divelab/Sys2Bench huggingface dataset:
Question: Martha takes a road trip from point A to point B. She drives x percent of the distance at 60 miles per hour and the remainder at 30 miles per hour. If Martha's average speed for the entire trip is represented as a fraction in its reduced form, in terms of x, which of the following is the numerator?
Options:
A) 18,000
B) 300
C) 1,100
D) 3,000
E) 30,000
Rationale: total distance = d
total time taken = x/(100*60) + (100-x)/(100*30)
speed = distance / time
gives numerator = 18000
Answer : A
Answer: A
Question: A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of A?
Options:
A)3377
B)2899
C)2500
D)2778
E)10000
Rationale: A:B:C = 2/3:1/6:1/6 = 4:1:1
x * 2/100 * 2/3 = 200
A capital = 15000*2/3 = 10000
Answer: E
Answer: E
Question: If xy = 5 and x^2 + y^2 = 15, then x/y + y/x =
Options:
A)2 2/5
B)3
C)5 1/3
D)7
E)60
Rationale: x/y+y/x=(x^2+y^2)/xy =substitute given we get 15/5=3 answer B
Answer: B
Question: For a finite sequence of non zero numbers, the number of variations in sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 1, -3, 2, 5, -4, -5 ?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Given sequence: {1, -3, 2, 5, -4, -6}
The questions basically asks: how manypairs of consecutive termsare there in the sequence such that the product of these consecutive terms is negative.
1*(-3)=-3=negative;
-3*2=-6=negative;
2*5=10=positive;
5*(-4)=-20=negative;
(-4)*(-6)=24=positive.
So there are 3 pairs of consecutive terms of the sequence for which the product is negative.
Answer: B.
Answer: B
Question: A class of students bought a total of 572 pencils. If each student in the class bought at least 17 pencils, then what is the greatest possible number of students in the class?
Options:
A)31
B)32
C)33
D)34
E)35
Rationale: 572/17=33 plus remainder.
The answer is C.
Answer: C
Question: 3 of the 4 expressions (1), (2), (3) & (4) given below are exactly equal . Which of the expression is not equal to the other four expressions?
Options:
A)(A – B)2 + 9AB
B)(A – B)2 + 4AJ
C)(A – B)2 + 4AB
D)(A – B)2 + 2AB
E)(A – B)2 + 1AB
Rationale: Explanation:
1) (A + B)2 – 4AB = A2 + 2AB + B2 - 4AB = A2 + B2 - 2AB
2) (A – B)2 + 4AB = A2 – 2AB + B2 + 4AB = A2+ B2 + 2AB
3) A2 +B2 – 4AB + 2AB = A2 + B2 - 2AB
4) A2 – B2 + 2B(B – A) = A2 – B2 + 2B2 – 2AB = A2 + B2 – 2AB
Therefore, (1) = (3) = (4) ≠ (2)
Therefore, expression (2) is wrong
ANSWER:C
Answer: C
Question: A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
Options:
A)238
B)777
C)350
D)377
E)267
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 39 = 50/3
3(x + 300) = 1950 è x = 350m.Answer:C
Answer: C
Question: I travel the first part of my journey at 40 kmph and the second part at 60 kmph and cover the total distance of 240 km to my destination in 5 hours. How long did the first part of my journey last
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: The total time of journey = 5 hours.
Let 'x' hours be the time that I travelled at 40 kmph
Therefore, 5–x hours would be time that I travelled at 60 kmph.
Hence, I would have covered x×40+(5−x)60 kms in the 5 hours = 240 kms.
Solving, for x in the equation 40x+(5–x)×60=240, we get
40x+300–60x=240
⇒20x=60 or x= 3 hours
ANSWER:C
Answer: C
Question: The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:
Options:
A)29
B)16
C)7
D)6
E)5
Rationale: Let C.P. of each article be Re. 1 C.P. of x articles = Rs. x.
S.P. of x articles = Rs. 20.
Profit = Rs. (20 - x).
{\color{Black} \therefore \left ( \frac{20-x}{x}\times 100=25 \right )}
2000 - 100x = 25x
125x=2000
x=16
Answer: B
Answer: B
Question: Two numbers are respectively 40% and 30% more than a third number. The second number expressed in terms of percentage of the first is ?
Options:
A)95%
B)93%
C)90%
D)80%
E)none of these
Rationale: Here, x = 40 and y = 30;
Therefore second number
= [[( 100 + y)/ (100 + x )] x 100 ]% of first number
= [[( 100 + 30)/ (100 + 40 )] x 100 ]% of first number
= 92.8% of the first
ANSWER:B
Answer: B
Question: A car travels a certain distance taking 7 hrs in forward journey, during the return journey increased speed 12km/hr takes the times 5 hrs. What is the distance traveled
Options:
A)210 kms
B)30 kms
C)20 kms
D)40 kms
E)none of these
Rationale: If x is the distance, then
difference in speeds =
x/5 - x/7 = 12
2x/35=12
x= 12*35/2 = 210 kms. ANSWER:A
Answer: A
Question: Which of the following options is the possible total number of people in a hall given that the number of people is a multiple of both 6 and 16?
Options:
A)42
B)66
C)54
D)48
E)50
Rationale: the number of people are a multiple of both 6 and 16, so it must be divisible by 6 and 16.
using the elimination method look for a number that is both divisible by 6 and 16,
of all the options only 56 is divisible by 8 and 14.
[ 48/6=8 and 48/16=3]
answer :D
Answer: D
Question: What is the present worth of Rs. 132 due in 2 years at 5% simple interest per annum?
Options:
A)Rs. 83
B)Rs. 108
C)Rs. 120
D)Rs. 132
E)Rs. 142
Rationale: Explanation:
Let the present worth be Rs. x.
Then, S. I. = Rs. (132-x).
110 x = 13200
x = 120
Answer: C
Answer: C
Question: If e persons take y days to complete z similar jobs, how long does it take y persons to complete 1 such job?
Options:
A)z
B)x
C)x/y
D)z/x
E)y/z
Rationale: the Q doesn't seem to be having the any correct answer as a choice..
since we are looking for days, lets keep days in end and work out a solution..
e person can do z jobs in y days..
so e person can do 1 job in y/z days..
and 1 person can do 1 job in y^2/z days..
so y person can complete 1 job in y^2/zy=y/z..
so the answer should be y/z=E
Answer: E
Question: Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Joseph, working together at their respective rates, can paint the room in two hours, what fraction of the room can Joseph paint in 20 minutes?
Options:
A)1/6x
B)x/(x-6)
C)(x-2)/6x
D)x/(x-2)
E)(x-2)/x
Rationale: Let J be Joseph's rate per hour.
1/x + J = 1/2 of a room per hour
J = 1/2 - 1/x, of a room per hour
In 20 minutes Joseph can paint 1/3*(1/2-1/x) = 1/6-1/3x = (x-2)/6x
The answer is C.
Answer: C
Question: At a meeting of the 7 Joint Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the 7 Chiefs of Staff be seated around a circular table?
Options:
A)120
B)480
C)960
D)2520
E)5040
Rationale: 7 people can be arranged around circular table in (7-1)!=6! # of ways.
Consider the two people (A and B) who do not want to sit together as one unit: {AB}. Now, 6 units {AB}, {C}, {D}, {E}, {F} and {G} can can be arranged around circular table in (6-1)!=5! # of ways. A and B can be arranged within their unit in two ways {AB} and {BA}. Thus the # of ways those two people sit together is 2*5!.
The number of ways they do not sit together = {Total} - {Restriction} = 6! - 2*5! = 5!(6 - 2) = 480.
Answer: B.
Answer: B
Question: The function f is defined for all positive integers n by the following rule: f(n) is the product of the distinct prime factors of n. If f(n) < 80 and n is not prime, what is the greatest possible value of f(n)?
Options:
A)75
B)69
C)60
D)55
E)63
Rationale: Since we need the largest value of f (n), we will start with the largest option.
Option A: 75 = 3*5*5. This is not a product of distinct prime numbers. Hence incorrect
Option B: 69 = 3*23. This is a product of distinct prime numbers.
Rest all the options are smaller that 69.
Correct Option: B
Answer: B
Question: A 3-digit number 4a3 is added to another 3-digit number 984 to give a 4-digit number 13b7, which is divisible by 11. Then, (a + b) = ?
Options:
A)10
B)11
C)12
D)15
E)16
Rationale: 4 a 3 |
9 8 4 } ==> a + 8 = b ==> b - a = 8
13 b 7 |
Also, 13 b7 is divisible by 11 => (7 + 3) – (b + 1) = (9 – b)
(9 – b) = 0
b = 9
(b = 9 and a = 1) => (a + b) = 10.
Answer A
Answer: A
Question: If log 27 = 1.461, then the value of log 9 is:
Options:
A)0.934
B)0.945
C)0.954
D)0.958
E)0.974
Rationale: log 27 = 1.461
log (33 ) = 1.461
3 log 3 = 1.461
log 3 = 0.487
log 9 = log(32 ) = 2 log 3 = (2 x 0.487) = 0.974.
Answer: Option E
Answer: E
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
Options:
A)4538
B)4535
C)4539
D)4530
E)4532
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls
= 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 5
= Rs. 4530
Answer: D
Answer: D
Question: A girl has exactly 5 quarters, 9 dimes, and 10 nickels in her pocket. If she withdraws a number of these coins at random, how many coins would she have to withdraw to ensure that she has at least a 50 percent chance of withdrawing at least one quarter?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: When the probability of NOT drawing a quarter is 50% or less, then the probability of drawing a quarter is at least 50%.
P(not drawing a quarter with 2 coins) = 19/24 * 18/23 = 57/92 > 50%
P(not drawing a quarter with 3 coins) = 57/92 * 17/22 = 969/2024 < 50%
The answer is B.
Answer: B
Question: There are 36 hours in a day, 90 minutes in an hour and 60 seconds in one minute. What is the angle between hour hand and minute hand when time is 15:50?
Options:
A)191.10 degree
B)141.10 degree
C)101.10 degree
D)111.10 degree
E)121.10 degree
Rationale: Hour hand speed = 360/(18*90) =2/9 DPM
Minute hand speed =360/90 = 4 DPM
Now 18 hours have 360 degree
then 1 hour has 360/18= 20 degree
so 15 * 20 make 300 degree
hour hand = 300 + 50 * 2/9 =311.10 degree
minute hand = 50 * 4= 200 degree
here is the difference 311.10-200= 111.10 degree
ANSWER:D
Answer: D
Question: A 260 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
Options:
A)230 m
B)240 m
C)260 m
D)320 m
E)330 m
Rationale: Relative speed = (120 + 80) km/hr
=	(200 x(5/18))m/sec
=	(500/9)m/sec.
Let the length of the other train be x metres.
Then,	(x + 260)/9 = 500/9
x + 260 = 500
x = 240.
B
Answer: B
Question: 1-1-1-1-1-1
do any operations between the numbers to make the sum as 37 ?
Options:
A)34
B)35
C)36
D)37
E)38
Rationale: 1+1+1 = 3
3 Factorial = 6
6 to the power 1+1 = 6^2 = 36
36 + 1 = 37
ANSWER:D
Answer: D
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
Options:
A)10 seconds
B)15 seconds
C)20 seconds
D)12 seconds
E)None of these
Rationale: Speed of the boat downstream = 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m = 60/5 = 12 seconds.
ANSWER:D
Answer: D
Question: Look at this series: 5, 8, 6, 9, 7, ... What number should come next?
Options:
A)4
B)11
C)10
D)8
E)12
Rationale: This is a simple alternating addition and subtraction series. In the first pattern, 3 is added; in the second, 2 is subtracted.
5+3 =8
6+3 =9
8-2 =6
9-2 =7
Now 7+3 = 10
Answer is C
Answer: C
Question: A man purchases 8 pens for Rs.9 and sells 9 pens for Rs.8, how much profit or loss does he make?
Options:
A)30.98%loss
B)20.98%loss
C)20.97%loss
D)20.68%loss
E)20.98%loss
Rationale: 81 ---- 17
100 ----- ? è
20.98%loss
Answer: B
Answer: B
Question: In a triangle if the length of sides are as given below which one will not form triangle?
Options:
A)(5,5,5)
B)(5,4,5)
C)(4,4,9)
D)(3,4,5)
E)(3,5,5)
Rationale: (4,4,9)
using property :"sum of two side of a triangle is greater than its third side (4+4) is not greater than 9
ANSWER:C
Answer: C
Question: A certain car averages 15 miles per gallon of gasoline when driven in the city and 40 miles per gallon when driving on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway?
Options:
A)28
B)30
C)32
D)36
E)38
Rationale: 10*1/15 gpm+50*1/40 gpm=1.85 total gallons
60 total miles/1.85 total gallons=32.4 average mpg
C. 32
Answer: C
Question: A man invests some money partly in 4% stock at 48 and partly in 10% stock at 110.To obtain equal dividends from both,he must invest the money in the ratio :
Options:
A)3 : 4
B)3 : 5
C)4 : 5
D)6 : 5
E)None
Rationale: Solution
For an income of Rs. 1 in 9% stock at 96, investment = Rs. (48/4)= Rs. 12 .
For an income of Rs. 1 in 12% stock at 120, investment = Rs.(110/10) = Rs. 10.
∴ Ratio of investments = 12 :10 = 6:5
Answer D
Answer: D
Question: In a two-digit number, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 52, then the number is:
Options:
A)11
B)13
C)24
D)35
E)46
Rationale: Let the ten's digit be x. Then, unit's digit = x + 2. Number = 10x + (x + 2) = 11x + 2
Sum of digits = x + (x + 2) = 2x + 2
(11x + 2)(2x + 2) =52
22(x)(x) + 26x - 48 = 0
11(x)(x) +13x - 24 = 0
(x - 1)(11x +24) = 0
x = 1
Hence, required number = 11x + 2 = 13.
ANSWER:B
Answer: B
Question: If in a $270 mln portfolio of stock, twice as much is invested in stock A as is invested in all the other stocks, how much is invested in all the other stocks?
Options:
A)90mln
B)80mln
C)70mln
D)60mln
E)50mln
Rationale: Let x denote the amount invested in all the other stocks. Then the amount invested in stock A is 2x. As we have the $270 mln portfolio, x+2x=3x=270 mln from where x=90 mln.
Answer: A
Answer: A
Question: A train running at the speed of 60 km/hr crosses a pole in 15 seconds. What is the length of the train?
Options:
A)187 m
B)250 m
C)876 m
D)150 m
E)267 m
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train
= (Speed x Time)
= (50/3 * 15) m
= 250 m.
Answer: B
Answer: B
Question: The radius of the two circular fields is in the ratio 3: 5 the area of the first field is what percent less than the area of the second?
Options:
A)23%
B)62%
C)92%
D)64%
E)22%
Rationale: r = 3 πr2 = 9
r = 5 πr2 = 25
25 π – 16 π
100 ---- ? => 64%
Answer: D
Answer: D
Question: What is the median from the below series 90, 92, 93, 88, 95, 88, 97
Options:
A)91.71
B)82
C)92
D)98
E)100
Rationale: Ordering the data from least to greatest, we get:
88, 88, 90, 92, 93, 95, 96
The median quiz score was 91.71 (Four quiz scores were higher than 91.71 and four were lower.)
A
Answer: A
Question: When 1/20% of 6,000 is subtracted from 1/10 of 6,000, the difference is
Options:
A)50
B)200
C)380
D)598
E)400
Rationale: 1/20 % of 6000 = 3
1/10 of 6000 = 600
600-3 = 598
Ans:D
Answer: D
Question: An investment R gained an interest payment of $250 each month when the annual interest rate was 8%, how much more should we invest annually if we want to gain 12% more per month with a new annual interest rate of 7.5% ?
Options:
A)$9,360
B)$9,100
C)$8,250
D)$7,300
E)$7,150
Rationale: Answer is D : 7,300
An investment R gained an interest payment of $250 each month when the annual interest rate was 8%,Interest per annum with 8% interest rate is = 250* 12 = Principal * Interest Rate(8/100)
This gives Principal as 37,500$
For an revised interest of 12% more and new interest rate of 7.5% , ie. 250* 12 * 1.12 = Principal * Interest Rate (7.5/100)
This gives the new Principal as 44,800.
The question is how much more should we invest, so 44,800 - 37,500 = 7,300.D
Answer: D
Question: A salesmanâ€™s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1000 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 600 more than that by the previous schema, his sales were worth
Options:
A)12000
B)14000
C)15000
D)20000
E)60000
Rationale: [1000 + (X-4000) * (2.5/100)] - X * (5/100) = 600
X = 12000
ANSWER A
Answer: A
Question: An automotive test consisted of driving a car the same distance three separate times, first at an average rate of 4 miles per hour, then 5 miles per hour, then 6 miles per hour. If the test took 111 hours to complete, how many miles was the car driven during the entire test?
Options:
A)530
B)520
C)560
D)500
E)540
Rationale: x is the segment to be traveled
x/4+x/5+x/6 =111
or 74x/120 =111
x =180 miles . total distance =3*180 = 540 miles
E
Answer: E
Question: The average of 1st 3 of 4 numbers is 16 and of the last 3 are 15. If the sum of the first and the last number is 13. What is the last numbers?
Options:
A)7
B)6
C)5
D)4
E)3
Rationale: A + B + C = 48
B + C + D = 45
A + D = 13
A – D = 3
A + D = 13
2D = 10
D = 5
Answer: C
Answer: C
Question: What is the price of a orange?
(a) 14 banana and 35 oranges cost Rs. 84
(b) with a 50% discount on banana, Rs. 12 can buy 4 bananas and 5 oranges
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: 14X1+35X2=84
4XO.5+5X2=12
So price of banana =1 and orange=2
ANSWER:B
Answer: B
Question: The ratio of male to female in a class is 2:3. the career preference of the students in the class are to be represented in a circle graph. If the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by half of the males and half of the females in the class?
Options:
A)a)180 degree
B)b) 168 degree
C)c)191 degree
D)d)192 degree
E)e)204 degree
Rationale: let the common ratio be x.. so M=2x and F=3x and Total=5x
1/2 of M= 2x/2 and 1/2 of F= 3x./2.
Total preferring that carrer =x+3x/2=5x/2..
Now 5x= 360, so x=360/5=72..
so 72*5/2=180
A
Answer: A
Question: Earl can stuff advertising circulars into envelopes at the rate of 36 envelopes per minutes and Ellen requires a minutes and half to stuff the same number of envelops.Working together,how long will it take Earl and Ellen to stuff 120 envelopes
Options:
A)2 minutes
B)5 minutes
C)7 minutes
D)3 minutes
E)4 minutes
Rationale: earl takes 1 min. for 36 envelopes.
ellen takes 3/2 mins for the same. so ellen can stuff ((36)/(3/2)) in 1 min. i.e., 24 envelopes a min.
so both of them when work together can stuff 36+24=60 envelopes in 1 min.
for 120 envelopes they will take 120/60 mins. i.e., 2 mins.
ANSWER:A
Answer: A
Question: 40 percent of the ducks included in a certain side effects study were male. If some of the ducks had side effects during the study and 40 percent of the ducks who had side effects were male, what was the ratio of the side effect rate for the male ducks to the side effect rate for the female ducks?
Options:
A)1
B)9/14
C)2/3
D)7/8
E)8/7
Rationale: Say total male = 40
Total female =60
Required ratio =( .4/40)/ (.6/60) = 1 A is the answer
Answer: A
Question: What will be the simple interest on Rs. 80,000 at 16(2/3) % per annum for 9 months?
Options:
A)8,000
B)9,000
C)10,000
D)11,000
E)None of these
Rationale: Explanation:
Given:
1) Principal = Rs. 80,000
2) Rate of interest = 16(2/3)%
3) Time = 9 months
Rate of interest = 16(2/3)%=50/3
Time =	9/12=3/4 years
Simple Interest =	(P × R × T)/100
Substituting the given values, we get
Simple Interest =	80,000/100	×	50/3	×	3/4
Simple Interest = Rs.10,000
ANSWER IS C
Answer: C
Question: Pat, kate and mark charged a total of 216 hours to a certain project . If pat charged twice as much time to the project as kate and 1/3 as much times as mark, how many more hours did mark charge to the project than kate.
Options:
A)18
B)36
C)120
D)90
E)108
Rationale: Let Kate charge for x hours,
then Pat charged for 2x and Mat - for 6x.
So, 2x+6x+x = 216 -total hours charged for,
x= 24.
Mat charged 6x-x or 5x for more hours than kate, or for 120 hours .
C is correct
Answer: C
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 30% on the cost price?
Options:
A)62.5
B)62.3
C)65
D)62.2
E)62.9
Rationale: CP = 47.50
SP = 47.50*(130/100)
= 61.75
MP*(95/100)
= 61.75
MP = 65
Answer:C
Answer: C
Question: If two numbers are in the ratio 1:2. If 10 is added to both of the numbers then the ratio becomes 2:3 then find the smallest number?
Options:
A)10
B)20
C)30
D)40
E)50
Rationale: Explanation:
1:2
x + 10 : 2x + 10 = 2 : 3
3[x + 10] = 2[2x + 10]
3x + 30 = 4x + 20
9x - 8x = 40 - 30
x = 10
Then smallest number is = 1
1 * 10 = 10
Answer : A
Answer: A
Question: What is the least number of squares tiles required to pave the floor of a room 8 m 82 cm long and 2 m 52 cm broad?
Options:
A)14
B)20
C)40
D)44
E)48
Rationale: Length of largest tile = H.C.F. of 882 cm and 252 cm = 126 cm.
Area of each tile = (126 x 126) cm2.
Required number of tiles =882 x 252/(126^2)= 14.
ANSWER:A
Answer: A
Question: There are 5 girls and 5 boys. If they are to be seated in a row, what is the probability that no two girls sit together?
Options:
A)A)1/10!
B)B)2*5!5!/10!
C)C)6!6!/10!
D)D)6!6!/12!
E)E)6!7!/12!
Rationale: If girls are alternate, then only no 2 girls can be together.
So among 10 places, girls can be seated in 5 alternate places in 5! ways.
And boys can be seated in the remaining 5 places in 5! ways.
Therefore total number of ways = 5! * 5!
But there could be 2 such arrangements-->
1. When first place is filled by a girl
2. When first place is filled by a boy
Therefore total number of ways = 2*5! * 5!
Also total number of ways to fill 10 places = 10!
Hence probability =2∗5!5!/10!
Answer:B
Answer: B
Question: Sides of a triangle are 13 cm.14cm.and 15cm.respectively.calculate the area of triangle.
Options:
A)80
B)82
C)84
D)86
E)88
Rationale: let a=13cm, b=14cm.and c=15 cm.
s=1/2(13+14+15)=21,(s-a)=8,(s-b)=7 and (s-c)=6
Area=√21*8*7*6=84 sq.cm
Answer C
Answer: C
Question: Which of the following CANNOT yield an integer when divided by 7 ?
Options:
A)The sum of three consecutive integers
B)An integer with only even prime factors
C)The product of two odd integers
D)An integer divisible by 8
E)An even integer
Rationale: An integer to be divisible by 7, must have 7 in its prime factorization. Thus an integer with only even prime factors (2^n) CANNOT be divisible by 7.
As for the other options:
(A) The sum of three consecutive integers --> if the three integers are {-1, 0, 1}, then their sum is 0 and 0 IS divisible by 7.
(C) The product of two odd integers --> 1*7=7 --> 7 is divisible by 7.
(D) An integer divisible by 8 --> 0 is divisible by both 7 and 8.
(E) An even integer --> 0=even is divisible by 7.
Answer: B.
Answer: B
Question: A shopkeeper sells two articles at Rs.1000 each, making a profit of 20% on the first article and a loss of 20% on the second article. Find the net profit or loss that he makes?
Options:
A)22
B)33
C)55
D)4
E)9
Rationale: SP of first article = 1000
Profit = 20%
CP = (SP)*[100/(100+P)] = 5000/6 = 2500/3
SP of second article = 1000
Loss = 20%
CP = (SP)*[100/(100-L)] = 5000/4 = 1250
Total SP = 2000
Total CP = 2500/3 + 1250 = 6250/3
CP is more than SP, he makes a loss.
Loss = CP-SP = (6250/3)- 2000 = 250/3
Loss Percent = [(250/3)/(6250/3)]*100 =
0.04 * 100 = 4%.Answer: D
Answer: D
Question: Virat buys an old car for Rs. 50000 and spends Rs. 4000 on its repairs. If he sells the scooter for Rs. 60000, his gain percent is:
Options:
A)11 (1/9) %
B)11 (1/8) %
C)11 (4/9) %
D)13 (1/9) %
E)51 (1/9) %
Rationale: Explanation:
C.P. = Rs. (50000 + 4000) = Rs. 54000
S.P. = Rs. 60000.
Gain% = ( (6000 / 54000) * 100 ) % = 11 (1/9)%
ANSWER: A
Answer: A
Question: A train passes a station platform in 36 sec and a man standing on the platform in 22 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
Options:
A)288
B)210
C)881
D)1277
E)121
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 22 = 330 m.
Let the length of the platform be x m . Then,
(x + 330)/36 = 15 => x = 210 m.
Answer: B
Answer: B