divelab/Sys2Bench huggingface dataset:
Question: In the Hillside summer camp there are 50 children. 80% of the children are boys and the rest are girls. The camp administrator decided to make the number of girls only 10% of the total number of children in the camp. How many more boys must she bring to make that happen?
Options:
A)55
B)50
C)40.
D)30.
E)25.
Rationale: Given there are 50 students , 80% of 50 = 40 boys and remaining 10 girls.
Now here 80% are Boys and 20% are Girls.
Now question is asking about how many boys do we need to add, to make the girls percentage to 20 or 20%..
If we add 50 to existing 40 then the count will be 90 and the girls number will be 10 as it.
Now boys are 90% and girls are 10%. ( out of 100 students = 90 boys + 10 girls ).
IMO option B is correct.
Answer: B
Question: 12 men complete a work in 9 days. After they have worked for 6 days, 6 more men join them. How many days will they take to complete the remaining work?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: 1 man's 1 day work = 1/108
12 men's 6 day's work = 1/9 * 6 = 2/3
Remaining work = 1 - 2/3 = 1/3
18 men's 1 day work = 1/108 * 18 = 1/6
1/6 work is done by them in 1 day.
1/3 work is done by them in 6 * 1/3 = 2 days.
Answer: A
Answer: A
Question: If |p+q|=|p-q|, then p*q must be equal to:
Options:
A)0
B)-2
C)-1
D)1
E)1
Rationale: Solution 1: Distance perspective
|p-q| = |p+q| ==> The distance of p and q is equal to the distance of p and -q.
<=======(-q)=======0=======(q)======>
Only 0 is the value that has a distance equal to q and -q.
Solution 2:
|p-q| = |p+q| (square both)
p^2 -2pq + q^2 = p^2 + 2pq + q^2
4pq = 0
pq = 0
Answer: A
Answer: A
Question: In what time a sum of money double itself at 7% per annum simple interest?
Options:
A)33 1/8%
B)33 1/3%
C)14 2/7%
D)32 1/3%
E)23 1/3%
Rationale: P = (P*7*R)/100
R = 14 2/7%
Answer: C
Answer: C
Question: Franklin has s pairs of shoes, which is 1/5 as many as Bailey and twice as many as Smith. In terms of s, how many pairs of shoes do the three of them have combined?
Options:
A)7/2*s
B)2s
C)13/2*s
D)4s
E)15/2*s
Rationale: == s +5s + s/2 ==> 6s + 1/2 s = 13/2*s
Ans .C
Answer: C
Question: On 3,000 invested at a simple interest rate 6 p.c.p.a, 900 is obtained as interest in certain years. In order to earn 1,600 as interest on 4,000 in the same number of years, what should be the rate of simple interest?
Options:
A)7 p.c.p.a.
B)8 p.c.p.a.
C)9 p.c.p.a.
D)Data inadequate
E)None of these
Rationale: Time = 900×100/3000×6 = 5 years
Rate = 1600×100/5×4000 = 8%
Answer B
Answer: B
Question: Mukesh borrowed a sum of Rs. 10000 at simple interest from a bank. After two years he takes Rs. 12000 more as loan and discharge all the debt at the end of next 3 years depositing Rs. 27160 to the bank. What is the rate of interest per annum?
Options:
A)5%
B)6%
C)8%
D)10%
E)None of these
Rationale: si=27160-(principal amount)=27160-22000=5160.
now,(10000*5*R/100) + (12000*3*R/100)=5160.
500R+360R=5160.....Rate=6%.
ANSWER:B
Answer: B
Question: The speeds of three asteroids were compared. Asteroids X-13 and Y-14 were observed for identical durations, while asteroid Z-15 was observed for 2 seconds longer. During its period of observation, asteroid Y-14 traveled three times the distance X-13 traveled, and therefore Y-14 was found to be faster than X-13 by 4000 kilometers per second. Asteroid Z-15 had an identical speed as that of X-13, but because Z-15 was observed for a longer period, it traveled five times the distance X-13 traveled during X-13's inspection. Asteroid X-13 traveled how many kilometers during its observation?
Options:
A)500
B)1,600/3
C)1,000
D)1,500
E)2,500
Rationale: ST+2S = 5ST
T+2 = 5T
2=4T
t= 1/2
We are looking for distance (d=s*t) so we need to solve for speed now that we have time.
Speed y14 - speed x13
Speed = d/t
3d/t - d/t = 4000 (remember, t is the same because both asteroids were observed for the same amount of time)
2d = 4000
2 = 2000
d=s*t
d=2000*(1/2)
d=1000
ANSWER: C
Answer: C
Question: Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 8 as quotient and the 15 as remainder
Options:
A)1235
B)1557.9
C)1378
D)1635
E)1489
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 8x + 15
7x = 1350
x = 192.9
Large number = 192.9+1365 = 1557.9
B
Answer: B
Question: Indu gave Bindu Rs.5000 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
Options:
A)1
B)2
C)7
D)4
E)8
Rationale: 5000 = D(100/4)2
D = 8
Answer:E
Answer: E
Question: Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 15 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?
Options:
A)120
B)80
C)48
D)192
E)40
Rationale: Four members worked in ration 2:3:5:6, hence as everyone mentioned, individual work could be taken as 2x, 3x,5x, and 6x. Also this gives us total work as 16x.
But we are told that one of these individual works is 15hrs. hence, possible scenarios, if
(1)2x =15 => 16x = 120 (2) 3x =15 => 16x = 80 (3) 5x =15 => 16x = 48 (4) 6x =15 => 16x = 40
Hence Answer is D 192 which can not be any of these.
Answer: D
Question: Anil and suresh started a business with Rs.50,000 and 40,000 respectively. After 6 months Rakesh joined them with capital of Rs.60,000 They got a profit of Rs.6000, then profit of Rakesh is
Options:
A)Rs.1500
B)Rs.3000
C)Rs.2000
D)Rs.1000
E)Rs.4000
Rationale: Ratio of investments of Anil, Suresh & Rakesh=(50000*12) : (40000*12) : (60000*6)=5 : 4 : 3
Profit of Rakesh in Rs. 6000 = 3*6000/(5+4+3) =1500
ANSWER:A
Answer: A
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 100 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)34 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 + 100 = 340 m.
Time taken = 340/10 = 34 sec.
Answer:C
Answer: C
Question: The percentage increase in the area of a rectangle, if each of its sides is increased by 20%
Options:
A)33
B)37
C)44
D)99
E)277
Rationale: Explanation:
Let original length = x metres and original breadth = y metres.
Original area = xy
Increased length = and Increased breadth =
New area =
The difference between the Original area and New area is:
Increase % == 44%]
Answer: C) 44%
Answer: C
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good.
Options:
A)20/61
B)20/63
C)20/62
D)20/87
E)20/18
Rationale: Required probability
= (⁵C₃ . ⁴C₁)/⁹C₄ = (10 * 4)/126
= 20/63
Answer: B
Answer: B
Question: The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 224 different signs. If the company used 222 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 224 signs?
Options:
A)246
B)248
C)892
D)15,128
E)20,256
Rationale: # of 2-letter codes possible from 224 different signs = 224*224.
# of 2-letter codes possible from 222 different signs = 222*222.
The difference= 224^2 - 222^2 = (224 - 222)(224 + 222) = 892.
Answer: C.
Answer: C
Question: How many different positive integers exist between 10^4 and 10^5, the sum of whose digits is equal to 2?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: 10001
10010
10100
11000
20000
TOTAL NO. =5
C
Answer: C
Question: Molly's age in 18 years will be six times her age seven years ago. What is Molly's present age?
Options:
A)8
B)9
C)10
D)12
E)15
Rationale: Let x be Molly's present age.
x + 18 = 6(x-7)
x = 12
The answer is D.
Answer: D
Question: Two goods trains each 125 m long are running in opposite directions on parallel tracks. Their speeds are 45 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)40
B)12
C)48
D)51
E)44
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 125 + 125 = 250 m.
Required time = 250 * 6/125 = 12 sec.
Answer: Option B
Answer: B
Question: A car covers a certain distance at aspeed of 240 kmph in 5 hours. To cover the same distance in 1hr, it must travel at a speed of?
Options:
A)567 km/hr
B)678 km/hr
C)782 km/hr
D)789 km/hr
E)720 km/hr
Rationale: Distance = (240 x 5) = 1200 km.
Speed = Distance/Time
Speed = 1200/(5/3) km/hr. [We can write 1 hours as 5/3 hours]
Required speed = 1200 x 3 km/hr = 720 km/hr.
5
E
Answer: E
Question: If (2^14)(25^S) = 5(10^m) what is the value of m ?
Options:
A)7
B)8
C)15
D)16
E)14
Rationale: given
2^14 * 25^s = 5 * 10^2
=> 2^14 * 5^(2s) = 2^m * 5^(m+1)
Ans E
on comparing the power of 2 => m=14
Answer: E
Question: How many integers between 7000 and 8000 that have distinct digits and increase from left to right ?
Options:
A)30
B)48
C)60
D)20
E)100
Rationale: Since the numbers must be distinct and increasing from left to right,
The only arrangements we could come-up with are:
745_ --> 4
746_ --> 3
747_ --> 2
748_ --> 1
756_ --> 3
757_ --> 2
758_ --> 1
767_ --> 2
768_ --> 1
778_ --> 1
Number of integers =20
D
Answer: D
Question: Some of the 50% solution of acid was removed and this was replaced with an equal amount of 14% solution of acid. As a result, a 23% solution of acid was obtained. What fraction of the original solution was replaced?
Options:
A)1/2
B)1/3
C)2/3
D)3/4
E)4/5
Rationale: Let x be the fraction of the original solution that was replaced.
0.5*(1-x)+0.14(x)=0.23
0.36x=0.27
x=3/4
The answer is D.
Answer: D
Question: What will be the output of the following code statements?
Integer a = 12, b = 45, c = 6 print (a × b / c) – c
Options:
A)65
B)84
C)29
D)26
E)81
Rationale: Explanation:
Apply BODMAS rule
12 × 45 = 540/6-6 =90 –6 =84
Answer:B
Answer: B
Question: This topic is locked. If you want to discuss this question please re-post it in the respective forum.
The sum of the first 51 positive even integers is 2550. What is the sum of the even integers from 100 to 200 inclusive?
Options:
A)5,100
B)7,650
C)10,100
D)15,500
E)20,100
Rationale: even numbers from 100 to 200=100/2+1=51
Sum= (200+100)x51/2=7650
So B is the ans.
Answer: B
Question: In the list 3, 3, 4, 5, 5, 5, 5, 7, 11, 21, what fraction of the data is less than the mode?
Options:
A)2/9
B)3/10
C)2/5
D)2/3
E)7/9
Rationale: Mode: The mode of any set is the term which has the highest frequency (Occurrence)
Highest frequent term in the set is 5 (with frequency 4) hence
Mode = 5
three terms (3, 3, 4) out of a total of 10 terms are less than mode of the set.
Fraction of set that are less than Mode of set = 3/10
Answer: Option B
Answer: B
Question: On a game show, there are three tables. Each table has three boxes (one Zonk!, one cash prize, and one Grand Prize). The contestant can choose one box from each table for a total of three boxes. If any of the boxes are a Zonk!, the contestant loses everything. What is the probability of getting NO Zonk! from any of the three boxes chosen?
Options:
A)1/5
B)1/3
C)8/27
D)1/27
E)7/8
Rationale: NO Zonk!:
1st box = No Zonk! = 2/3
2nd box = NO Zonk! = 2/3
3rd box = No Zonk! = 2/3
(2/3)(2/3)(2/3) = 8/27
8/27 is the probability of NO Zonk!, so...
Answer: C
Answer: C
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. 6 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)s.4529
B)s.4586
C)s.4597
D)s.4530
E)s.5436
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 * 6
=Rs.5436
Answer: E
Answer: E
Question: How many total number of ways in which b distinct objects can be put into two different boxes is
Options:
A)n2
B)2n
C)2b
D)3n
E)None of these
Rationale: Let the two boxes be B1 and B2. There are two choices for each of the b objects. So, the total number of ways is
2 × 2 ×.....× 2 (b times ) = 2b
Answer C
Answer: C
Question: What is the next number in the sequence : 13,17,25,32,37,47,58,71__?
Options:
A)78
B)79
C)71
D)76
E)73
Rationale: next no. = previous + (sum of digits)
13 + (1+3) = 17
17 + (1+7) = 25
25 + (2+5) = 32
32 + (3+2) = 37
37 + (3+7) = 47
47 + (4+7) = 58
58 +(5+8) = 71
71 + (7+1) = 79
ANSWER:B
Answer: B
Question: Simplify: (4 – 6) – (12+17+3)-(3+5)
Options:
A)-10
B)-42
C)-44
D)-41
E)50
Rationale: Solution:
(4-6)-(12+17+3)-(3+5)
=(-1)-32-8
=-1-32-8
=-33-8
-41
Answer: (D)
Answer: D
Question: An error 2% in excess is made while measuring the side ofa square. The % of error in the calculated area of the square is?
Options:
A)4.00%
B)4.04%
C)4.25%
D)4.30%
E)4.45%
Rationale: 100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.
(A2 - A1) = [(102)2 - (100)2]
= (102 + 100) x (102 - 100)
= 404 cm2.
Percentage error = 404 x 100 % = 4.04%
100 x 100
B
Answer: B
Question: Country C imposes a two-tiered tax on imported cars: the first tier imposes a tax of 16% of the car's price up to a certain price level. If the car's price is higher than the first tier's level, the tax on the portion of the price that exceeds this value is 8%. If Ron imported a $14,000 imported car and ended up paying $1440 in taxes, what is the first tier's price level?
Options:
A)$1600
B)$6000
C)$6050
D)$7050
E)$4000
Rationale: Let T be the tier price, P be total price = 14000
Per the given conditions:
0.16T + 0.08(P-T) = 1440 ----> T= 8000. E is the correct answer.
Answer: E
Question: If (x+3)^2/(3x+29)=2, then the difference between the two possible values of x is:
Options:
A)8
B)10
C)12
D)14
E)16
Rationale: (x+3)^2/(3x+29)=2
(x+3)^2=2(3x+29)
x^2+6x+9=6x+58
x^2-49=0
(x-7)(x+7)=0
x=7 or x=-7
The answer is D.
Answer: D
Question: What time will be taken by an amount of Rs. 900 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
Options:
A)7
B)8
C)9
D)2
E)1
Rationale: Explanation:
P= Rs 900
Rate = 4.5*
SI= Rs 81
=> SI= Time*P*rate
calculating for rate,
=> Time= SI/rate*P
= 81/4.5%*900
=> 2 years
Thus, it will take 2 years to yield Rs 81.
ANSWER: D
Answer: D
Question: A rectangular table seats 6 people on each of two sides, with every person directly facing another person across the table. If 12 people choose their seats at random, what is probability that person P directly faces person Q?
Options:
A)1/13
B)1/12
C)1/11
D)1/10
E)1/9
Rationale: Person P will be seated somewhere at the table.
Each of the other 11 people has an equal chance of sitting opposite person P.
The probability that person Q sits across is 1/11.
The answer is C.
Answer: C
Question: If |x - 5| = 23 what is the sum of all the values of x.
Options:
A)46
B)10
C)56
D)-46
E)28
Rationale: There will be two cases
x-5 = 23 and x-5 = -23
Solve for x => x=23+5=> x=28 or x= -23 + 5 => x= -18
The sum of both values will be 28 + -18 = 10
Answer is B
Answer: B
Question: n is an integer chosen at random from the set
{5, 7, 9, 11 }
p is chosen at random from the set
{2, 6, 10, 14, 18}
What is the probability that n + p = 7 ?
Options:
A)0.1
B)0.2
C)0.25
D)0.05
E)0.4
Rationale: Set N: there is 4 ways to chose a number
Set P: there is 5 ways to chose a number
so total outcome is 4*5 = 20 which is represent 20 pairs of number
now we have 1 pairs can give us 7 which are (5,2) .
1/20 = 0.05
Answer D
Answer: D
Question: The letters of the word 'SERITI' are written in all possible orders and these words are written in alphabetical order. Then what is the rank of the word 'SERITI'
Options:
A)- 238
B)- 245
C)- 307
D)- 315
E)- 275
Rationale: Total Number of Words = 6!/2! = 360 [(number of characters)/(repeating group )!]
After S, we have T and E.
Number of words starting with T = 5!/2! = 60
Number of words starting with U = 5!/2! = 60
So any word starting with S will have rank < 360 - 60(for Us) - 60(for Ts) = 240
Only option A < 240, so Answer is A.
Answer: A
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
Options:
A)2/29
B)2/20
C)2/21
D)2/22
E)2/23
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³C₂/¹⁵C₂ = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = ²C₂/¹⁵C₂ = (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow = (³C₁ * ²C₁)/¹⁵C₂ = (2 * 3 * 2)/(15 * 14) = 2/35
Required probability = 1/35 + 1/105 + 2/35
= 3/35 + 1/105 = 1/35(3 + 1/3)
= 10/(3 * 35) = 2/21
Answer: C
Answer: C
Question: What is the smallest number which, when increased by 9, is divisible by 8, 11, and 24?
Options:
A)237
B)246
C)255
D)264
E)273
Rationale: LCM(8,11,24)=24x11=264
So the least divisible number is 264, and the number we are looking for is 264-9=255.
The answer is C.
Answer: C
Question: Dora walked 3 kilometers. She walked first 1.5 kilometers in 20 meter per sec and the rest 1.5 kilometers in 60 meter per sec. what is the average speed?
Options:
A)28m/s
B)30m/s
C)32m/s
D)34m/s
E)36m/s
Rationale: Since the distance traveled is same, we can apply direct formula= 2XS1XS2/(S1+S2)
2X20X60/80= 30. 'B' is the answer.
Answer: B
Question: There is a train and car. The ratio between the speed of a train & a car is 24:19 respectively. Also, a bus covered a distance of 320 km in 5 hours. The speed of the bus is 2/3rd of the speed of the train. How many kilometers will the car cover in 4 hours?
Options:
A)276
B)290
C)304
D)318
E)332
Rationale: The speed of the bus is 320/5 = 64 km/hr
The speed of the train is (64*3)/2 = 96 km/hr
The speed of the car is 96/24 * 19 = 76 km/hr
The distance covered by the car in 4 hours is 76 × 4 = 304 km
The answer is C.
Answer: C
Question: What is the probability that Jamie and Tom will get selected for a job they both applied for in a company, given that their chances of getting selected is 2/3 and 5/7 respectively?
Options:
A)13/25
B)2/5
C)9/20
D)11/20
E)10/21
Rationale: Explanation:
P(Jamie) = 2/3
P(Tom) = 5/7
E = {Jamie and Tom both get selected}
P(E) = P(Jamie)*P(Tom)
= 2/3 * 5/7
= 10/21
ANSWER: E
Answer: E
Question: What is the are of an equilateral triangle of side 16 cm?
Options:
A)64√5
B)64√9
C)44√3
D)64√3
E)14√3
Rationale: Area of an equilateral triangle = √3/4 S2
If S = 16, Area of triangle = √3/4 * 16 * 16 = 64√3 cm2;
Answer: D
Answer: D
Question: The edge of three cubes of metal is 3 dm, 4 dm and 5 dm. They are melted and formed into a single cube. Find the edge of the new cube?
Options:
A)15
B)7
C)9
D)6
E)3
Rationale: 33 + 43 + 53 = a3 => a
= 6
Answer:D
Answer: D
Question: An engine moves at the speed of 30 kmph without any coaches attached to it.Speed of the train reduces at the rate that varies directly as the square root of the number of coaches attached.When 9 coaches are attached speed decreases to 18 kmph. What will be the speed of train when 16 coaches are attached.
Options:
A)14
B)16
C)18
D)20
E)22
Rationale: 1.
No. of coaches =9
sqr root=3
speed decreases by 12
12=k*3
k=4
No. of coaches=16
swr root=4
decrease=4*4=16
New speed=30-16=14
A
Answer: A
Question: A husband and wife can complete a certain task in 1 and 2 hours respectively. Their children, Rae and Herman, can complete the same task in 4 and 5 hours, respectively. What is the ratio of the couple's time working together to complete the task to the children's time working together to complete the task?
Options:
A)a)15:46
B)b)3:10
C)c)12:23
D)d)5:18
E)e)10:3
Rationale: couples one hour work=1/1+1/2=3/2
so total time=2/3..
now, kids one hour work=1/4+1/5=9/20
so total time=20/9..
ratio=2/3:20/9=3/10
ans B
Answer: B
Question: Rs.2500 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.140. How much was lent at 5%?
Options:
A)2288
B)27669
C)1766
D)1000
E)2871
Rationale: (x*5*1)/100 + [(2500 - x)*6*1]/100 = 140
X = 1000
Answer: D
Answer: D
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at speed of 25 kmph. At what time will they meet?
Options:
A)9 a.m.
B)10 a.m.
C)10.30 a.m.
D)11 a.m.
E)None
Rationale: Sol.
Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20 x km.
Distance covered by B in (x-1) hours = 25(x-1) km.
∴ 20x + 25(x-1) = 110
⇔ 45x = 135
⇔ x = 3.
So, they meet at 10 a.m.
Answer B
Answer: B
Question: When positive integer A is divided by positive integer B, the result is 5.15. Which of the following could be the reminder when A is divided by B?
Options:
A) 2
B) 8
C) 7
D) 3
E) 5
Rationale: the remainder will be obtained from the decimal part when A is divided by B i.e. 0.15
0.15 = 15/100 = 3/20 so possible remainders are 3,6,12,9,15. Only option D-3 satisfies this
Ans - D
Answer: D
Question: In how many ways 8 different tickets W can be distributed between Jane and Bill if each is to receive any even number of tickets and all 8 tickets to be distributed.
Options:
A)From 2 to 6 inclusive.
B)From 98 to 102 inclusive.
C)From 122 to 126 inclusive.
D)From 128 to 132 inclusive.
E)From 196 to 200 inclusive.
Rationale: Possibilities
J 8 6 4 2 0
B 0 2 4 6 8
# of ways 8C8 8C6 8C4 8C2 8C0
W=1+28+70+28+1 = 128 Answer is D.
Answer: D
Question: How many pieces of 0.35 meteres can be cut from a rod 12.5 meteres long
Options:
A)30
B)40
C)35
D)60
E)70
Rationale: Explanation:
We need so simple divide 42.5/0.85,
=(1250/35) = 35
Option C
Answer: C
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
Options:
A)3/7
B)3/2.
C)3/88
D)3/8.
E)2/2.
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2.
Answer: B
Answer: B
Question: If 35 + 125 = 17.88, then what will be the value of 80 + 65 ?
Options:
A)13.41
B)20.46
C)21.66
D)22.35
E)23.25
Rationale: 35 + 125 = 17.88
35 + 25 x 5 = 17.88
35 + 55 = 17.88
85 = 17.88
5 = 2.235
80 + 65 = 16 x 5 + 65
= 45 + 65
= 105 = (10 x 2.235) = 22.35
Answer: Option D
Answer: D
Question: A rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing. If the poles of the fence are kept 5 metres apart, how many poles will be needed?
Options:
A)55
B)56
C)57
D)58
E)59
Rationale: Solution
Perimeter of the plot	= 2 ( 90 + 50 )
= 280 m.
Number of poles	= (280 / 5)
= 56 m.
Answer B
Answer: B
Question: If abc ≠2 and the sum of the reciprocals of a, b, and c equals the reciprocal of the product of a, b, and c, then a =
Options:
A)(1 + bc)/(b + c)
B)(1 – bc)/(b + c)
C)(1 + b + c)/(bc)
D)(1 – b – c)/(bc)
E)(1 – b – c)/(b + c)
Rationale: Answer is A though it took me around 4 minutes to get that.
Answer: A
Question: If (5^7)(9^4)=3(15^x), what is the value of x?
Options:
A) 7
B) 9
C) 11
D) 13
E) 15
Rationale: (5^7)(9^4)=3(15^x)
=> 5^7 * 3^8 = 3 * 3^x * 5^x
=> 5^7 * 3^8 = 3^(x+1) * 5^x
Value of x = 7
Answer A
Answer: A
Question: How many words, with or without meaning, can be formed using all letters of the word EQUATION using each letter exactly once?
Options:
A)38,320
B)39,320
C)40,320
D)38,400
E)39,400
Rationale: The Word EQUATION has exactly 8 letters which are all different.
Therefore the number of words that can be formed = Number of permutations of 8 letters taken all at a time.
= P (8, 8) = 8!
= 8 × 7 x 6 × 5 x 4 x 3 x 2 × 1
= 40,320
ANSWER:C
Answer: C
Question: 325 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees
Options:
A)13
B)12
C)14
D)16
E)18
Rationale: 26 trees have 25 gaps between them,
Required distance (325/25) = 13
A
Answer: A