divelab/Sys2Bench huggingface dataset:
Question: There were two candidates in an election. Winner candidate received 62% of votes and won the election by 312 votes. Find the number of votes casted to the winning candidate?
Options:
A)806
B)744
C)912
D)1200
E)1400
Rationale: W = 62% L = 38%
62% - 38% = 24%
24% -------- 312
62% -------- ? => 806
ANSWER:A
Answer: A
Question: In how many ways can you seat 5 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end?
Options:
A)720
B)1720
C)48
D)5040
E)10080
Rationale: Since Rohit does not want to sit on the middle seat or at either end (3 chairs), then he can choose 2 chairs to sit. The remaining 4 people can sit in 4! ways. Thus the # of arrangements is 2*4! = 48.
Answer: C.
Answer: C
Question: Due to construction, the speed limit along an 10-mile section of highway is reduced from 55 miles per hour to 15 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options:
A)A) 6.24
B)B) 8
C)C) 29.1
D)D) 15
E)E) 24
Rationale: Old time in minutes to cross 10 miles stretch = 10*60/55 = 10*12/11 = 10.9
New time in minutes to cross 10 miles stretch = 10*60/15 = 10*4 = 40
Time difference = 29.1
Ans:C
Answer: C
Question: How many integers from 0 to 50 inclusive have a remainder of 3 when divided by 11?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: The numbers should be of the form 11c+3.
The minimum is 3 when c=0.
The maximum is 47 when c=4.
There are 5 such numbers.
The answer is A.
Answer: A
Question: How many times do the hands of a clock coincide in a day?
Options:
A)22
B)26
C)29
D)21
E)27
Rationale: The hands of a clock coincide 11 times in every 12 hours
(Since between 11 and 1, they coincide only once,
i.e. at 12 o'clock).
=> The hands coincide 22 times in a day.
Answer is A.
Answer: A
Question: If 2ab - c = 2a(b - c), which of the following must be true?
Options:
A)a=0 and c=0
B)a=1/2 and b=2
C)b=1 and c=0
D)a=1 or b=0
E)a=1/2 or c=0
Rationale: 2ab - c = 2a(b - c)
=> 2ab - c = 2ab - 2ac
=> - c = - 2ac
=> c = 2ac
=> c - 2ac = 0
=> c (1 - 2a) = 0
Either c = 0 or 1 - 2a = 0 i.e. a = 1/2.
Hence, E
Answer: E
Question: If r and y are both odd prime numbers and r < y, how many distinct positive integer factors does 2ry have?
Options:
A)3
B)4
C)6
D)8
E)12
Rationale: Since 2ry prime factors are r^1*y^1*2^1, its total number or factors must be (1+1)(1+1)(1+1)=2^3=8. Thus, I think D would be the correct answer.D
Answer: D
Question: A new tower has just been built at the Verbico military hospital; the number of beds available for patients at the hospital is now 5 times the number available before the new tower was built. Currently, 1/3 of the hospital's original beds, as well as 1/5 of the beds in the new tower, are occupied. For the purposes of renovating the hospital's original wing, all of the patients in the hospital's original beds must be transferred to beds in the new tower. If patients are neither admitted nor discharged during the transfer, what fraction of the beds in the new tower will be unoccupied once the transfer is complete?
Options:
A)11/30
B)43/60
C)17/30
D)19/30
E)11/15
Rationale: I think B - 43/60 is the correct answer.
Here goes:
Lets assume originally the number of beds = x
After the new tower, the total combined no of beds = 5x
So old = x, New = 4x
Now 1/3 of x are occupied and 1/5 of 4x are occupied which simplifies to (4/5)x
We are shifting 1/3 of x to the new ward so there will now be:
1/3 of x plus 4/5 of x occupied in the new ward. Add them up to get 17/15 of x
There are 4x beds in New Tower so ratio is:
(17/15)x / 4x = 17/60 of x
Subtract that from 60/60 of x and you get the number of un-occupied beds to total capacity of New Tower = 43/60.
B
Answer: B
Question: Which of the following is equal to (x+1)!/x!?
Options:
A)x-1
B)1+(1/x)
C)1
D)x+1
E)x
Rationale: (x + 1)! = (x + 1) * x!
(x + 1)!/x! = x + 1
Answer: D
Answer: D
Question: Two trucks each 250m long are running in opposite directions on parallel paths. Their speeds are 30 km/hr and 20 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
Options:
A)77 sec
B)66 sec
C)48 sec
D)55 sec
E)36 sec
Rationale: Relative speed = 20 + 30 = 50 km/hr.
50 * 5/18 = 125/9 m/sec.
Distance covered = 250 + 250 = 500 m.
Required time = 500 * 9/125 = 36 sec.
Answer: E
Answer: E
Question: During a recent track meet, Peter ran x meters of the 100 meter dash in 9 seconds; running at the same rate, how many seconds will it take Peter to run z meters of the 200 meter dash?
Options:
A)9/xz
B)9zx
C)9x/z
D)9z/x
E)xz/9
Rationale: Speed of Peter = x/9 meters per second
Time needed to run z meters = DISTANCE/SPEED = z / (x/9) =9z/x
Option D
The values 100m and 200m have no role to play here and are just given to confuse you.
Answer: D
Question: Rounded to three decimal places, 1.003^4 =
Options:
A)1.004
B)1.006
C)1.008
D)1.012
E)1.016
Rationale: As compared to 1, 0.003 is a very small quantity. Thus, we can write (1+0.003)^4 is nearly equal to (1+4*0.003) = 1.012.As the question asks for approximation to three decimal places, the further terms will anyways not come into picture.
D.
Answer: D
Question: A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 2 less, he would have made a profit of 10%. The C.P. of the article was
Options:
A)344
B)218
C)400
D)388
E)211
Rationale: Explanation:
Let original Cost price is x
Its Selling price = (105/100) * x = 21x/20
New Cost price = (95/100) * x = 19x/20
New Selling price = (110/100 )* (19x/20 )= 209x/200
[(21x/20) - (209x/200)] = 2
=> x = 400
Answer: C) Rs 400
Answer: C
Question: The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 30% alcohol, is?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: 4.5 4.5
30% 70%
30% ----- 4.5
70% ------? => 10.5 - 4.5 = 6 ml
ANSWER:D
Answer: D
Question: How many 3 digit numbers can be formed from the digits 2,3,5,6,7 and 9 which are divisible by 5 and none of the digits is repeated?
Options:
A)84
B)23
C)45
D)20
E)15
Rationale: Since each desired number is divisible by 5,
so we much have 5 at the unit place.
The hundreds place
can now be filled by any of the remaining 4 digits .
so, there4 ways of filling it.
Required number of numbers = (1 * 5 * 4)
= 20
Ans: D
Answer: D
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 60 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
Options:
A)12 sec
B)24 sec
C)40 sec
D)60 sec
E)62 sec
Rationale: Relative speed = 60 + 30 = 90 km/hr.
90 * 5/18 = 25 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 /25 = 40 sec.
ANSWER:C
Answer: C
Question: Each digit 1 through 5 is used exactly once to create a 5-digit integer. If the 1 and the 2 cannot be adjacent digits in the integer, how many 5-digit integers are possible?
Options:
A) 48
B) 66
C) None of these
D) 78
E) 90
Rationale: Number of arrangements using 5 distinct digits = 5!
Number of arrangements in which 1 and 2 are adjacent - consider 1 and 2 together as one group. Now you have 4 numbers/groups to arrange which can be done in 4! ways. In each of these arrangements, 1 and 2 can be arranged as 12 or 21.
Number of arrangements in which 3 and 4 are not adjacent = 5! - 2*4! = 72
Answer : C
Answer: C
Question: John completes a piece of work in 8 days, Rose completes the same work in 16 days. If both of them work together, then the number of days required to complete the work is?
Options:
A)6 days
B)5.33 days
C)10 days
D)12 days
E)14 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 8 × 16/24 = 5.33 days
Answer : B
Answer: B
Question: One out of every 6000 computer chips is defective. If 2 out of every 30 defective chips have defective processors and there are 30 defective processors in the first batch, how many computer chips are there in the first batch?
Options:
A)450
B)900
C)90,000
D)2700,000
E)900,000
Rationale: (D) Read the whole question to get the feel of what they are asking you to find. Then start with the smallest amount and work your way outwards. We are told that two out of every 30 defective chips have a defective processor. Let x be the total number of defective processors in the batch. Because we know 2 out of every 30 defective chips will have defective processors, and the total number of defective processors in the batch is 30, we can write out an equation: (2/30)x = 30. This can be simplified to (1/15)x = 30. Multiplying each side by 15, we arrive at x = 450. This tells us that there are 450 defective chips in the whole batch. Because we know that 1 out of every 1000 chips is defective, we can set up a proportion. If 1 out of every 6000 chips is defective, then 450 out of y chips would be defective, where y is the total number of chips in the batch. This can be set up as an equation as follows: 1/6000 = 450/y. Solve for y and you will get the total number of chips in the batch: 2700,000.
The answer is (D).
Answer: D
Question: Special codes are designated by either a 5-letter or a 6-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different codes that can be designated with this system?
Options:
A)2 (26)^6
B)26(26)^5
C)27(26)^5
D)26(26)^6
E)27(26)^6
Rationale: 26^5+26^6 = 26^5(1+26)=27*26^5
The answer is C.
Answer: C
Question: Two mechanics were working on your car. One can complete the given job in six hours, but the new guy takes 10 hours. They worked together for the first two hours, but then the first guy left to help another mechanic on a different job. How long will it take the new guy to finish your car?
Options:
A)7/4
B)4/3
C)15/4
D)56/15
E)17/5
Rationale: Rate(1)=1/6
Rate(2)=1/10
Combined = 8/30
Work done in 2 days=8/15
Work left = 7/15
Rate * Time = Work left
1/8 * Time = 7/15
Time=56/15
D
Answer: D
Question: 15, 30, 22, 44, 36, 72, ?
Options:
A)43
B)25
C)58
D)47
E)64
Rationale: E
64
This is an alternating multiplication and subtracting series with a pattern x2, -8, x2, -8.
Answer: E
Question: Mary has 2 puppies,9 birds, 4 fishes.How many pets are there in all?
Options:
A)12
B)08
C)19
D)15
E)20
Rationale: 2+9+4=15. Answer is D
Answer: D
Question: A man can row a boat at 25 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
Options:
A)60/31 hours
B)80/13 hours
C)30/13 hours
D)30/19 hours
E)32/13 hours
Rationale: Speed downstream = 25 + 6 = 31 kmph.
Time required to cover 60 km downstream
= d/s = 60/31
= 60/31 hours.
Answer:A
Answer: A
Question: Jhon works for 60 days. for the day he is present he is paid 7.00/- and for the day he is
absent he is paid 3.00/- per day. if he is paid 170/-.how many days he is present.
Options:
A)35
B)36
C)37
D)38
E)39
Rationale: let no. days be = x and no. days he is absent = 60-x , so 7x - 3(60-x) = 170
x = 35
ANSWER:A
Answer: A
Question: Mary has x dollars more than Kathy has, and together they have a total of y dollars. Which of the following represents the number of dollars that Kathy has?
Options:
A)(y – x)/6
B)(y – x)/5
C)5(y – x)/2
D)3(y – x)/2
E)(y – x)/2
Rationale: To solve, we will set up two equations. Let's start by defining two variables.
A = number of dollars Kathy has
B= number of dollars Mary has
We are given that Mary has x dollars more than Kathy. We set up an equation:
B= x + A
We are next given that together they have a total of y dollars. We can set up our second equation:
A + B = y
Since we know that B = x + A, we can substitute x + A for B into the second equation A+ B = y.
Notice that, after the substitution, we will only have variables of A, x, and y. Thus, we have:
A + x + A = y
2A + x = y
2A = y – x
A = (y – x)/2
Answer : E
Answer: E
Question: In 1995, the Johnsons spent $800 on the family’s water bills. Anticipating that water rates would increase in 1996 by 50%, the Johnsons cut back their water usage. By how much must the Johnsons have reduced their 1996 water usage to pay exactly the same amount in 1996 as they paid in 1995?
Options:
A)33 1⁄3%
B)40%
C)50%
D)66 2⁄3%
E)100%
Rationale: In 1995 , water usage for Johnson's = w
and cost per unit of water = c
cw = 800
=> w=800/c -- 1
In 1996 , cost per unit of water = 1.5 c
Water usage for Johnson's so as to pay same amount as in 1995= w'
1.5c * w' = 800
=> w' = 800/1.5c
=> w' = (2/3c)*800
From 1 and 2 , we get
w' = 2/3 w
(w-w')/w = 1/3
Answer A
Answer: A
Question: The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.2 the sixth number is?
Options:
A)9.5
B)10
C)10.3
D)11.5
E)12
Rationale: Explanation:
1 to 11 = 11 * 10.9 = 119.9
1 to 6 = 6 * 10.5 = 63
6 to 11 = 6 * 11.2 = 67.2
63 + 67.2 = 130.2 – 119.9 = 10.3
6th number = 10.3
Option C
Answer: C
Question: Two trains of equal lengths take 12 sec and 20 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
Options:
A)16 sec
B)12 sec
C)17 sec
D)15 sec
E)23 sec
Rationale: Speed of the first train = 120/12 = 10 m/sec.
Speed of the second train = 120/20 = 6 m/sec.
Relative speed = 10 + 6 = 16 m/sec.
Required time = (120 + 120)/16 = 15 sec.
Answer: D
Answer: D
Question: If 80 percent of 600 is 50 percent of x, then x=?
Options:
A)960
B)1000
C)1020
D)1080
E)1075
Rationale: 0.8 * 600 = 0.5 * x
x = 8/5 * 600 = 960
Answer: A
Question: If Rs.1000 be invested at interest rate of 5% & the interest be added to the principal every 10 yrs, then the no. of yrs in which it will amount to Rs.2000 is:
Options:
A)15
B)17 1/3
C)16 2/3
D)19 2/5
E)21 1/5
Rationale: Total time= (10+6 2/3) = 16 2/3 years
C
Answer: C
Question: A man can row upstream at 25 kmph and downstream at 65 kmph, and then find the speed of the man in still water?
Options:
A)45
B)86
C)30
D)78
E)38
Rationale: US = 25
DS = 65
M = (65 + 25)/2
= 45
Answer: A
Answer: A
Question: The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4?
Options:
A)29
B)23
C)73
D)76
E)22
Rationale: Average after 11 innings = 36
Required number of runs
= (36 * 11) - (32 * 10) = 396 - 320
= 76.
Answer:D
Answer: D
Question: Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
Options:
A)5/7
B)3/5
C)4/7
D)1/7
E)2/7
Rationale: Original share of 1 person = 1/8
New share of 1 person = 1/7
Increase = (1/7 - 1/8	= 1/56)
Therefore, Required fraction = (1/56)/(1/8)	= (1/56)x (8/1)	= 1/7
Answer is D.
Answer: D
Question: In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected?
Options:
A)112
B)500
C)992
D)882
E)712
Rationale: We can select one boy from 20 boys in 20 ways.
We select one girl from 25 girls in 25 ways
We select a boy and girl in 20 * 25 ways i.e., = 500 ways.
Answer:B
Answer: B
Question: 65 boys can complete a work in 30 days.how many men need to complete twice the work in 20 days
Options:
A)160
B)170
C)180
D)195
E)200
Rationale: one man can complete the work in 30*65=1950 days = one time work
to Complete the work twice it will be completed in
let M be the no. of worker assign for this therefore the eqn becomes
M*20=2*1950
M=195 workers
ANSWER:D
Answer: D
Question: A certain tire company can produce tires at a cost of $22,500 per batch plus $8 per tire. The company can sell tires to the wholesaler at a cost of $20 per tire. If a batch of 15,000
tires is produced and sold, what is the company’s profit per tire?
Options:
A)$9.00
B)$9.50
C)$10.50
D)$13.50
E)$20.00
Rationale: CP(15000 tires) = $22500 +($8×15000) =$142500
SP (15000 tires) = $20×15000 = $300000
Profit = SP-CP
= $300000-$142500= $157500
PROFIT/TIRE = $157500/15000 = $10.50
Answer C
Answer: C
Question: Two trains start from P and Q respectively and travel towards each other at a speed of 50 km/hr and 40 km/hr respectively. By the time they meet, the first train has traveled 100 km more than the second. The distance between P and Q is?
Options:
A)900 km
B)300 km
C)700 km
D)800 km
E)100 km
Rationale: A
900 km
At the time of meeting, let the distance traveled by the second train be x km. Then, distance covered by the first train is (x + 100) km.
x/40 = (x + 100)/50
50x = 40x + 4000 => x = 400
So, distance between P and Q = (x + x + 100)km = 900 km.
Answer: A
Question: A train 125 m long passes a man, running at 4 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
Options:
A)49 kmph
B)50 kmph
C)51 kmph
D)52 kmph
E)54 kmph
Rationale: Explanation:
Speed of the train relative to man
= (125/10) m/sec = (25/2) m/sec.
[(25/2) x (18/5)] km/hr = 45 km/hr.
Let the speed of the train be 'x' km/hr.
Then, relative speed = (x - 4) km/hr.
x - 4 = 45 => x = 49 km/hr.
ANSWER IS A
Answer: A
Question: Marts income is 40 percent more than Tims income and Tims income is 40 percent less than Juans income. What percentage of Juans income is Marts income
Options:
A)124%
B)b) 120 %
C)c) 96 %
D)d) 80 %
E)e) 84 %
Rationale: M = (140/100)T
T = (60/100)J
=> M = (84/100)J
Answer E.
Answer: E
Question: The editor of an anthology of short stories will select authors from a pool of 12 authors, of which 5 are female. If the anthology is to include the work of 7 authors of which at least 2 are female, in how many ways can the editor select the authors?
Options:
A)734
B)745
C)756
D)767
E)778
Rationale: 12C7 = 792
The number of ways to select 7 males is 7C7 = 1
The number of ways to select 6 males and 1 female is 7C6*5C1 = 35
792 - 1 - 35 = 756
The answer is C.
Answer: C
Question: Hammers and wrenches are manufactured at a uniform weight per hammer and a uniform weight per wrench. If the total weight of two hammers and three wrenches is one-third that of 6 hammers and 5 wrenches, then the total weight of one wrench is how many times that of one hammer?
Options:
A)1/4
B)2/3
C)1
D)3/2
E)2
Rationale: x be the weight of a hammer and y be the weight of a wrench.
(2x+3y)=1/3*(7x+5y)
3(2x+3y)=(7x+5y)
6x+9y=7x+5y
4y=x
y=x/4
Ans - A
Answer: A
Question: Solve x^2 – 3x – 4 = 0.
Options:
A)(9,2)
B)(7,3)
C)(1,3)
D)(-1,4)
E)(2,5)
Rationale: This one factors easily:
x^2 – 3x – 4 = 0
(x + 1)(x – 4) = 0
x + 1 = 0 or x – 4 = 0
x = –1 or x = 4
The solution is x = –1, 4
Ans: D
Answer: D
Question: Firm A's revenues are described by the equation Ra = 17.12x and its costs by Ca = 12.87x + 2700.
Firm B's revenues are described by the equation Rb = 13.27x and its costs by Cb = 8.77x + 1500.
(x denotes the quantity of sales).
If A's volume of sales increases from 1000 to 2000 over the same period that B's volume increases from 2000 to 3000, the percent increase in profits for the firm with the biggest dollar increase in profits is
Options:
A)20%
B)30%
C)60%
D)50%
E)33%
Rationale: Ok, I do not know whether it is exactly what you want to hear but I did it that way: first look at difference between revenue and variable cost => take the bigger one (b) which gives you: 4.5x-1500 just plug in 2000 and 3000. you get 7500 and 12000 (difference 4500). 4500> 0.5*7500 so 60%
C
Answer: C
Question: A group of four women and three men have tickets for seven adjacent seats in one row of a theatre. If the three men will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers?
Options:
A)7! – 2!3!2!
B)7! – 4!3!
C)7! – 5!3!
D)7 × 2!3!2!
E)2!3!2!
Rationale: 7 people can be seated in 7! ways
take 3 men as one unit ----> tot 5 people can be seated in 5 ways *(no. of ways in which 4 women can be seated amng themselves ) * ( no. of ways in which 3 men cen be seated amng themselves)=5*4!*3!=5!*3!
tot no. of ways in which 3 men are not seated in adjacent seats=tot arrangements - 5!*3!=7!-5!*3!
ANSWER:C
Answer: C
Question: Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 percent fescue. If a mixture of X and Y contains 30 percent ryegrass, what percent of the weight of this mixture is X ?
Options:
A)10%
B)33.33 %
C)40%
D)50%
E)66.66 %
Rationale: Qnty.(cheaper)/Qty.(dearer)=(dearer-mean)/(mean-cheaper)
Thus Qy/Qx=(40-30)/(30-25)=2
Therefore Qy=2 Qx and Qy+Qx = 100% (total). Hence Qx = 33.33%
ANSWER:B
Answer: B
Question: How many seconds will a train 100 meters long take to cross a bridge 170 meters long if the speed of the train is 36 kmph?
Options:
A)26
B)72
C)25
D)82
E)27
Rationale: Explanation:
D = 100 + 170 = 270
S = 36 * 5/18 = 10 mps
T = 270/10 = 27 sec
Answer: Option E
Answer: E
Question: if m>0 and a is m percent of b, then, in terms of m, b is what percent of a?
Options:
A)a)100m
B)b)1/10^-4m
C)c)1/m
D)d)10/m
E)e)10,000/m
Rationale: Given (m*b)/100=a
to find (b/a)*100
Rearranging first equation
b/a*100 = 100*100/m
=10000/m
Answer B
Answer: B
Question: In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder. The dividend is?
Options:
A)86
B)90
C)92
D)94
E)96
Rationale: Divisor = (6 * 3) + 2 = 20
5 * Quotient = 20
Quotient = 4.
Dividend = (Divisor * Quotient) + Remainder
Dividend = (20 * 4) + 6 = 86.
A)
Answer: A
Question: There are two sections A and B of a class consisting of 36 and 44 students respectively. If the average weight of section A is 40kg and that of section B is 35kg, find the average weight of the whole class?
Options:
A)7.25kg
B)17.25kg
C)37.25kg
D)27.25kg
E)34.25kg
Rationale: total weight of(36+44) students=(36*40+44*35)kg =2980kg.
Therefore weight of the total class=(2980/80)kg =37.25kg.
Option C
Answer: C
Question: Find a sum for first 5 prime no's from number series?
Options:
A)24
B)28
C)30
D)34
E)36
Rationale: Required sum = (2 + 3 + 5 + 7 + 11) = 28
Note: 1 is not a prime number
Option B
Answer: B
Question: Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder?
Options:
A)1234
B)1540
C)1650
D)1632
E)1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Large number = 270+1365 = 1635
E
Answer: E
Question: The ratio between the length and the breadth of a rectangular plot is 7 : 5. If the perimeter of the plot is 360 metres, what is its area?
Options:
A)1320 sq.metres
B)4260 sq.metres
C)6870 sq.metres
D)7875 sq.metres
E)None of these
Rationale: Let the length and breadth be 7x and 5x respectively.
Then, P = 2(7x + 5x) = 360 â‡’ x = 15
Area = 7 Ã— 15 Ã— 5 Ã— 15 = 7875 sq.m.
Answer D
Answer: D
Question: The average (arithmetic mean) of the 5 positive integers k, m, r, s, and t is 16, and k < m < r < s < t. If t is 30, what is the greatest possible value of the median of the 5 integers?
Options:
A)16
B)18
C)19
D)20
E)28
Rationale: We need to find the median which is the third value when the numbers are in increasing order. Since k<m<r<s<t, the median would be r.
The average of the positive integers is 16 which means that in effect, all numbers are equal to 16. If the largest number is 30, it is 14 more than 16. We need r to be maximum so k and m should be as small as possible to get the average of 16. Since all the numbers are positive integers, k and m cannot be less than 1 and 2 respectively. 1 is 15 less than 16 and 2 is 14 less than 16 which means k and m combined are 29 less than the average. 30 is already 14 more than 16 and hence we only have 29 - 14 =15 extra to distribute between r and s. Since s must be greater than r, r can be 16+12 = 28 and s can be 16+13 = 29.
So r is 28.
Answer (E)
Answer: E