3%
Answer: D
Answer: D
Question: A person borrows 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 61⁄4 % p.a. for 2 years. Find his gain in the transaction per year.
Options:
A)112.50
B)125
C)150
D)167.5
E)None of these
Rationale: Gain in 2 years
= [(5000×25/4×2/100)−(5000×4×2/100)]
= (625 – 400) = 225.
∴ Gain in 1 year = (225⁄2) = 112.50
Answer A
Answer: A
Question: A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?
Options:
A)299
B)267
C)269
D)400
E)276
Rationale: 2*12 : 3*12 : 4*24
1: 3: 4
1/8 * 3200 = 400
Answer: D
Answer: D
Question: Draw one card from an ordinary deck of card and what are the chances it will be a King or Club?
Options:
A)4 in 52
B)1 in 52
C)4 in 13
D)1 in 13
E)1 in 12
Rationale: To write this as a simple mathematical solution:
13/52 + 4/52 -1/52 = 16/52 = 4/13
(Suits of Clubs) + (Number of Kings) - (Kings of Clubs) = 16/52 = 4/13
Correct answer is C.
Answer: C
Question: A certain set of numbers has an average (arithmetic mean) of 50 and a standard deviation of 50.5. If a and n, two numbers in the set, are both within 2 standard deviations from the average, then which of the following could be the sum of a and n?
Options:
A)-200
B)-130
C)-104
D)51
E)305
Rationale: 2 standard deviations from the average is frommean - 2*SDtomean + 2*SD, thus from 50-2*50.5=51 to 50+2*50.5=151:
-51 < a < 151
-51 < n < 151
-102 < a+n < 302.
Only option D is in this range.
Answer: D.
Answer: D
Question: A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 700 more than D, what is B's share?
Options:
A)Rs. 500
B)Rs. 1400
C)Rs. 2000
D)Rs. 2500
E)none of the above
Rationale: Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.
Then, 4x - 3x = 700
x = 700.
B's share = Rs. 2x = Rs. (2 x 700) = Rs. 1400.
Answer = B
Answer: B
Question: Approximately how many cubic feet of water are needed to fill a circular swimming pool that is 100 feet across and 4 feet deep?
Options:
A)15000
B)30000
C)50000
D)70000
E)90000
Rationale: Answer Should be B.
V= \pir^2h= \pi*50^2*4= approximately 30000
Answer: B
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 140 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
Options:
A)28 sec
B)16 sec
C)38 sec
D)18 sec
E)17 sec
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 140 = 380 m.
Time taken = 380/10 = 38 sec.
Answer:C
Answer: C
Question: In a certain state, the ratio of registered Republicans to registered Democrats is 3 to 2, and every registered voter is either a Republican or a Democrat. If 80 percent of the Republicans and 25 percent of the Democrats are expected to vote for Candidate X, and everyone else is expected to vote for Candidate Y, by what percent is Candidate X expected to win the election?
Options:
A)2%
B)5%
C)16%
D)20%
E)25%
Rationale: Since we were expected to find a percentage figure - It thought that it might be easier to pick a 'smart number' to represent the total number of voters (republicans and democrats). Therefore, I picked 100 (as the total number of voters) and thus 30:20 represents the number ratio of Republicans:Democrats. If 80% of Republicans (which is (60*0.8) = 48) and 25% of Democrats (40*0.25 = 10) voted for candidate X, means that out of total of 100 voters; 58 (48 + 10) voters voted for candidate X and 42 voted for candidate Y. Thus we can infer that candidate X is expected to win the election by 16 (58-42) votes. Therefore candidate X is expected to win the election by (16/100) votes which is equivalent to 16%.
I think the answer is C.
Answer: C
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green?
Options:
A)23/35
B)23/38
C)23/29
D)23/12
E)23/11
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green
= (⁶C₁ * ⁹C₁)/¹⁵C₂ + ⁶C₂/¹⁵C₂
= (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7
= 46/70 = 23/35
Answer:A
Answer: A
Question: In how many years Rs 160 will produce the same interest at 8% as Rs. 500 produce in 4 years at 8%
Options:
A)13
B)13.5
C)11.5
D)12.5
E)12
Rationale: Explanation:
Clue:
Firstly we need to calculate the SI with prinical 500,Time 4 years and Rate 8%, it will be Rs. 160
Then we can get the Time as
Time = (100*160)/(160*8) = 12.5
Option D
Answer: D
Question: Revenues were recorded for Store A and Store B over a period of three months. In the first month, Store A's revenues were $40,000 higher than Store B's revenues. In the second month, Store A's revenues were $10,000 higher than Store B's revenues. If Store A's average (arithmetic mean) monthly revenue for the three months was $2,000 greater than Store B's average monthly revenue, then Store B's revenue in the third month was how much greater than Store A's revenue?
Options:
A) $14,000
B) $15,000
C) $44,000
D) $46,000
E) $50,000
Rationale: Answer: CIt may be tempting to come up with a lot of variables, one each for each month's revenue for each company. However, focus on the differences. In the first month, the difference was +40 in favor of A. (Note that we can drop the thousands since every number in the question is in terms of thousands.) In the second, the difference was +10 in favor of A. The average was +2 in favor of A. With these numbers, use the average formula to find the third month (T):
(40 + 10 + T)/3 = 2
50 + T = 6
T = -44
Since positive numbers indicate a difference in favor of A, negative numbers are in favor of B. -44 represents a $44,000 advantage in favor of Store B. Choice (C) is correct.
Answer: C
Question: 7^6 + 7^6 + 7^6 + 7^6 =
Options:
A)7^7
B)4^6
C)4^8
D)4^9
E)4^12
Rationale: Hi shakticnb,
Certain Quant questions on the GMAT are just about 'organizing' the information in a specific way. If you find yourself getting confused by a prompt, think about how you might change the way that the information is presented to you.
Here, for example, we're asked for....
7^6 + 7^6 + 7^6 + 7^6 =
Now, the GMAT doesn't really expect us to calculate this sum (but we could if we had to), but we are expected to find a way to organize this information... If, instead of all of those exponents, we had...
X + X + X + X =
What would the sum be?
Clearly, it would be 4(X) = 4X.....since we're just combining 'like' terms. Take that same idea with this prompt and you have...
7^6 + 7^6 + 7^6 + 7^6 =
7(7^6)
This can be re-written as...
(7^1)(7^6)
...and now we can use exponent rules; since we're MULTIPLYING 'bases' that are the same, we ADD the exponents...
(7^1)(7^6) = 7^7
Final Answer:
A
Answer: A
Question: The value of x + x(x^x) when x = 3 is
Options:
A)84
B)88
C)45
D)90
E)55
Rationale: Solution:
x + x(x^x)
Put the value of x = 3 in the above expression we get,
3 + 3(3^3)
= 3 + 3(3 Ã— 3x3)
= 3 + 3(27)
= 3 + 81
= 84
Answer: (a)
Answer: A
Question: a train length 100 m going with speed 10m/sec another train 150m long going with speed 15m/sec.the distance between two train is 50m.then how much time second train will take to cross the first train?
Options:
A)60sec
B)40sec
C)30sec
D)45sec
E)1min10sec
Rationale: net speed=15-10=5m/sec
net distance=100+150+50=300
total time =300/5=60sec
answer A
Answer: A
Question: A toothed wheel of diameter 50cm is attached to a smaller wheel of diameter 30cm. How many revolutions will the smaller wheel make when the larger one makes 15 revolutions?
Options:
A)18
B)20
C)25
D)30
E)32
Rationale: Distance moved by toothed wheel in 15 revolutions= (15*2*22/7*25)
Distance moved by smaller wheel in 1 revolution= (2*22/7*15)
Therefore, required number of revolutions= (15*44/7*25*7/ 44*15)= 25
ANSWER:C
Answer: C
Question: The cash difference between the selling prices of an book at a profit of 8% and 16% is $3. The ratio of the two selling prices is:
Options:
A)55:23
B)52:33
C)52:53
D)27:29
E)51:34
Rationale: Let C.P. of the book be $x.
Then, required ratio = 108% of x / 116% of x
= 108/116 = 27/29 = 27:29
D
Answer: D
Question: A table is bought for Rs.900/- and sold at Rs.810/- find the loss percentage
Options:
A)10% Loss
B)10% Gain
C)20% Loss
D)20% Gain
E)30% Gain
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (810 ~ 900)/900 = 10% Loss
A
Answer: A
Question: How many multiples of 3 are there between 5 and 59, 5 and 59 inclusive ?
Options:
A)16
B)22
C)18
D)11
E)9
Rationale: 3 multiples are ...6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,...,
the answer is =18
Answer is C
Answer: C
Question: Which of these lines in the xy-plane does not contain any point with two negative coordinates?
Options:
A)y = 3x
B)y = x + 8
C)y = x^2 - 4
D)y = x^3 + 2x
E)y = x^2
Rationale: x^2 is 0 when x is 0 and positive for all other values of x.
The answer is E.
Answer: E