divelab/Sys2Bench huggingface dataset:
Question: Set R has a mean of 11 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most?
Options:
A){15, 13}
B){11, 14}
C){10, 12}
D){14, 19}
E){14, 11}
Rationale: The lesser the variance( values closer to mean) ,lower the standard deviation. As discussed in question the mean is 11,the values (10,12) are closer than others.
Hence Answer : C
Answer: C
Question: There are 9 orators A, B, C, D, E, F, G,H and I. In how many ways can the arrangements be made so that A always comes before B and B always comes before C.
Options:
A)9! / 3!
B)8! / 6!
C)5! x 3!
D)8! / (5! x 3!)
E)8! / (5! x 4!)
Rationale: Select any three places for A, B and C. They need no arrangement amongst themselves as A would always come before B and B would always come before C.
The remaining 6 people have to be arranged in 6 places.
Thus, 9C3 x 6! = 9! / 3!
ANSWER:A
Answer: A
Question: A circular rim A having a diameter of 24 inches is rotating at the rate of x inches/min. Another circular rim B with a diameter of 30 inches is rotating at the rate of y inches/min. What is the value of y in terms of x, if both the rims reach their starting positions at the same time after every rotation.
Options:
A)5x/4
B)4x/3
C)6x/5
D)8x/7
E)9x/8
Rationale: t = S1/V1 = S2/V2
or, 24/x = 30/y
or, y = 30x/24 = 5x/4 (Answer A)
Answer: A
Question: What is the value of 1×1!+2×2!+3!×3!+............n×n!;where n! means n factorial or n(n−1)(n−2)...1
Options:
A)n(n−1)(n−1)!
B)n(n−1)(n−1)!
C)n(n−1)(n−1)!
D)(n+1)!−1!
E)None of these
Rationale: Explanation :
1×1!=(2−1)×1!=2×1!−1×1!=2!−1!2×2!=(3−1)×2!=3×2!−2!=3!−2!3×3!=(4−1)×3!=4×3!−3!=4!−3!......n×n!=(n+1−1)×n!=(n+1)(n!)−n!=(n+1)!−n!Summing up all these terms, we get (n+1)! - 1!
Answer : D
Answer: D
Question: Fortuner, the latest SUV by Toyota Motors, consumes diesel at the rate of 1400×[1000x+x]1400×[1000x+x] litres per km, when driven at the speed of xx km per hour. If the cost of diesel is Rs 35 per litre and the driver is paid at the rate of Rs 125 per hour then find the approximate optimal speed (in km per hour) of Fortuner that will minimize the total cost of the round trip of 800 kms?
Options:
A)30 km per hour
B)32 km per hour
C)49 km per hour
D)54 km per hour
E)65 km per hour
Rationale: Given that the diesel consumption is at the rate
1400×[1000x+x]1400×[1000x+x]
Cost of diesel = Rs 35 per litre
Payment to the driver = Rs 125 per hour.
Also given that the SUV is driven at the speed of xx km per hour.
Total cost (c)(c)
=1400×[1000x+x]×800×35+125×800x=1400×[1000x+x]×800×35+125×800x
=70000x+70x+100000x=70000x+70x+100000x
Now differentiating both sides in the above equation with respect to xx.
dcdx=−170,000x2+70=0dcdx=−170,000x2+70=0
⇒ x=49 km per hour.
C
Answer: C
Question: The ratio of two numbers is 3:4 and their sum is 21. The greater of the two numbers is?
Options:
A)12
B)14
C)16
D)17
E)19
Rationale: 3:4
Total parts = 7
= 7 parts --> 21 (7 Ã— 3 = 21)
= 1 part ---->3 (1 Ã— 3 = 4)
= The greater of the two number is = 4
= 4 parts ----> 12 (4 Ã— 3 = 12)
A
Answer: A
Question: A plane flies 880 km with the wind and 720 km against the wind in the same length of time. If the speed of the wind is 20 km/h, what is the speed of the plane in still air?
Options:
A)140 km/h
B)160 km/h
C)180 km/h
D)200 km/h
E)220 km/h
Rationale: The speed of the plane in still air = x km/h
The speed of the wind is 20 km/h
Speed with the wind = (x + 20) km/h
Speed against the wind = (x â€“ 20) km/h
Time = Distance/ Speed
880 / (x+20) = 720 / (x-20)
880(x-20) = 720(x+20)
88x - 1760 = 72x + 1440
16x = 3200
x = 200
Therefore, the speed of the plane in still air is 200 km/h.
The answer is D.
Answer: D
Question: Two trains, each 100 meters long, moving in opposite directions, completely pass each other in 24 seconds. If one train is moving twice as fast the other, then what is the speed of the faster train (in km/hr)?
Options:
A)12 km/hr
B)16 km/hr
C)20 km/hr
D)24 km/hr
E)28 km/hr
Rationale: Let the speed of the slower train be x m/s
Then, the speed of the faster train is 2x m/s
The relative speed is 3x m/s
(100 + 100)/24 = 3x
x = 25/9 m/s
So, the speed of the faster train is 50/9 = 50/9 * 18/5 = 20 km/hr
The answer is C.
Answer: C
Question: We can rent a cabin for x dollars per day for the first 5 days and then y dollars for each additional day. How much will it cost to rent a cabin for z days, where z>5?
Options:
A)5x + zy
B)5y+(z-5)x
C)xz + 5y
D)5x - z + y
E)5x+(z-5)y
Rationale: The first 5 days cost 5x.
The next (z-5) days cost (z-5)y.
The total cost is 5x+(z-5)y.
The answer is E.
Answer: E
Question: If 4a – 2b – 2c = 32 and √3a-√(2b+2c)=4, what is the value of a + b + c?
Options:
A)3
B)9
C)10
D)12
E)14
Rationale: when we look at the two equations, we can relize some similarity, so lets work on it..
3a – 2b – 2c = 32 can be written as √3a^2-√(2b+2c)^2=32
{√3a-√(2b+2c)}{√3a+√(2b+2c)}=32..
or 4*√3a+√(2b+2c)=32..
or √3a+√(2b+2c)=8..
now lets work on these two equations
1)√3a-√(2b+2c)=4..
2)√3a+√(2b+2c)=8..
A) add the two eq..
√3a+√(2b+2c)+√3a-√(2b+2c)=12..
2√3a=12..
or √3a=6..
3a=36..
a=12.
B) subtract 1 from 2..
√3a+√(2b+2c)-√3a+√(2b+2c)=4..
2√(2b+2c)=4..
√(2b+2c)=2..
2b+2c=4..
or b+c=2..
from A and B a+b+c=12+2=14..
D
Answer: D
Question: By selling a book for 290, 20% profit was earned. What is the cost price of the book?
Options:
A)A)215
B)B)241
C)C)230
D)D)235
E)E)240
Rationale: SP = 120% of CP; :. CP = 290 × 100/120 = 241
Option 'B'
Answer: B
Question: One year payment to the servant is Rs. 200 plus one shirt. The servant leaves after 9 months and receives Rs. 120 and a shirt.Then find the price of the shirt.
Options:
A)126
B)217
C)127
D)120
E)182
Rationale: 12 months == Rs 200 + shirt --(1)
9 months == Rs 120 + shirt --(2)
After subtracting equation (2) from (1) we get,(shirt is cancelled)
3 months = Rs 80
12 months = (80 × 12)/3= 320
Hence from equation (1) we get 320 = 200 + shirt
Therefore shirt = 120 Rs/-
Answer: D
Answer: D
Question: Three friends Ram, Rahul and Raj divide $1000 amongs them in such a way that if $1, $2 and $8 are removed from the sums that Ram, Rahul and Raj received respectively, then the share of the sums that they got will be in the ratio of 6 : 7 : 10. How much did Raj receive?
Options:
A)$434
B)$458
C)$438
D)$448
E)$478
Rationale: Explanatory Answer
Let the sums of money received by A, B and C be x, y and z respectively.
Then x - 1 : y - 2 : z -8 is 6a : 7a : 10a
When $1, $2 and $8 are removed, we are removing a total of $11 from $1000.
Therefore, 6a + 7a + 10a = 1000 - 11 = 989
i.e., 23a = 989
or a = 43
We know that z - 8 = 10a = 10 * 43 = 430
Therefore, z = 430 + 8 = $438
The correct choice is (c)
Answer: C
Question: What is the smallest possible common multiple of three integers, all larger than 22?
Options:
A)27.
B)54.
C)846.
D)19,656.
E)23
Rationale: The Least common positive multiple would be for the immediate least number(s) after 22 i.e 22.
Since nowhere is it stated that the three integers must be different, the integers could be 22,22 and 22... leading to least possible positive common multiple to be 22. Answer E.
Answer: E
Question: The annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years R in which the population would be doubled assuming there is no emigration or immigration is
Options:
A)20
B)R=25
C)R=30
D)R=35
E)40
Rationale: Suppose the population of the country in current year is 1000.
So annual increase is 1000 + 39.4 - 19.4=1020
Hence every year there is an increase of 2%.
2000= 1000(1+(2/100))^n
n=35 Answer is D.
Answer: D
Question: If Jan 1, 2006 was a Friday, What was the day of the week Jan 1, 2010?
Options:
A)Friday
B)Thursday
C)Tuesday
D)Saturday
E)Wednesday
Rationale: Explanation :
Given that Jan 1 2006 was a Friday
Number of odd days in the period 2006-2009
= 3 normal years + 1 leap year
= 3 x 1 + 1 x 2 = 5 (note that we have taken the complete year 2006 because the period in 2006 is from 01-Jan-2006 to 31-Dec-2006, which is the whole year 2006. Then the complete years 2007, 2008 and 2009 are also involved)
Hence Jan 1 2010 = (Friday + 5 odd days) = Wednesday.. Answer : Option E
Answer: E
Question: A 6-liter solution is 35% alcohol. How many liters of pure alcohol must be added to produce a solution that is 50% alcohol?
Options:
A)1.5
B)1.8
C)2.1
D)2.4
E)2.7
Rationale: Let x be the amount of pure alcohol required.
0.35(6) + x = 0.5(x+6)
0.5x = 3 - 2.1
x = 1.8 liters
The answer is B.
Answer: B
Question: At what rate of interest (compounded yearly)will Rs.10,000 amount to Rs.12100 in 2 years?
Options:
A)9%
B)11%
C)8%
D)10%
E)20%
Rationale: If rate=r, then 10000[1+(r/100)]^2 =12100 ,(100+r)^2 /100^2 =121
r^2 +200r -2100=0
(r-10)(r+210)=0
r=10
ANSWER:D
Answer: D
Question: A thief is spotted by a policeman from a distance of 160 meters. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 8km/hr and that of the policeman 10 km/hr, how far the thief will have run before he is overtaken?
Options:
A)350m
B)240m
C)440m
D)640m
E)None of them
Rationale: Relative speed of the policeman = (10-8) km/hr =2 km/hr.
Time taken by police man to cover
(160m/1000) x 1/2 hr = 2/25hr.
In 2/25 hr/s, the thief covers a distance of 8 x 2/25 km = 16/25 km = 640 m
Answer is D.
Answer: D
Question: A watch passes through three hands and each gains 25%. If the 3rd sells it for Rs250, what did the 1st pay for it?
Options:
A)110
B)120
C)128
D)134
E)154
Rationale: First Purchased = 250 Wes= 128
C
Answer: C
Question: A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
Options:
A)22
B)77
C)30
D)99
E)12
Rationale: US = 25
DS = 35
M = (35 + 25)/2 = 30
Answer: C
Answer: C
Question: ((1^5m)/(5^5m))((1^18)/(4^18)) = 1/(2(10)^35)
What is m?
Options:
A)7
B)18
C)34
D)35
E)36
Rationale: ((1^5m)/(5^5m))((1^18)/(4^18)) = 1/(2(10)^35)
((1/5)^5m ) * ((1/2)^36) = 1/ (2 * (2*5)^35))
2^36 will cancel out,since 1 can be written as 1^35 ,So (1/5)^5m= (1/5)^35
((1/5)^5m ) * ((1/2)^36) = 1/[(2^36)*(5^35)]
So, m=7
Answer A
Answer: A
Question: Mary's income is 40 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. What percent of Juan's income is Mary's income?
Options:
A) 124%
B) 120%
C) 96%
D) 80%
E) 84%
Rationale: Juan's income = 100 (assume);
Tim's income = 60 (40 percent less than Juan's income);
Mary's income = 84 (40 percent more than Tim's income).
Thus, Mary's income (84) is 84% of Juan's income (100).
Answer: E.
Answer: E
Question: What strength of 20 ml alcohol should be added to 10ml of 50% alcohol to get an average strength of 20% alcohol.
Options:
A)0.5 %
B)5 %
C)50 %
D)5.5 %
E)0.05 %
Rationale: 20*x + 10*0.5 = (20 + 10)*0.2 --> x = 0.05 = 5%.
Answer: B.
Answer: B
Question: In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:
Options:
A)2800
B)2700
C)2900
D)2200
E)2300
Rationale: B
Number of valid votes = 80% of 7500 = 6000.
Valid votes polled by other candidate = 45% of 6000
= (45/100 x 6000) = 2700.
Answer: B
Question: How much is 80% of 45 is greater than 4/5 of 25?
Options:
A)15
B)57
C)16
D)16
E)73
Rationale: (80/100) * 45 â€“ (4/5) * 25
36 - 20 = 16
Answer: C
Answer: C
Question: A gets 3 times as much money as B gets, B gets only Rs.25 more then what C gets. The three gets Rs.695 in all. Find the share of B?
Options:
A)130
B)120
C)218
D)144
E)145
Rationale: A+B+C = 695
A = 3B
3B+B+B-25 = 695
5B = 720
B = 144
Answer: D
Answer: D
Question: A train having a length of 240 m passes a post in 24 seconds. How long will it take to pass a platform having a length of 630 m?
Options:
A)120 sec
B)99 sec
C)89 sec
D)87 sec
E)85 sec
Rationale: Explanation:
v = 240/24 (where v is the speed of the train) = 10 m/s
t = (240+630)/10 = 87 seconds
Answer: Option D
Answer: D
Question: In the coordinate plane, a circle centered on point (-3, 4) passes through point (1, 1). What is the area of the circle?
Options:
A)9π
B)18π
C)25π
D)37π
E)41π
Rationale: r^2=(-3-1)^2+(4-1)^2=16+9=25
Area of circle=πr^2=25π
Answer : C
Answer: C
Question: A coin is tossed two times. What is the probability that there is at the least one tail?
Options:
A)3/4
B)1/3
C)3/7
D)3/5
E)1/31
Rationale: Let P(T) be the probability of getting least one tail when the coin is tossed two times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/4 ; P(T) = 1 - 1/4
= 3/4
Answer: A
Answer: A
Question: Two-third of a positive number and 144/216 of its reciprocal are equal. The number is:
Options:
A)5/12
B)12/5
C)25/144
D)144/25
E)1
Rationale: Let the number be x. Then,
2/3 x = 144/216 * 1/x
x2 = 144/216 * 3/2 = 144/144
x = 1
ANSWER:E
Answer: E
Question: A son and father goes for boating in river upstream . After rowing for 1 mile son notices the hat of his father falling in the river. After 5 min he tells his father that his hat has fallen. So they turn round and are able to pick the hat at the point from where they began boating after 5min. Find the speed of river in miles/hours ?
Options:
A)7 mile/hr
B)6 mile/hr
C)8 mile/hr
D)1 mile/hr
E)2 mile/hr
Rationale: Explanation:
Let the speed of river and boat be 'r' m/min and 'b' m/min.
so relative speed in upstream (b-r)m/min and in downstream (b+r)m/min.
Now in upstream distnce covered in 5 min is 5(b-r)miles
so total distnce covered => 1 + 5(b-r)miles in upstream
In downstream distance covered in 5min is 5(b+r)miles
Now 1 + 5(b-r) = 5(b+r)
1+5b-5r = 5b+5r
1 = 10r
r = 1/10 mile/min => 6 mile/hr.
Answer: B
Answer: B
Question: The balance of a trader weighs 20% less than it should. Still the trader marks up his goods to get an overall profit of 30%. What is the mark up on the cost price?
Options:
A)4%
B)8%
C)25%
D)16.66%
E)9%
Rationale: The most natural way to deal with 'weights' questions is by assuming values.
Say the trader's balance shows 100 gms. It is actually 80 gms because it weighs 20% less. Say, the cost price is $80 ($1/gm). Since he gets a profit of 30%, the selling price must be 80+(30/100)*80 = $104
Since the cost price is actually supposed to be $100 (for 100 gms) and the selling price is $104, the mark up is simply 4%.
Ans : A
Answer: A
Question: A bullet train 140 m long is running at 60 kmph. In how much time will it pass a platform 310 m long?
Options:
A)34 Seconds
B)22 Seconds
C)41 Seconds
D)24 Seconds
E)27 Seconds
Rationale: 27 Seconds
Distance travelled = 140 + 310m = 450m
Speed = 60 * 5/8 = 50/3m
Time = 450 * 3/50 = 27 Seconds
ANSWER E
Answer: E
Question: If a and b are integers and (2^a)(3^b) is a factor of 180^40, what is the largest possible value of ab?
Options:
A)2a
B)5a
C)20a
D)40a
E)80a
Rationale: (2^a)(3^b) is a factor of 180^40
We need to find the largest possible value of ab.
We know that 180 = 2^2*5^1*3^2
Therefore 180^40 will have 2 powers of 3 in it.
Hence in (2^a)(3^b), b has to 2
Therefore value of ab = 2a
Correct Option: A
Answer: A
Question: Weight of M, D and I is 74. Sum of D and I is 46 greater than M. I is 60% less than D. What is D's weight.
Options:
A)22
B)10
C)88
D)26
E)18
Rationale: M + D + I = 74 - - - (1)
(D + I) - M = 46 - - - (2)
I = 410410 D ⇒⇒ 5I = 2D ⇒⇒ I = 2D/5 - - - (3)
Adding (1) and (2) we get 2D + 2I = 120
Substituting the value of I in the above equation,
2D+2(2D5)=1202D+2(2D5)=120
⇒⇒ 14D = 600
⇒⇒ D = 300/7 = 42.8
Ans:B
Answer: B
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
Options:
A)10 km/hr
B)50 km/hr
C)14 km/hr
D)17 km/hr
E)77 km/hr
Rationale: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.
Answer: B
Answer: B
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)177
B)166
C)350
D)198
E)161
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: One fourth of one third of two fifth of a number is 15. What will be the 40% of that number is?
Options:
A)120
B)130
C)150
D)180
E)250
Rationale: (1/4) * (1/3) * (2/5) * x = 15 then x = 15 * 30 = 450
40% of 450 = 180
ANSWER D
Answer: D
Question: In a restaurant, the profit is 110% of the cost. If the cost increases by 12% but the selling price remains constant, approximately what percentage of the selling price is the profit?
Options:
A)30%
B)47%
C)90%
D)100%
E)None of these
Rationale: Explanation :
Let C.P.= Rs. 100. Then, Profit = Rs. 110, S.P. = Rs. 210.
New C.P. = 112% of Rs. 100 = Rs. 112
New S.P. = Rs. 210.
Profit = Rs. (210 - 112) = Rs. 98.
Required percentage = (98 /210 *100) % = 47 % appox
Answer : B
Answer: B
Question: A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f(x) at x = 10 ?
Options:
A)-119
B)-159
C)-110
D)-180
E)-105
Rationale: Explanation :
Let, the quadratic equation be ax2 + bx + c. So, f(x) = ax2 + bx + c
At x = 0, the value of function is 1.
x = 0, f(x) = 1
ax2 + bx + c = a * 0 + b * 0 + c = c
c = 1.
At x = 1, f(x) = 3
x = 1, f(x) = 3
a *1 + b * 1 + c = 3
Since c = 1, a + b = 2.
Also, we know that f(x) is maximum when x = 1. If f(x) is maximum, (dx/dt)(f(x)) = 0
Differentiating f(x), we have d/dt (ax2 + bx + c) = 2ax + b
At x = 1, 2ax + b = 0.
2a + b = 0.
b = -2a.
Substituting we have a + b = 2, or a + -2a = 2. a = -2. So, b = 4.
So the equation is -2x2 + 4x + 1.
At x = 10, the value is -2 * 100 + 4 * 10 + 1 i.e -159.
Answer : B
Answer: B
Question: A began a business with Rs. 85,000. He was joined afterwards by B with Ks. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1 ?
Options:
A)4 months
B)5 months
C)6 months
D)8 months
E)7 months
Rationale: Suppose B joined for x months . Then, ( 85000 * 12 )/(42500 * x) = 3. or x = (85000 * 12) / (42500 * 3) = 8.
So, B joined for 8 months.Answer: D
Answer: D
Question: Potato chips are on sale, buy 2 get 1 free. There are only 9 bags of chips left (4 plain and 5 bbq). A shopper randomly grabs 3 bags. What is the probability the shopper will grab exactly 3 bags of bbq chips?
Options:
A)2/3
B)1/3
C)1/5
D)5/42
E)7/42
Rationale: Combination Probability Formula: nCr = n!/[r!(n-r)!]
Total possible, select 3 bags from 9 bags = 9C3 = 9!/[3!(9 - 3)!] = 84.
To have 3 bbq there must be 0 plain, select 0 plain from 4 = 4C0 = 1.
And, select 3 bbq from 5 = 5C3 = 10.
3 bbq and 0 plain = (1)(10) = 10
Probability = (number outcomes favorable)/(total number outcomes) = 10/84 = 5/42
Answer: D
Answer: D
Question: A train 180 m long passed a pole in 3 sec. How long will it take to pass a platform 330 m long?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Speed = 180/3
= 60 m/sec.
Required time
= (180 + 300)/60
= 8 sec.
Answer:D
Answer: D
Question: The average temperature of Monday, Tuesday, Wednesday and Thursday was 38∘ and that of Tuesday, Wednesday, Thursday and Friday was 40∘. If the temperature on Monday was 32∘, the temperature of Friday was :
Options:
A)40∘
B)39∘
C)38∘
D)30∘
E)None of these
Rationale: Explanation:
M+T+W+Th=(4×38)=152
Monday temperature is 32. So T+W+Th=(152-32)=120
T+W+Th+F=(4×40)=160
F = (160-120)=40∘
Correct Option: A
Answer: A
Question: The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is?
Options:
A)0.5909
B)0.5904
C)0.5902
D)0.5907
E)0.5901
Rationale: P(winning prize atleast on one ticket)
= 1 - P("Losing on all tickets")
= 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)
= (1.64)(0.36) = 0.5904
Answer:B
Answer: B
Question: 18 beavers, working together in a constant pace, can build a dam in 12 hours. How many hours will it take 12 beavers that work at the same pace, to build the same dam?
Options:
A)2.
B)4.
C)5.
D)6
E)18.
Rationale: Total Work = 18*12= 216 Beaver hours
12 Beaver * x =216Beaver hours
x=216 / 12=18
ANSWER:E
Answer: E
Question: The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
Options:
A)299
B)266
C)299
D)750
E)261
Rationale: Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 25 è x = 25 * 60 / 2 = 750
Answer: D
Answer: D
Question: A train running at the speed of 60 km/hr crosses a pole in 36 seconds. What is the length of the train?
Options:
A)186 m
B)176 m
C)100 m
D)600 m
E)765 m
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train
= (Speed x Time) = (50/3 * 36) m
= 600 m.
Answer: D
Answer: D
Question: What is the measure of the angle Y made by the diagonals of the any adjacent sides of a cube.
Options:
A)30
B)45
C)60
D)75
E)90
Rationale: C.. 60 degrees
All the diagonals are equal. If we take 3 touching sides and connect their diagonals, we form an equilateral Triangle. Therefore, each angle would be 60.C
Answer: C
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 40 years now, the son's age five years back was:
Options:
A)A)15
B)B)67
C)C)56
D)D)89
E)E)34
Rationale: Let the son's present age be x years. Then, (40 - x) = x
2x = 40.
x = 20.
Son's age 5 years back (20 - 5) = 15 years.
Answer:A
Answer: A
Question: If the average of w, b, c, 14 and 15 is 12. What is the average value of w, b, c and 29
Options:
A)12
B)13
C)14
D)15
E)16
Rationale: w+b+c+14+15 = 12*5 = 60
=>w+b+c = 60-29 = 31
w+b+c+29 = 31+29= 60
Average = 60/4 = 15
Answer D
Answer: D
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
Options:
A)120 m
B)240 m
C)300 m
D)500 m
E)550 m
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x = 240 m.
ANSWER 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, 4, 10, 14, 18}
What is the probability that n + p = 13 ?
Options:
A)0.15
B)0.2
C)0.25
D)0.3
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 3 pairs can give us 13 which are (7,6), (9,4) and (11,2) .
3/20 = 0.15
Answer A
Answer: A
Question: A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 3,000 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?
Options:
A)6.28%
B)7.14%
C)7.86%
D)8.25%
E)8.63%
Rationale: The amount of sodium chloride is 0.05*10,000 = 500 gallons
500/7000 = 1/14 which is about 7.14%
The answer is B.
Answer: B
Question: At a dinner party every two guests used a bowl of rice between them, every three guests used a bowl of dal between them and every four used a bowl of meat between them. There were altogether 65 dishes. How many guests were present at the party ?
Options:
A)60
B)65
C)90
D)95
E)None of these
Rationale: no. of rice bowl=x
no. of dal bowl=y
no. of meat bowl=z
then, x+y+z=65(eq 1)
also, 2x=3y=4z
substituting value of y&z in terms of x in eq 1, x=30.
as 1 rice bowl is shared between 2 guests, therefore there are 60 guests...
ANSWER:A
Answer: A