divelab/Sys2Bench huggingface dataset:
Question: A bag contains 4red, 6blue and 3green balls. If 3 balls are picked at random, what is the probability that both are BLUE?
Options:
A)11/144
B)12/455
C)10/143
D)11/125
E)14/368
Rationale: P(Both are red),
=6C3/13C3
=10/143
C
Answer: C
Question: A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 400. Find the total worth of the stock?
Options:
A)20070
B)20000
C)20029
D)29087
E)27028
Rationale: Let the total worth of the stock be Rs. x.
The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50
The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50
Total SP = 11x/50 + 38x/50 = 49x/50
Overall loss = x - 49x/50 = x/50
x/50 = 400 => x = 20000
Answer: B
Answer: B
Question: From the given equation find the value of x: x² − 3x + 2
Options:
A)3
B)2
C)5
D)6
E)7
Rationale: (x − 1)(x − 2)
x = 1 or 2.
C
Answer: C
Question: It takes nine 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)13.58
B)13.87
C)14.24
D)14.59
E)14.85
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*9) = 1/540 of the video per second.
The combined rate is 1/15 + 1/540 = 37/540 of the video per second.
The time required to load the video is 540/37 = 14.59 seconds.
The answer is D.
Answer: D
Question: Four people are on an elevator that stops at exactly 4 floors. What is the probability that exactly one person will push the button for each floor?
Options:
A)4!/4^4
B)4^4/4!
C)4/4!
D)4/4^4
E)1/4^4
Rationale: Each person out of 4 has 4 options, hence total # of outcomes is 4^4;
Favorable outcomes will be 4!, which is # of ways to assign 4 different buttons to 4 people
So basically # of arrangements of 4 distinct objects: 4!.
P=favorable/total=4!/4^4
Answer: A.
Answer: A
Question: A man cycling along the road noticed that every 15 minutes a bus overtakes him and every 5 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?
Options:
A)5 minutes
B)6 minutes
C)8 minutes
D)9 minutes
E)15/2 minutes
Rationale: Let's say the distance between the buses is d. We want to determine Interval=\frac{d}{b}, where b is the speed of bus.
Let the speed of cyclist be c.
Every 15 minutes a bus overtakes cyclist: \frac{d}{b-c}=15, d=15b-15c;
Every 5 minutes cyclist meets an oncoming bus: \frac{d}{b+c}=4, d=4b+4c;
d=15b-15c=5b+5c, --> b=2c, --> d=15b-15b/2=15b/2.
Interval=\frac{d}{b}=\frac{15/2b}{b}=15/2
Answer: E (15/2 minutes).
Answer: E
Question: The first three terms of an infinite sequence are 2, 7, and 22. After the first term, each consecutive term can be obtained by multiplying the previous term by 3 and then adding 1. What is the sum of the tens digit and the units digit of the 51st term in the sequence?
Options:
A)9
B)8
C)7
D)6
E)4
Rationale: Following the rule of Infinite sequence we obtain the terms of the sequence as mentioned below
02,07,22,67, 202, 607, 1822, 5467...
Observe the last two digits of the sequence which have the cyclicity of4and the last two digits repeat in the order {02, 07, 22, 67}
Also 51st Term =6*8 +3
i.e. 51th Terms will have same Last two digits as 3rd term of the sequence = 22
i.e. Sum of lat two digits of 35th Term = 2+2 = 4
E
Answer: E
Question: A boy has twelve trousers and 17 shirts. In how many different ways can he select a trouser and a shirt?
Options:
A)299
B)278
C)204
D)108
E)271
Rationale: The boy can select one trouser in twelve ways.
The boy can select one shirt in 17 ways.
The number of ways in which he can select one trouser and one shirt is 12 * 17
= 204 ways.
Answer: C
Answer: C
Question: A fort had provision of food for 150 men for 50 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:
Options:
A)29	1/5
B)37	1/4
C)42
D)54
E)48
Rationale: we have food for 150 men for 50 days.
After 10 days food left for 150 men for 40 days.
so
150 : 40
now we have 125 men and x days
125 : 150 :: 40 : x
x = (150*40)/125 = 48 days.
ANSWER:E
Answer: E
Question: A contractor undertakes to do a piece of work in 40 days. He engages 100 men at the begining and 100 more after 35 days and completes the work in stipulated time. If he had not engaged the additional men, how many days behind schedule would it be finished?
Options:
A)2
B)5
C)6
D)8
E)9
Rationale: Explanation:
\inline \fn_jvn [(100\times 35)+(200\times 5)] men can finish the work in 1 day
\inline \fn_jvn \therefore 4500 men can finish the work in 1 day. 100 men can finish it in \inline \fn_jvn \frac{4500}{100} = 45 days.
This is 5 days behind Schedule
Answer: B) 5
Answer: B
Question: There are n arithmetic means between 3 and 45 such that the sum of these arithmetic means is 552. find the value of n.
Options:
A)11
B)15
C)17
D)21
E)23
Rationale: Arithmetic mean = 552/ n = 1/2( 3 +45 ) , = 24
n = 552/24 =23
ANSWER:E
Answer: E
Question: Find the simple interest on $6000 at 15% per annum for 9 months?
Options:
A)$492
B)$512
C)$675
D)$745
E)$1020
Rationale: P = $6000
R = 15%
T = 9/12 YEARS = 3/4 YEARS
S.I. = P*R*T/100 = 6000*15*3/400 = $675
Answer is C
Answer: C
Question: If 2x + y = 7 and x + 2y = 5, then xy/3 =
Options:
A) 1
B) 4/3
C) 17/5
D) 18/5
E) 4
Rationale: 2*(x+2y = 5) equals 2x+4y=10
2x+4y=10
- 2x + y= 7
= 3y=3
Therefore Y = 1
Plug and solve...
2x + 1 = 7
2x=6
x=3
xy/3= 3*1/3
=1
A
Answer: A
Question: The average (arithmetic mean) of four distinct positive integers is 10. If the average of the smaller two of these four integers is 12, which of the following represents the maximum possible value of the largest integer?
Options:
A)4
B)16
C)12
D)8
E)1
Rationale: Let the distinct number be A,B,C, and D
Its given A > B > C > D
also A + B + C + D =40 and A + B = 12 means C + D = 28
Since the question ask for the largest possible number we should choose the least value for A and B,C. So D should be 16. If D=16 then C = 12 > A,B <12
Answer : B
Answer: B
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 22, the how old is B?
Options:
A)7
B)9
C)8
D)11
E)10
Rationale: Explanation:
Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 22
⇒ 5x = 20
⇒ x = 4.
Hence, B's age = 2x = 8 years.
Answer: C
Answer: C
Question: Village X has a population of 72000, which is decreasing at the rate of 1200 per year. Village Y has a population of 42000, which is increasing at the rate of 800 per year .in how many years will the population of the two villages be equal?
Options:
A)15
B)19
C)11
D)18
E)13
Rationale: Let the population of two villages be equal after p years
Then, 72000-1200p=42000+800p
2000p=30000
p=15
Answer is A.
Answer: A
Question: There are some 2 wheelers and 4 wheelers parked total number of wheels present is 240 then how many 4 wheelers were there
Options:
A)20
B)30
C)40
D)50
E)60
Rationale: 2x+4x=240;
x=40;
then two whl=2*40=80
4 whl =4*40=160;
ans: 160/4= i-e 40
ANSWER:C
Answer: C
Question: Express 50 mps in kmph?
Options:
A)172
B)160
C)150
D)180
E)120
Rationale: 25 * 18/5 = 180 kmph
Answer:D
Answer: D
Question: (112 x 54) = ?
Options:
A)60000
B)70000
C)80000
D)88000
E)None
Rationale: (112 x 54) = 112 x 10 4	=	112 x 104	=	1120000	= 70000
2	24	16
B)
Answer: B
Question: If PENCIL is coded as 45 and TRASH is coded as 36, then MEMORY is coded as
Options:
A)33
B)59
C)60
D)72
E)None
Rationale: PENCIL= 16+5+14+3+9+12=59 i.e 5*9=45
TRASH= 20+18+1+19+8=66 i.e 6*6=36
MEMORY 13+5+13+15+18+25=89 8*9=72
ANSWER:D
Answer: D
Question: 3889 + 14.952 - ? = 3854.002
Options:
A)47.95
B)49.95
C)45.97
D)47.59
E)45.79
Rationale: Let 3889 + 14.952 - x = 3854.002.
Then x = (3889 + 14.952) - 3854.002
= 3903.952 - 3854.002
= 49.95.
Answer is B
Answer: B
Question: In May, the grounds keeper at Spring Lake Golf Club built a circular green with an area of 36π square feet. In August, he doubled the distance from the center of the green to the edge of the green. What is the total area of the renovated green?
Options:
A)100PI
B)144PI
C)70
D)80
E)90
Rationale: AREA OF CIRCLE 36PI SQ FEET =PI R^2 THEREFORE R =6
NOW GREEN RADI DOUBLED I.E R =12 AREA =144 PI
B
Answer: B
Question: In a 800 m race around a stadium having the circumference of 200 m, the top runner meets the last runner on the 5th minute of the race. If the top runner runs at twice the speed of the last runner, what is the time taken by the top runner to finish the race ?
Options:
A)20 min
B)15 min
C)10 min
D)5 min
E)None of these
Rationale: After 5 minutes (before meeting), the top runner covers 2 rounds i.e., 400 m and the last runner covers 1 round
i.e., 200 m.
∴ Top runner covers 800 m race in 10 minutes.
Answer C
Answer: C
Question: A man sells a horse for Rs.1000 and loses something, if he had sold it for Rs.1090, his gain would have been double the former loss. Find the cost price of the horse?
Options:
A)1080
B)1040
C)1070
D)1030
E)1060
Rationale: CP = SP + 1CP = SP - g
1000 + x = 1090 - 2x
3x = 90 => x = 30
CP = 1000 + 30 = 1030
Answer: D
Answer: D
Question: If x=1/4, which expression has the greatest value?
Options:
A)x^(1/3)
B)x^(1/2)
C)1/(2x)
D)x/.03
E)x^(-3)
Rationale: Options A and B are both less than 1.
Option C: 1/(2(1/4)) = 4/2 = 2
Option D: (1/4) / 0.03 = 1/0.12 = 8.333...
Option E: (1/4)^(-3) = 4^3 = 64
The answer is E.
Answer: E
Question: The speed of a boat in still water is 50kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
Options:
A)kmph
B)kmph
C)kmph
D)kmph
E)kmph
Rationale: Speed downstream = 50 + 20 =70 kmph
Speed upstream = 50 - 20 = 30 kmph
Answer:B
Answer: B
Question: In an election, candidate Smith won 52% of the total vote in Counties A and Q. He won 61% of the vote in County A. If the ratio of people who voted in County Q to County B is 3:1, what percent of the vote did candidate Smith win in County Q ?
Options:
A)A.25%
B)B.27%
C)C.34%
D)D.43%
E)E.49%
Rationale: (61%)*3x + (y%)*x = (52%)*4x
y = 25% of County Q
hence answer is A.
Answer: A
Question: Find the face value of 8 in 8213456
Options:
A)8000
B)80
C)8
D)800
E)80000
Rationale: Face value is the value of digit itself
face value of 8 = 8
Answer : C
Answer: C
Question: If (a – b) is 13 more than (c + d) and (a + b) is 3 less than (c – d), then (a – c) is:
Options:
A)6
B)2
C)3
D)4
E)5
Rationale: (a – b) – (c + d) = 13 and (c – d) – (a + b) = 3
=> (a – c) – (b + d) = 13 and (c – a) – (b + d) = 3
=> (b + d) = (a – c) – 13 and (b + d) = (c – a) – 3
=> (a – c) – 13 = (c – a) – 3 => 2(a – c) = 10 => (a – c) = 5
ANSWER:E
Answer: E
Question: The price of a T.V. set worth Rs. 20000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
Options:
A)A)19009
B)B)19074
C)C)19008
D)D)19000
E)E)19002
Rationale: Explanation:
Money paid in cash = Rs. 1000
Balance payment = (20000 - 1000) = Rs. 19000
Answer: Option D
Answer: D
Question: What is the remainder when the infinite sum (1!)² + (2!)² + (3!)² + ··· is divided by 1152?
Options:
A)12
B)41
C)152
D)802
E)None
Rationale: Explanation :
We have to find out the remainder when (1!)² + (2!)² + (3!)² + ··· is divided by 1152
1152 = 27 * 32
=> (6!)2 is divisble by 1152
=> All (n!)2 are divisible by 1152 as long as n > 5
So, our problem is now reduced to
Rem [((1!)² + (2!)² + (3!)² + (4!)² + (5!)²)/1152]
= Rem[(1 + 4 + 36 +576 + 14400) / 1152]
= Rem [15017/1152]
= 41
Answer : B
Answer: B
Question: A shopkeeper bought 600 oranges and 400 bananas. He found 15% of oranges and 7% of bananas were rotten. Find the percentage of fruits in good condition?
Options:
A)92.5%
B)88.2%
C)85.2%
D)96.8%
E)78.9%
Rationale: Total number of fruits shopkeeper bought = 600 + 400 = 1000
Number of rotten oranges = 15% of 600
= 15/100 × 600
= 9000/100
= 90
Number of rotten bananas = 7% of 400
= 28
Therefore, total number of rotten fruits = 90 + 28= 118
Therefore Number of fruits in good condition = 1000 - 118 = 882
Therefore Percentage of fruits in good condition = (882/1000 × 100)%
= (88200/1000)%
= 88.2%
Answer:B
Answer: B
Question: If a class of 10 students has four men, how many ways can the men and women be arranged in a circle so that no two men sit next to each other?
Options:
A)5!4!
B)5!5!
C)4!3!
D)10!
E)10!/5!
Rationale: for no two men to sit together, either all are in even or odd position
fix one at any one position then rest three can be fixed in 3! ways...
also rest four position of women can be fixed in 4!..
total ways 4!3!
C
Answer: C
Question: A cask initially contains pure alcohol up to the brim. The cask can be emptied by removing exactly 5 liters at a time . Each time this is done, the cask must be filled back to the brim with water. The capacity of the cask is 15 liters. When the cask is completely emptied and filled back to the brim two times, what is the ratio of alcohol to water in the cask
Options:
A)4/5
B)3/5
C)4/6
D)3/6
E)2/6
Rationale: You are given that the initial quantity of the cask is 15 l. So for the changing of the liquids,
The first time you remove 5 l of pure alcohol---> 10 l of alcohol remaining and you add 5 l of water. Ratio of alcohol in the remaining mixture = 10/(10+5) = 10/15 =2/3, similarly water = 1/3.
The second time you remove 5 l of the mixture having alcohol = 5*2/3 = 10/3 --> remaining alcohol = 10-10/3 =20/3
Similarly, the amount of water removed = 5*1/3=5/3 ---> remaining water = 5-5/3=10/3 but you also add 5 l more of water --> total water now = 5+10/3 = 25/3
Finally, ratio asked = 20/3 / 25/3 = 20/25 = 4/5
A is the correct answer.
Answer: A
Question: The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places?
Options:
A)720
B)144
C)120
D)36
E)204
Rationale: The word MEADOWS has 7 letters of which 3 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.
Hence the total ways are 24 * 6 = 144.
ANSWER:B
Answer: B
Question: Train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. The length of train P is three-fourths the length of train Q. What is the ratio of the speed of train P to that of train Q?
Options:
A)15 : 8
B)14 : 8
C)17 : 8
D)13 : 8
E)12 : 8
Rationale: A
15 : 8
Given that train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds.
Let the length of train P be LP and that of train Q be LQ
given that LP = 3/4 LQ
As the train P and Q crosses the pole in 30 seconds and 75 seconds respectively,
=> Speed of train P = VP = LP/30
Speed of train Q = VQ = LQ/75
LP = 3/4 LQ
=> VP = 3/4 LQ/(30) = LQ/40
Ratio of their speeds = VP : VQ
= LQ/40 : LQ/75 => 1/40 : 1/75 = 15 : 8
Answer: A
Question: A man can swim in still water at 6 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
Options:
A)1.7
B)1.9
C)1.1
D)2
E)1.2
Rationale: M = 6
S = x
DS = 6 + x
US = 6 - x
6 + x = (6 - x)2
6 + x = 12 -2x
3x = 12-6=6
x = 2
Answer:D
Answer: D
Question: Convert 300 miles into km?
Options:
A)360km
B)480km
C)510km
D)320km
E)500km
Rationale: 1 mile = 1.6 km approximately
300mile = 300*1.6 = 480km
Answer is B
Answer: B
Question: What number continues the sequence?
25, 50, 27, 46, 31, 38, 39, ?
Options:
A)21
B)22
C)23
D)24
E)25
Rationale: B
22
There are two alternate sequences, the first increases by 2, 4, 8 etc and the second decreases by 4, 8, 16 etc.
Answer: B
Question: If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions uses all four of the digits 1, 2, 3, and 4, what is the greatest number of four-digit extensions that the company can have?
Options:
A)4
B)6
C)12
D)16
E)24
Rationale: Since the phone number must be even, the unit's digit can be either 2 or 4.
When the unit's digit is 2 --> number of possibilities is 3! = 6
When the unit's digit is 4 --> number of possibilities is 3! = 6
Largest number of extensions = 6 + 6 =12
Answer:C
Answer: C
Question: A couple spent $198 in total while dining out and paid this amount using a credit card. The $198 figure included a 20 percent tip which was paid on top of the price which already included a sales tax of 10 percent on top of the price of the food. What was the actual price of the food before tax and tip?
Options:
A)$130
B)$140
C)$150
D)$160
E)$170
Rationale: Let the price of the meal be x.
After a 10% sales tax addition, the price is 1.1*x
After a 20% tip on this amount, the total is 1.2*1.1*x = 1.32x
1.32x = 198
x = $150
The correct answer is C.
Answer: C
Question: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
Options:
A)5 kmph
B)7 kmph
C)9 kmph
D)8 kmph
E)1 kmph
Rationale: Speed downstream = d/t = 85/(2 1/2) = 34 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (34 - 18)/2 = 8 kmph
Answer:D
Answer: D
Question: T is the set of all positive integers x such that x^2 is a multiple of both 27 and 375. Which of the following integers must be a divisor of every integer x in T?
I. 9
II. 15
III. 27
Options:
A)I only
B)II only
C)I and II only
D)I and III only
E)I, II, and III
Rationale: Solution:
T->{x} where x^2 is a multiple of both 27 and 375 means 3^3 and (5^3)*3
means x must contain 3^2 and 5^2
so with these conditions we know that 9=3^2 and 15=3*5 both have required factors for the divisibility of lowest int for x which is 9*25
but 27 is not a divisor because it can't divide 9*25 fully.
so Ans : C
Answer: C
Question: Four different children have jelly beans: Aaron has 5, Bianca has 7, Callie has 8, and Dante has 19. How many jelly beans must Dante give to Aaron to ensure that no child has more than 1 fewer jelly beans than any other child?
Options:
A) 2
B) 3
C) 4
D) 5
E) 7
Rationale: Since Bianca and Callie are both within 1 jelly bean of each other and Aaron has 5, Dante must provide 3 of his 19 jelly beans so each child has no more than 1 fewer jelly bean than any other child.
Dante + Aaron = 19+5 =24/2 = 12
19-2 = 7 so Dante must provide 3 jelly beans to Aaron.
Answer (E)
Answer: E
Question: 3 buffaloes eat as much as 4 cows or 2 oxen. At a farm there are 15 buffaloes, 8 oxen and 24 cows. The fodder for these cattle is available for 24days. If 8 more cows & 9 more buffaloes are brought in, how long will the fodder last?
Options:
A)16
B)15
C)17
D)18
E)21
Rationale: Sol. 2 oxen = 3 buffaloes = 4 cows 8 oxen = 16 cows and 15 buffaloes = 20 cows 16 cows + 20 cows + 24 cows = 60 cows Since fodder is available for 60 cows for 24 days
So fodder will be available for (60 + 8 + 12) = 80 cows c 24x60 .0 .
for-^—=18 days.
D
Answer: D
Question: Four bells begin to toll together respectively at the intervals of 8, 10, 12 and 16 seconds. After how many seconds will they toll together again?
Options:
A)246 seconds
B)242 seconds
C)240 seconds
D)243 seconds
E)253 seconds
Rationale: LCM of 8,10,12 and 16 is
240
LCM=240
ANSWER:C
Answer: C
Question: The hypotenuse of a right triangle is 2 centimeters more than the longer side of the triangle. The shorter side of the triangle is 7 centimeters less than the longer side. Find the length of the hypotenuse.
Options:
A)17
B)18
C)19
D)20
E)21
Rationale: Let a and b be the two sides of the triangle such that a is longer than b. The statement "the hypotenuse of a right triangle is 2 centimeters more than the longer side of the triangle" may be fomulated by
h = a + 2 or a = h - 2
The statement "the shorter side of the triangle is 7 centimeters less than the longer side" may be formulated .
b = a - 7 or b = (h - 2) - 7 = h - 9
We now use Pythagora's theorem to write a third equation
h 2 = a 2 + b 2
Substitute a by h - 2 and b by h - 9 in the above equation to obtain an equation in one variable only.
h 2 = (h - 2) 2 + (h - 9) 2
Simplify and rewrite the above equation in standard form.
h 2 -22 h + 85 = 0
Solve for h.
h = 5 and h = 17.
Only the solution h = 17 gives a and b positive and it is the length of the hypotenuse of the triangle.
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.800 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?
Options:
A)3999
B)10000
C)2500
D)2772
E)2912
Rationale: A:B:C = 2/3:1/6:1/6 = 4:1:1
x * 2/100 * 2/3 = 800
B capital = 60000*1/6 = 10000.Answer: B
Answer: B
Question: A train 250 m long is running at a speed of 27 km/hr. In what time will it pass a bridge 200 m long?
Options:
A)40
B)45
C)50
D)55
E)60
Rationale: Speed = 27 * 5/18 = 15/2 m/sec
Total distance covered = 250 + 200 = 450 m
Required time = 450 * 2/15 = 60 sec
Answer: E
Answer: E
Question: A work which could be finished in 9 days was finished 3 days earlier after 10 more men joined. The number of men employed was?
Options:
A)24
B)27
C)20
D)35
E)25
Rationale: C
20
x ------- 9
(x + 10) ---- 6
x * 9 = (x + 10)6
x = 20
Answer: C
Question: How many hours are there in 1200 minutes?
Options:
A)10
B)20
C)85
D)86
E)88
Rationale: We know that there are 60 minutes in 1 hour.Divide the number of minutes by the number of minutes in 1 hour. We get, divide 1200 by 601200 ÷ 60 = 20
So there are 20 hours in 1200 minutes.
ANSWER IS B
Answer: B
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
Options:
A)11
B)20
C)99
D)77
E)18
Rationale: 900 ---- 180
100 ---- ? => 20%
Answer: B
Answer: B
Question: Of the 75 cars on a car lot, 45 have air-conditioning, 35 have power steering, and 12 have both air-conditioning and power steering. How many of the cars on the lot have neither air-conditioning nor power steering?
Options:
A) 7
B) 8
C) 10
D) 15
E) 18
Rationale: Total -Neither = All Air Conditioning + All Power steering - Both
or 75 - Neither = 45 + 35 -12 = 68.
=> Neither = 7, hence A.
Answer : A
Answer: A
Question: When n liters of fuel was added to a tank that was already 1/3 full, the tank was filled to 7/3 of its capacity. In terms of n, what is the capacity of the tank, in liters?
Options:
A)1/2 n
B)4/3 n
C)3/2 n
D)9/4 n
E)7/3n
Rationale: A is the answer.
To solve this problem, draw diagram or use algebra. I'm more comfortable with algebra.
Given
- tank was already 1/3 full.
- When n ltr added, it became 7/3
So 1/3 + n = 7/3
n = 7/3 - 1/3
n = 6/3
capacity of the tank is full fraction . i.e. 1 i.e. 3/3
so the question is 3/3 is how much times n
= 3/3 = 1 = xn
so x = 3/6
and total = 3/6n=1/2n
Answer: A
Question: If r < y < -1, which of the following is true?
Options:
A)r/y > ry
B)y/r > r+y
C)y/r > ry
D)y/r < r+y
E)y/r > r/y
Rationale: Consider :
r= -3
y= -2
then put for every option. U'll get ans B.
Answer: B
Question: Find the value of 72518 x 9999 = m?
Options:
A)345434667
B)246465757
C)465767867
D)725107482
E)645354643
Rationale: 72518 x 9999 = 72518 x (10000 - 1)
= 72518 x 10000 - 72518 x 1
= 725180000 - 72518
= 725107482
D
Answer: D
Question: If the sides of a triangle are 26 cm, 18 cm and 10 cm, what is its area?
Options:
A)90
B)110
C)130
D)140
E)150
Rationale: The triangle with sides 26 cm, 18 cm and 10 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle = 1/2 * 18 * 10 = 90 cm2
Answer: Option A
Answer: A
Question: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
Options:
A)7 kmph
B)6 kmph
C)5 kmph
D)8 kmph
E)2 kmph
Rationale: Speed downstream = d/t = 85/(2 1/2) = 34 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (34 - 18)/2 = 8 kmph
Answer:D
Answer: D