divelab/Sys2Bench huggingface dataset:
Question: A bullet train 130 m long is running with a speed of 50 kmph. In what time will it pass a man who is running at 10 kmph in the direction opposite to that in which the bullet train is going?
Options:
A)23 sec
B)13 sec
C)12 sec
D)11 sec
E)16 sec
Rationale: B
13 sec
Speed of the bullet train relative to man = (50 + 10) kmph
= 60*5/18 m/sec = 30/3 m/sec.
Time taken by the bullet train to cross the man = Time taken by it to cover 130 m at (30/3) m / sec
= (130*3/30) sec = 13 sec
Answer: B
Question: A book is bought for $60 and sold for $78. What is the profit in percentage?
Options:
A)10
B)20
C)30
D)40
E)50
Rationale: 78/60 = 1.3
The answer is C.
Answer: C
Question: Two bullet trains of equal lengths take 10 seconds and 50 seconds respectively to cross a telegraph post. If the length of each bullet train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
Options:
A)13 sec.
B)15 sec.
C)12 sec.
D)17 sec.
E)16.7 sec.
Rationale: Speed of the first bullet train = 120/10 m/sec = 12 m/sec.
Speed of the second bullet train = 120/50 m/sec = 2.4 m/sec.
Relative speed = (12 + 2.4) = 14.4 m/sec.
Required time = (120 + 120)/14.4 sec = 16.7 sec.
E
Answer: E
Question: Convert 30miles into yards?
Options:
A)25630 yards
B)35200 yards
C)52800 yards
D)42560 yards
E)41520 yards
Rationale: 1 mile = 1760 yards
30 miles = 30*1760 = 52800 yards
Answer is C
Answer: C
Question: x varies inversely as square of y. Given that y = 2 for x = 1. The value of x for y = 6 will be equal to?
Options:
A)1/5
B)1/8
C)1/3
D)1/9
E)1/2
Rationale: Given x = k/y2, where k is a constant.
Now, y = 2 and x = 1 gives k = 4.
x = 4/y2 => x = 4/62, when
y = 6 => x = 4/36 = 1/9.
Answer: D
Answer: D
Question: Frank the Fencemaker needs to fence in a rectangular yard. He fences in the entire yard, except for one full side of the yard, which equals 40 feet. The yard has an area of 320 square feet. How many feet offence does Frank use?
Options:
A)14
B)47
C)54
D)56
E)240
Rationale: Area = Length x Breadth
320 = 40 x Breadth
So, Breadth = 8 Units
Fencing required is -
Breadth + Breadth + Length
8 + 8 + 40 => 56 feet
Answer must be (D) 56
Answer: D
Question: There are 39 distinct numbers in set M, there are 28 distinct numbers in set N, and there are 12 distinct numbers that are in both sets M and N. Set H is the set containing the elements that are in at least one of sets M and N. How many elements are in set H?
Options:
A)39
B)40
C)55
D)58
E)63
Rationale: {Total} = {M} + {N} - {Both}
{Total} = 39 + 28 - 12 = 55.
Answer: C.
Answer: C
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:
Options:
A)18 km/hr
B)26 km/hr
C)36 km/hr
D)42 km/hr
E)52 km/hr
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12
--> 2x = 20
--> x = 10.
--> Speed of each train = 10 m/sec = 10 x 18/5 km/hr = 36 km/hr.
Answer : C.
Answer: C
Question: What is the present worth of Rs. 143 due in 2 years at 5% simple interest per annum?
Options:
A)288
B)266
C)120
D)277
E)130
Rationale: Let the present worth be Rs. x. Then,
S.I. = (143 - x)
(x * 5 * 2) / 100 = (143 - x)
10x = 14300 - 100x
110x = 14300 => x = 130.
Answer: E
Answer: E
Question: A and B started a business jointly A's investment was thrice the investment of B and the period of his investment was two times the period of investment of B. If B received Rs. 4000 as profit, then their total profit is ?
Options:
A)28029
B)28000
C)28001
D)28012
E)28129
Rationale: Suppose B invested Rs. x for y months. Then, A invested Rs. 3x for 2y months.
So, A : B = (3x * 2y) : (x * y) = 6xy : xy = 6 : 1.
B's profit : Total profit = 1 : 7.
Let the total profit be Rs. x Then, 1/7 = 4000/x or x = 28000.
Answer: B
Answer: B
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
Options:
A)140
B)149
C)148
D)17
E)143
Rationale: Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 10 units
Area of the rectangle = lb = 14 * 10 = 140 sq.units
Answer: Option A
Answer: A
Question: Pipe A can fill a tank in 6 hours. Due to a leak at the bottom, it takes 9 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
Options:
A)16 hours
B)15 hours
C)18 hours
D)17 hours
E)None of these
Rationale: Explanation:
Let the leak can empty the full tank in x hours 1/6 - 1/x = 1/9
=> 1/x = 1/6 - 1/9 = (3 - 2)/18 = 1/18
=> x = 18.
ANSWER IS C
Answer: C
Question: Today is Thursday. I came home from a trip 3 days before the day after last Monday. How many days have I been home?
Options:
A)1 day
B)2 days
C)7 days
D)6 days
E)10 days
Rationale: D
6 days
The day after last Monday was Tuesday. If I came home 3 days before that, I came home on Saturday, Sunday, Monday, Tuesday, Wednesday, and Thursday = 6 days.
Answer: D
Question: In a right angled triangle, two sides are consecutive whole number in which one side is hypotenuse. what could be the possible length of third side?
Options:
A)360
B)361
C)362
D)363
E)364
Rationale: (x+1)--> hypotenuse
x--> base
h--> height
x^2 + h^2 = (x+1)^2
x^2 + h^2 = x^2 + 1 + 2x
h^2 = 1 + 2x
now put the value given in the option in place of h,
the value of h that give the whole no. value of x is the right answer
i.e 361
ANSWER:B
Answer: B
Question: A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?
Options:
A)4
B)6
C)7
D)8
E)2
Rationale: 45*12 : 54*x = 2: 1
x = 5
12 -5 = 7
Answer: C
Answer: C
Question: Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers?
Options:
A)8
B)9
C)7
D)5
E)4
Rationale: Explanation:
x â€“ y = 5
4x â€“ 6y = 6
x = 12 y = 7
Answer:C
Answer: C
Question: If two integers x, y (x>y) are selected from -10 to 11 (inclusive), how many possible cases are there?
Options:
A)150
B)180
C)190
D)210
E)231
Rationale: If two integers x, y (x>y) are selected from -10 to 9 (inclusive), how many possible cases are there?
A. 150
B. 180
C. 190
D. 210
E. 240
--> 22C2=22*21/2=231. Therefore, the answer is E.
Answer: E
Question: A 49 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
Options:
A)12
B)20
C)88
D)77
E)14
Rationale: 1: 2/5 = 5: 2
2/7 * 49 = 14
Answer: E
Answer: E
Question: Ayush was born two years after his father's marriage. His mother is five years younger than his father but 25 years older than Ayush who is 10 years old. At what age did the father get married ?
Options:
A)28years
B)29years
C)30years
D)31years
E)32years
Rationale: Explanation:
Ayush's present age = 10 years.
His mother's present age = (10 + 25) years = 35 years.
Ayush's father's present age = (35+ 5) years = 40 years.
Ayush's father's age at the time of Ayush's birth = (40 - 10) years = 30 years.
Therefore Ayush's father's age at the time of marriage = (30 - 2) years = 28 years.
Answer: A) 28 year
Answer: A
Question: 1, 6, 24, 60, 120, 210, ___ ?
Options:
A)336
B)366
C)330
D)660
E)770
Rationale: it follow the pattern like this..
2^3-2=6
3^3-3=24
4^3-4=60
5^3-5=120
6^3-6=210 so...
7^3-7=336
ANSWER:A
Answer: A
Question: What will be the remainder when (67^67) + 67 is divided by 68?
Options:
A)52
B)62
C)66
D)68
E)72
Rationale: x^n + 1 will be divisible by x+1 only when n is odd
67^67+1 will be divisible by 67+1
(67^67+1)+66, when divided by 68 will give 66 as remainder
Answer is C
Answer: C
Question: What is the present worth of Rs. 132 due in 2 years at 5% simple interest per annum
Options:
A)110
B)120
C)130
D)140
E)150
Rationale: Explanation:
Let the present worth be Rs.x
Then,S.I.= Rs.(132 - x)
=› (x*5*2/100) = 132 - x
=› 10x = 13200 - 100x
=› 110x = 13200
x= 120
Option B
Answer: B
Question: A speaks the truth in 75% of cases and B in 80% of cases. In what percent of cases are they likely to contradict each other in narrating the same event?
Options:
A)0.225
B)0.37
C)0.32
D)0.35
E)0.55
Rationale: Different possible cases of contradiction occurs when A speaks the truth and B does not speak the truth or A does not speak the truth and B speaks the truth.
(3/4 x 1/5) + (1/4 x 1/5) = 7/20 = 35%
= 0.35
ANSWER:D
Answer: D
Question: if a@b = a * b^(1/2) then 2@4 = ?
self made
Options:
A)4
B)6
C)3
D)8
E)4
Rationale: 2* (4)^1/2= 2*2= 4
A is the answer
Answer: A
Question: If a is an integer greater than 7 but less than 25 and b is an integer greater than 34 but less than 44, what is the range of a/b?
Options:
A)21/34
B)1/12
C)15/64
D)17/35
E)7/6
Rationale: The way to approach this problem is 7<a<25 and 34<b<41
Minimum possible value of a is 8 and maximum is 24
Minimum possible value of b is 35 and maximum is 40
Range = max a/min b - min a/max b
(Highest - lowest)
24/35 - 8/40 = 17/35
Hence D
Answer: D
Question: Simplify: 0.05 * 0.05 * 0.05 + 0.04 * 0.04 * 0.04/ 0.05 * 0.05 – 0.05 * 0.04 + 0.04 * 0.04
Options:
A)0.06
B)0.09
C)0.07
D)0.04
E)0.05
Rationale: Given expression = (a^3 + b^3) / (a^2 – ab + b^2), where a = 0.05 , b = 0.04
= (a +b ) = (0.05 +0.04 ) =0.09
Answer is B.
Answer: B
Question: {140, 270, 250, n}
Which of the following could be the median of the 4 integers listed above?
I. 170
II. 210
III. 240
Options:
A)I only
B)II only
C)I and II only
D)II and III only
E)I, II, and III
Rationale: If 170 is the median, (n+250) / 2 = 170. Then n = 90. But n < 140, so 170 can not be the median.
If 210 is the median, (n+250) / 2 = 210. Then n = 170. Thus 210 can be the median.
If 240 is the median, (n+250) / 2 = 240. Then n = 230. Thus 240 can be the median.
The answer is D.
Answer: D
Question: A, B and C completed a piece of work, A worked for 6 days, B for 9 days and C for 4 days. Their daily wages were in the ratio of 3:4:5. Find the daily wages of C, if their total earning was Rs.1702?
Options:
A)s.109
B)s.115
C)s.100
D)s.103
E)s.102
Rationale: 3x 4x 5x
6 9 4
18x + 36x + 20x = 1702
74x = 1702 => x = 23
5x = 115 Rs.
Answer:B
Answer: B
Question: A man whose speed is 4 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1 kmph, find his average speed for the total journey ?
Options:
A)1 kmph
B)5 kmph
C)6 kmph
D)3.75 kmph
E)7 kmph
Rationale: Explanation:
Speed of Man = 4 kmph
Speed of stream = 1 kmph
Speed in DownStream = 5 kmph
Speed in UpStream = 3 kmph
Average Speed = (2 x 5 x 3)/8 = 3.75 kmph.
Answer: D
Answer: D
Question: 15 lts are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more lts of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16,What is the capacity of the container W?
Options:
A)A:45
B)B:25
C)C:37.5
D)D:36
E)E:42
Rationale: If you have a 37.5 liter capacity, you start with 37.5 L of A and 0 L of B.
1st Replacement
After the first replacement you have 37.5-15=22.5 L of A and 15 L of B. The key is figuring out how many liters of A and B, respectively, are contained in the next 15 liters of mixture to be removed.
The current ratio of A to total mixture is 22.5/37.5; expressed as a fraction this becomes (45/2) / (75/2), or 45/2 * 2/75. Canceling the 2s and factoring out a 5 leaves the ratio as 9/15. Note, no need to reduce further as we're trying to figure out the amount of A and B in 15 L of solution. 9/15 of A means there must be 6/15 of B.
Multiply each respective ratio by 15 to get 9 L of A and 6 L of B in the next 15L removal.
Final Replacement
The next 15L removal means 9 liters of A and 6 liters of B are removed and replaced with 15 liters of B. 22.5-9=13.5 liters of A. 15 liters of B - 6 liters + 15 more liters = 24 liters of B.
Test to the see if the final ratio = 9/16; 13.5/24 = (27/2) * (1/24) = 9/16. Choice C is correct.
Answer: C
Question: What amount does Kiran get if he invests Rs.8000 at 10% p.a. compound interest for two years, compounding done annually?
Options:
A)3388
B)2177
C)2877
D)1678
E)9680
Rationale: A= P{1 + R/100}n
=> 8000{1 + 10/100}2 = Rs.9680
Answer: E
Answer: E
Question: There is a box full of fruits,
all but two are grapes,
all but two are apples,
and all but two are oranges.
How many fruits are in the box ?
Options:
A)5 fruits
B)8 fruits
C)4 fruits
D)2 fruits
E)3 fruits
Rationale: E
There are 3 fruits (1 grapes, 1 apples, and 1 oranges).
Answer: E
Question: If the sides of a cube are in the ratio 5:4. What is the ratio of their diagonals?
Options:
A)4:3
B)5:4
C)4:7
D)3:4
E)4:5
Rationale: Explanation:
Diagonal of a Cube=a√3 where a is side
a1:a2 = 5:4
d1:d2 = 5:4 where√3 cancelled both side
ANSWER:B
Answer: B
Question: Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
Options:
A)$ 345
B)$ 231
C)$ 145
D)$ 745
E)$ 245
Rationale: Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 145.
So after completing the 1st week she will get $ (x+145).
Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.
= $ (x + 145 + 145)
= $ (x + 290)
So in this way end of every week her salary will increase by $ 145
correct answer C
Answer: C
Question: The set S contains fractions a/b, where a and b are positive integers, which don’t share any prime factor. How many of these fractions have the following property: when both numerator and denominator are increased by 1, the value of fraction is increased by 10%?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: he fraction with 1 added to the numerator & denominator is 10% larger than the original. A 10% increase is equivalent to multiplying by the multiplier 1.1 or 11/10. Thus
a+1/b+1=11/10×a/b
Now, cross multiply
10ab + 10 b = 11ab + 11a
10 b = 1ab + 11a
Divide by b.
10=a+11 a/b
10−a/11=a/b
From here, it's obvious that b has to have a factor of 11 in it, so I just said: let b = 11. Then (10 - a) = a, so a = 5, and we get the fraction
a/b=5/11
When we add 1 to the numerator and denominator, we get 6/12 = 1/2, which is 10% greater than 5/11.
The question demands that x and y should have no common factors except 1, so they are co-prime. From that list only on pair is co-prime
.
ANSWER:B
Answer: B
Question: In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
Options:
A)77
B)44
C)77
D)54
E)66
Rationale: Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 8 = 4/9(T - 8)
10T = 792 - 352 => T = 44.
Answer:B
Answer: B
Question: Let x be a positive integer, what is the remainder when 3^(3x+3)+3 is divided by 3?
Options:
A)4
B)2
C)3
D)1
E)5
Rationale: For: (3^(3x+3)+3)/3
Let n = 3x + 3
3^n
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243, last digit pattern repeats 3, 9, 7, 1, 3, ....
Rule: x^(m+n) = (x^m)(x^n)
(3^(3x))(3^3)
Rule: x^(mn) = (x^m)^n
3^(3)(3^x)(3^3) => Now, (7)(3)(7) + 3 = (7) + 3 => Finally, 10/3 and remainder is 1.
Answer: D
Answer: D
Question: A cube has one of its faces painted half red and half white. The other faces are completely painted white. What is the ratio between the red painted areas and the white painted areas of the cube?
Options:
A)1:6
B)1:11
C)2:5
D)1:8
E)3:11
Rationale: Let x be the area of each face of the cube.
The area painted red is x/2
The area painted white is x/2 + 5x = 11x/2
The ratio of red to white is (x/2):(11x/2) which is 1:11.
The answer is B.
Answer: B
Question: 1,3,5,7,9,..50 find term of sequnce for this.
Options:
A)1356
B)1557
C)1688
D)1700
E)2500
Rationale: This is an arithmetic progression, and we can write down
a=1a=1 ,d=2d=2 , n=50n=50 .
We now use the formula, so that
Sn=12n(2a+(n−1)l)Sn=12n(2a+(n−1)l)
S50=12×50×(2×1+(50−1)×2)S50=12×50×(2×1+(50−1)×2)
=25×(2+49×2)=25×(2+49×2)
=25×(2+98)=25×(2+98)
=2500=2500 .
E
Answer: E
Question: If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is ?
Options:
A)4/16
B)4/15
C)4/19
D)4/13
E)4/11
Rationale: P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.
P(SᴜK) = 13/52 + 4/52 - 1/52 = 4/13
Answer: D
Answer: D
Question: For every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12)=2x4x6x8x10x12. What is the greatest prime factor of f(30)?
Options:
A)2
B)5
C)11
D)13
E)19
Rationale: f(30) = 2*4*6*8*10*12*14*16*18*20*22*24*26*28*30
The greatest prime factor in this list is 13.
The answer is D.
Answer: D
Question: On average, Machine A will produce a completed item once every two minutes, and Machine B will produce a completed item once every eleven minutes. The number of items Machine A produces in a 24-hour period is approximately what percent greater than the number of items Machine B would produce in that same period?
Options:
A)25%
B)333%
C)150%
D)450%
E)233%
Rationale: Machine A: 1 item in 2 minutes --> 1/2 items in 1 minute;
Machine B: 1 item in 11 minutes --> 1/11 items in 1 minute.
In the same time period, Machine A produces (1/2-1/11)/(1/11)*100=~450% more items than machine B.
Answer:D
Answer: D
Question: If 7 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?
Options:
A) -7
B) -4
C) -3
D) 1
E) -10
Rationale: The phrase “7 is one solution of the equation” means that one value of x is 7. Thus, we first must plug 7 for x into the given equation to determine the value of k. So we have
7^2 + (3)(7) + k = 10
49 + 21 + k = 10
70 + k = 10
k = -60
Next we plug -60 into the given equation for k and then solve for x.
x^2 + 3x – 60 = 10
x^2 + 3x – 70 = 0
(x+10)(x-7) = 0
x = -10 or x = 7
Thus, -10 is the other solution. Answer E.
Answer: E
Question: What is the greatest number of four digits which is divisible by 15, 25, 40 and 75 ?
Options:
A)9600
B)9800
C)9700
D)9620
E)9670
Rationale: Greatest number of four digits = 9999
LCM of 15, 25, 40 and 75 = 600
9999 Ã· 600 = 16, remainder = 399
Hence, greatest number of four digits which is divisible by 15, 25, 40 and 75
= 9999 - 399 = 9600
Answer: Option A
Answer: A
Question: A rectangular room has the rectangular shaped rug shown as above figure such that the rug’s area is 200 square feet and its length is 10 feet longer than its width. If the uniform width between the rug and room is 10 feet, what is the area of the region uncovered by the rug (shaded region), in square feet?
Options:
A)32
B)1360
C)1000
D)46
E)104
Rationale: Rug's area = 200
which is (x) x (10+x) = 200
so x= 10
rug maintains a uniform distance of 10 feet
so room has dimension 10+20 and 20+20 i.e. 30 and 40
area of room 30x40 = 1200
area covered is 200
so uncovered area is 1200-200=1000 (ANSWER C)
Answer: C
Question: When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 5. What is the smallest positive integer p, such that (n + p) is a multiple of 30?
Options:
A)1
B)2
C)4
D)19
E)20
Rationale: When positive integer n is divided by 5, the remainder is 1 i.e., n=5x+1
values of n can be one of {1, 6, 11, 16, 21, 26, 31.............46, 51, 56,61..................}
Similarly,
When n is divided by 7, the remainder is 5..i.e., n=7y+5
values of n can be one of {5, 12, 19, 26, 33, 40, 47, 54, 61........}
combining both the sets we get
n={19, 52, ...........}
What is the smallest positive integer p, such that (n + p) is a multiple of 30 or 30x
in case of n=26 p=4
C is the answer.
Answer: C
Question: Find the no.of ways of arranging the boy and 8 guests at a circular table so that the boy always sits in a particular seat?
Options:
A)3!
B)8!
C)11!
D)12!
E)14!
Rationale: Ans.(B)
Sol. Total number of persons = 9 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 8 places in 8P8 = 8! Ways ... The number of required arrangements = 8! x 1= 8! = 8! ways
Answer: B
Question: How many factors does 16^2 have?
Options:
A)2
B)8
C)4
D)25
E)26
Rationale: 36^2 = 6*6*6*6 = 2^4*3^4
Total factors = (4+1)*(4+1) = 2*2 =4
Answer C.
Answer: C
Question: 3,4,7,10,13,16,19,22,find 10th term in series
Options:
A)27
B)28
C)29
D)30
E)32
Rationale: 3
3*1=3+1=4
3*2=6+1=7
3*3=9+1=10
3*4=12+1=13
3*5=15+1=16
3*6=18+1=19
3*7=21+1=22
3*8=24+1=25
3*9=27+1=28
ANSWER:B
Answer: B
Question: In a function they are distributing noble prize. In how many ways can 4 prizes be distributed among 6 boys when a boy gets any no. of prizes?
Options:
A)1300
B)1590
C)1296
D)1290
E)80
Rationale: Ans.(C)
Sol. In this case, repetitions are allowed, so all the four prizes can be given in 6 ways, i.e. (6 x 6 x 6 x 6) ways = 64 ways = 1296 ways Or nr ways = 64 ways = 1296 ways
Answer: C
Question: Express a speed of 36 kmph in meters per second?
Options:
A)10 mps
B)05 mps
C)09 mps
D)12 mps
E)11 mps
Rationale: A
10 mps
36 * 5/18 = 10 mps
Answer: A
Question: How many shots of 1cm radius can be prepared from a sphere of 3cm radius?
Options:
A)36
B)64
C)27
D)16
E)9
Rationale: 4/3 π * 3 * 3 * 3 = 4/3 π * 1 * 1 * 1 * x
x = 27
ANSWER:C
Answer: C
Question: Which number should replace both the asterisks in (* /21) x (*/189) = 1 ?
Options:
A)21
B)63
C)3969
D)147
E)167
Rationale: Answer
Let (y/21) x (y/189) = 1
Then , y2 = 21 x 189 = 21 x 21 x 9
∴ y = (21 x 3) = 63 .
Option: B
Answer: B
Question: A = {2, 3, 5, 7, 19}
B = {2, 4, 6, 13}
Two integers will be randomly selected from sets A and B, one integer from set A and one from set B, and then multiplied together. How many different products can be obtained?
Options:
A)15
B)16
C)19
D)20
E)36
Rationale: By looking at Set A, we can see that it's all primes. Thus, we should immediately break down the elements in Set B to their prime factors. That gives :
Set A = {2,3,5,7,11}
Set B = {2, 2x2, 3x2, 13}
Apart from 2x3x2 (taking 2 from set A) which is the same as 3x2x2(taking 3 from set A); there is nothing which can be repeated. Thus, the total unique product = 20-1 = 36.
E
Answer: E
Question: If two numbers are in the ratio 2:3. If 9 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
Options:
A)A)12
B)B)18
C)C)20
D)D)24
E)E)26
Rationale: 2:3
2x + 9 : 3x + 9 = 3 : 4
4[2x + 9] = 3[3x + 9]
8x + 36 = 9x + 27
9x - 8x = 36 - 27
x = 9
Then smallest number is = 2
2x = 18
Correct Option B
Answer: B
Question: A certain car averages 25 miles per gallon of gasoline when driven in the city and 35 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)33
D)36
E)38
Rationale: 10*1/25 gpm+50*1/35 gpm=1.82 total gallons
60 total miles/1.82 total gallons=32.9 average mpg
C. 33
Answer: C
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 200 m in 18 sec. then find the speed of the train?
Options:
A)40/3 m/sec
B)37/3 m/sec
C)50/3 m/sec
D)41/3 m/sec
E)55/3 m/sec
Rationale: Length of the train be ‘X’
(X + 150)/15 = (X + 200)/18
6X + 900 = 5X + 1000
X = 100m
Speed = (100+150)/15 = 50/3 m/sec
Answer: C
Answer: C