divelab/Sys2Bench huggingface dataset:
Question: The vertices of a rectangle in the standard (x,y) coordinate place are (0,0), (0,4), (7,0) and (7,4). If a line through (3,3) partitions the interior of this rectangle into 2 regions that have equal areas, what is the slope of this line?
Options:
A)0
B)2/5
C)-2
D)1
E)7/4
Rationale: CONCEPT: The readers need to know that a rectangle can be divided into two equal area by a Straight line only when the straight line passes through the Centre of the Rectangle (Intersection of its two diagonals)Draw a figure and know it for yourself.
The point of Intersections of the diagonals will be the midpoint of any diagonal i.e. Midpoint of (0,0), and (7,4) OR Midpoint of (0,4) and (7,0)
i.e. Either [(0+7)/2, (0+4)/2] OR [(0+7)/2, (4+0)/2] =[3.5, 2]
Slope of line passing through points (3,3) and (3.5,2) = (2-3)/(3.5-3) = - 1/0.5= -2
C
Answer: C
Question: log√ 8 / log 8 is equal to
Options:
A)1/√8
B)1/4
C)1/2
D)1/8
E)None
Rationale: Solution
log√ 8 / log 8	= log(8)1/2 / log 8
= 1/ 2 log 8 /log 8
= 1/ 2.
Answer C
Answer: C
Question: Three positive integers a, b, and c are such that their average is 40 and a ≤ b ≤ c. If the median is (a + 13), what is the least possible value of c?
Options:
A)41
B)44
C)45
D)46
E)47
Rationale: Solution
Given Data
3 positive integers
Average of a, b, and c = 40.
So, a+b+c3a+b+c3 =120 or a + b + c = 120
a ≤ b ≤ c
Median = (a + 13)
Median of these 3 numbers a, b, and c is ‘b’ because a ≤ b ≤ c
Therefore, b = a + 13
Objective To find the least value of 'c'
Theoretically, the least value of c is when c = b.
Therefore, a + (a + 13) + (a + 13) = 120 (b and c are equal and b, the median, is a + 13)
Or 3a =94 or a = 31.33
So, b = c = 31.33 + 13 = 44.33
However, we know that these numbers are all integers.
Therefore, a, b, and c cannot take these values.
So, the least value for c with this constraint is NOT likely to be when c = b
Let us increment c by 1. Let c = (b + 1)
In this scenario, a + (a + 13) + (a + 14) = 120
Or 3a = 93 or a=31 The value of the numbers is an integer
If a = 31, b = 44 and c = 45.
The least value for c that satisfies all these conditions is 45.
Correct answer is choice C.
Answer: C
Question: The sum of two numbers is 22. Five times one number is equal to 6 times the other. The bigger of the two numbers is
Options:
A)10
B)12
C)14
D)15
E)60
Rationale: a:b 5:6
a+b=22
5x+6x=22
x=2
then two numbers are 10,12
ANSWER:B
Answer: B
Question: What is the difference between the local value of 3 and 2 in the number 2324?
Options:
A)430
B)377
C)280
D)277
E)112
Rationale: Explanation:
300 â€“ 20 = 280
Answer: C
Answer: C
Question: What type of switch is this?
Options:
A)2
B)7
C)6
D)8
E)9
Rationale: Answer:B
Answer: B
Question: What is 120% of 13/24 of 600?
Options:
A)320
B)390
C)440
D)480
E)510
Rationale: 120% * 13/24 * 360 = 1.2 * 13 * 25 = 390
The answer is B.
Answer: B
Question: How many integers between 100 and 150, inclusive, can be evenly
divided by neither 3 nor 5?
Options:
A)33
B)28
C)27
D)26
E)24
Rationale: Numbers divisible by 3 start from 102 and end at 150
so total numbers are (150-102)/3 + 1 = 17
Numbers divisible by 5 start from 100 and end at 150
So total numbers are (150-100)/5 + 1 = 11
Total Numbers divisible by 15 start from 105 and end at 150
So total numbers are (150-105)/15 + 1 = 4
So 17+11-4 = 24
Answer : E
Answer: E
Question: A square was given. Inside the square there are white tiles and black tiles. Black tiles was among the diagonal of the square and dimensions of both white as well as black tiles is 1cm x 1cm. If there are 81 black tiles in the square. Then find the no of white tiles in it.
Options:
A)2399
B)1600
C)2679
D)1697
E)1711
Rationale: In a square, number of squares on the diagonal is equal to the tiles on a single row. If there are even number of square on a side, then total squares on the diagonal is 2n - 1, otherwise 2n. As the total tiles on the diagonal are given as 81, then number of tiles on a side = 2n - 1 = 81 so n = 41.
So number of white tiles = 412−81=1681−81412−81=1681−81 = 1600
Answer:B
Answer: B
Question: (23341379 × 72) = ?
Options:
A)1223441288
B)2142579288
C)2142339288
D)2142339277
E)1680579288
Rationale: 23341379 × 72
= 23341379(70 + 2)
= (23341379 × 70) + (23341379 × 2)
= 1633896530 + 46682758
= 1680579288
Answer is E.
Answer: E
Question: If positive integer n is divisible by both 5 and 21, then n must be divisible by which of the following?
Options:
A)8
B)15
C)18
D)24
E)48
Rationale: A number divisible by both 5,21 is 105 which s divisible by 15.
IMO : Answer B 15
Answer: B
Question: The length of a rectangle is reduced by 25%. By what % would the width have to be increased to maintainthe original area?
Options:
A)15%
B)20%
C)25%
D)33%
E)40%
Rationale: Sol. Required change = (25*100)/(100-25)=25%
D
Answer: D
Question: Natasha climbs up a hill, and descends along the same way she went up. It takes her 3 hours to reach the top and 2 hours to come back down. If her average speed along the whole journey is 3 kilometers per hour, what was her average speed (in kilometers per hour) while climbing to the top?
Options:
A)1.5
B)2.5
C)3.75
D)5
E)7.5
Rationale: Lets assume distance to top as X, so the total distance travelled by Natasha = 2x
Total Time taken = 3+ 2 = 5 Hrs
Avg speed = Total Dist/Total time taken = 2x/5
Avg speed of complete journey is given as = 3 Hrs
2 x/5 = 3
X = 7.5 miles
Avg speed while climbing = Distance/Time = 7.5/3 = 2.5
Option B
Answer: B
Question: In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is?
Options:
A)1
B)6
C)5
D)6
E)8
Rationale: Let the duration of the flight be x hours. Then,
600/x - 600/(x + 1/2) = 200
x(2x + 1) = 3 2x2 + x - 3 = 0
(2x + 3)(x - 1) = 0
x = 1 hr.
Answer: A
Answer: A
Question: Half a number plus 5 is 15.What is the number?
Options:
A)8
B)20
C)10
D)11
E)12
Rationale: Let x be the number. Always replace "is" with an equal sign
(1/2)x + 5 = 15
(1/2)x = 15 - 5
(1/2)x = 10
x = 20
correct answer is B
Answer: B
Question: What is the probability of flipping a fair coin nine times and the coin landing on heads on at least two flips?
Options:
A)57/64
B)119/128
C)251/256
D)503/512
E)509/512
Rationale: The number of possible outcomes is 2^9=512.
0 heads: There is 1 way to have all tails.
1 head: There are 9 ways to have one head.
P(0 or 1 head)=10/512=5/256
P(at least 2 heads)=1 - 5/256 = 251/256
The answer is C.
Answer: C
Question: The sum of three consecutive even numbers is 48. Find the middle number of the three?
Options:
A)14
B)16
C)18
D)24
E)64
Rationale: Three consecutive even numbers (2P - 2), 2P, (2P + 2).
(2P - 2) + 2P + (2P + 2) = 48
6P = 48 => P = 8.
The middle number is: 8P = 64.
ANSWER:E
Answer: E
Question: The length of a rectangle is increased by 25% and its breadth is decreased by 20%. What is the effect on its area?
Options:
A)1000
B)888
C)2889
D)2888
E)2881
Rationale: 100 * 100 = 10000
125 * 80 = 10000
No change
Answer:A
Answer: A
Question: Find the fourth proportional to 2.4, 4.6 and 7.6?
Options:
A)14.56
B)14
C)15.34
D)16.2
E)17
Rationale: Formula = Fourth propotional = (b × c)/a
A = 2.4 , B = 4.6 and C = 7.6
(4.6 × 7.6)/2.4 = 14.56
A
Answer: A
Question: What is the greatest prime factor of 3^8 - 1?
Options:
A)29
B)31
C)37
D)41
E)43
Rationale: 3^8-1 = (3^4-1)(3^4+1) = 80*82 = 8*10*2*41
The answer is D.
Answer: D
Question: A man purchased 3 blankets @ Rs.100 each, 2 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets?
Options:
A)278
B)900
C)278
D)450
E)772
Rationale: 10 * 150 = 1500
3 * 100 + 2 * 150 = 600
1500 – 600= 900
Answer:B
Answer: B
Question: Five percent of a certain grass seed is timothy. If the amount of the mixture needed to plant one acre contains 2 pounds of timothy, how many acres can be planted with 960 pounds of the seed mixture?
Options:
A)6
B)12
C)20
D)24
E)120
Rationale: If the mixture contains 2 pounds of timothy, the mixture must be 40 pounds.
Thus we need 40 pounds of mixture per acre.
960 / 40 = 24 acres
The answer is D.
Answer: D
Question: The true discount on Rs.1600 due to after a certain of 5% per annum is Rs.160. The time after which it is due is
Options:
A)27 months
B)20 months
C)23 months
D)12 months
E)15 months
Rationale: P.W. = Rs. (1600 - 160) = Rs. 1440∴ S.I. on Rs.1440 at 5% is Rs. 160.∴ Time = [100 * 160 / 1440 * 5] = 20/9 years = [20/9 * 12] months = 27 months. Answer : A
Answer: A
Question: A student chose a number, multiplied it by 4, then subtracted 142 from the result and got 110. What was the number he chose?
Options:
A)58
B)59
C)60
D)62
E)63
Rationale: Let x be the number he chose, then
4⋅x−142=110
4x=252
x=63
correct answer E
Answer: E
Question: Ayesha's father was 31 years of age when she was born while her mother was 34 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
Options:
A)2 years
B)4 years
C)6 years
D)8 years
E)1 years
Rationale: Explanation:
Mother's age when Ayesha's brother was born = 34 years.
Father's age when Ayesha's brother was born = (31 + 4) years = 35 years.
Required difference = (35 - 34) years = 1 years.
Answer: E
Answer: E
Question: How many keystrokes are needed to type numbers from 1 to 100?
Options:
A)192
B)100
C)90
D)110
E)None of these
Rationale: Explanatory Answer
While typing numbers from 1 to 100, there are 9 single digit numbers: from 1 to 9.
Each of these numbers requires one keystroke.
That is 9 key strokes.
There are 90 two-digit numbers: from 10 to 99.
Each of these numbers requires 2 keystrokes.
Therefore, 180 keystrokes to type the 2-digit numbers.
100 is a three-digit number which requires 3 keystrokes.
Totally, therefore, one requires 9 + 180 + 3 = 192 keystrokes.
Choice A is the correct answer.
Answer: A
Question: The average waight of A,B,C is 45 Kg. The avg wgt of A & B be 40Kg & that of B,C be 43Kg. Find the wgt of B.
Options:
A)34Kg
B)40Kg
C)42Kg
D)41Kg
E)31Kg
Rationale: . Let A,B,c represent their individual wgts.
Then,
A+B+C=(45*3)Kg=135Kg
A+B=(40*2)Kg=80Kg & B+C=(43*2)Kg=86Kg
B=(A+B)+(B+C)-(A+B+C)
=(80+86-135)Kg
=31Kg.
Answer is E.
Answer: E
Question: Insert the missing number. 2, 7, 10, 22, 18, 37, 26, 52,
Options:
A)34
B)52
C)46
D)62
E)68
Rationale: Explanation :
There are two series here
2, 10, 18, 26, ... (Increase by 8)
7, 22, 37, 52 ... (Increase by 15)
Hence, next term is 26+8 = 34
Answer : Option A
Answer: A
Question: 2400÷20÷10=?
Options:
A)43
B)12
C)15
D)20
E)24
Rationale: 2400 ÷ 20 = 120
120 ÷ 10 = 12
Answer is B
Answer: B
Question: If a positive odd integer N has p positive factors, how many positive factors will 6N have ?
Options:
A)p
B)2p
C)P+1
D)2p+1
E)Cannot be determined
Rationale: I have added some extra text to make this question more GMAT-like:
Let's TEST some values of N
Try N = 3
The factors of 3 are {1, 3}. Here, p =2
So, 2N = (2)(3) = 6
The factors of 6 are {1, 2, 3, 6}. So, we have a total of4
Now check the answer choices:
A) p =2No good. We want an output of4. ELIMINATE
B) 2p = (2)(2) = 4. PERFECT! KEEP B
C) P+1 =2+ 1 = 3 No good. We want an output of4. ELIMINATE
D) 2p+1 = (2)(2) + 1 = 5 No good. We want an output of4. ELIMINATE
E) Cannot be determined. POSSIBLE. KEEP E
Let's TEST another value of N
Try N = 7
The factors of 7 are {1, 7}. Here, p =2
So, 2N = (2)(7) = 14
The factors of 14 are {1, 2, 7, 14}. So, we have a total of4
Now check the REMAINING answer choices:
B) 2p = (2)(2) =4. PERFECT! KEEP B
E) Cannot be determined. POSSIBLE. KEEP E
Let's TEST one more (non-prime) value of N
Try N = 9
The factors of 9 are {1, 3, 9}. Here, p =3
So, 2N = (2)(9) = 18
The factors of 18 are {1, 2, 3, 6, 9}. So, we have a total of6
Now check the REMAINING answer choices:
B) 2p = (2)(3) =6. PERFECT! KEEP B
E) Cannot be determined. POSSIBLE. KEEP E
At this point, it SEEMS LIKELY that the correct answer is A
Answer: A
Question: If x and y and z are two-digit integers such that x > 40, y<70, and z is > 80 and < 90, which of the following is closest to the maximum possible value of xyz ?
Options:
A) 700
B) 607,959
C) 4,000
D) 7,000
E) 28,000
Rationale: To get the maximum possible value of xyz, we need maximize the value of x,y, and z.
max x can be = 99 (given x is a two-digit integer > 40)
max y can be = 69 (given y is a two-digit integer < 70)
max z can be = 89 (given z is a two-digit integer > 80 and < 90)
xy = 99*69*89 = 607,959
Answer (B)
Answer: B
Question: A certain lab experiments with white and brown mice only. In one experiment, 2/3 of the mice are white. If there are 12 brown mice in the experiment, how many mice in total are in the experiment?
Options:
A)39
B)33
C)26
D)21
E)36
Rationale: Let total number of mice = M
Number of white mice = 2/3 M
Number of brown mice = 1/3 M = 12
=> M = 36
Answer E
Answer: E
Question: The total of company C's assets in 1994 was 150% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of company C's assets in in 1992 was N dollars, which one of the following represents company C's assets in 1994:
Options:
A)7N
B)8N
C)9N
D)12.5
E)20
Rationale: Let's use actual numbers. Starting in 1992, let's say company C had $100 in assets.
In 1993, the total assets were 400% GREATER, which means 1992 PLUS 400% of 1992:
$100 + 4x$100 = $100 + $400 =$500
In 1994, the total assets were 150% GREATER than they were in 1993, which means 1993 PLUS 150% of 1993:
$500 + 1.5x$500 = $1250
This is 12.5 times the 1992 number, so the correct answer is 12.5N.
D
Answer: D
Question: A money lender finds that due to a fall in the annual rate of interest from 8% to 7 3/4 % his yearly income diminishes by Rs. 61.50, his capital is?
Options:
A)24,609
B)24,607
C)24,600
D)24,638
E)24,602
Rationale: Let the capital be Rs. x. Then,
(x * 8 * 1)/100 - (x * 31/4 * 1/100) = 61.50
32x - 31x = 6150 * 4
x = 24,600.
Answer:C
Answer: C
Question: Using all the letters of the word "THURSDAY", how many different words can be formed?
Options:
A)8
B)8!
C)7!
D)6
E)2
Rationale: Total number of letters = 8
Using these letters the number of 8 letters words formed is
⁸P₈ = 8!.
Answer:B
Answer: B
Question: There are 15 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?
Options:
A)272
B)167
C)157
D)352
E)380
Rationale: The total number of stations = 17
From 17 stations we have to choose any two stations and the direction of travel (i.e., Hyderabad to Bangalore is different from Bangalore to Hyderabad) in 17P₂ ways.
17P₂ = 17 * 16
= 272.
Answer: A
Answer: A
Question: What is the perimeter of a triangle with sides 7 and 3 that has the maximum possible area?
Options:
A)10 + 3√7
B)10 + 3√3
C)10 + √58
D)10 + √71
E)10 + √83
Rationale: We can maximize the area of the triangle by making these two sides the base and the height of a right angle triangle. Then the third side is the hypotenuse with a length of √(49+9) = √58
The perimeter is 10 + √58
The answer is C.
Answer: C
Question: Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph,
he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1
P.M.?
Options:
A)9 km/hour
B)10 km/hour
C)11 km/hour
D)12 km/hour
E)None of these
Rationale: Explanation:
We need to calculate the distance, then we can calculate the Ɵme and finally our answer.
Lets solve this,
Let the distance travelled by x km
Time = Distance/Speed
x10−x15=2[because, 2 pm - 12 noon = 2
hours]3x−2x=60x=60.Time=DistanceSpeedTime@10km/hr=6010=6hours
So 2 P.M. - 6 = 8 A.M
Robert starts at 8 A.M.
He have to reach at 1 P.M. i.e, in 5 hours
So, Speed = 60/5 = 12 km/hr
Answer: D
Answer: D
Question: If x and y are positive integers greater than 1 such that x – y and x/y are both even integers, which of the following numbers must be non-prime integers?
I. x
II. x + y
III. y/x
Options:
A)I only
B)II only
C)III only
D)I and II
E)I, II and III
Rationale: x - y is an even integer: Therefore, for the equation to hold true, both x and y have to be even.
x/y is an even integer: Therefore, this implies that x has to be greater than y.
We can eliminate option III as y/x will never be an integer (Since x>y)
Statement I, x: x>y, hence x has to greater than 2 and even, therefore divisible by 2 and non-prime.
Statement II, x+y: x+y will be divisible by at least 2 since both x and y are even, hence the sum is non prime.
Thus, option D is the correct answer
Answer: D
Question: If x is an integer, which of the following is a possible value of Q=(x^2 +2x – 7)/9?
Options:
A)-2.4
B)0.268
C)1.166 repeating
D)4.555 repeating
E)8.125
Rationale: x is an integer, which of the following is a possible value of Q=(x^2 +2x – 7)/9?
Used process of elimination
A. -2.4
when this is multiplied by 9, x is not an integer
B. 0.268
when this is multiplied by 9, x is not an integer
C. 1.166 repeating
when this is multiplied by 9, x is not an integer
D. 4.555 repeating
E. 8.125
when this is multiplied by 9, x is not an integer
Answer choice D seems to fit.D
Answer: D
Question: In a partnership between A, B and C. A's capital is Rs.4000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?
Options:
A)9400
B)12798
C)26908
D)11750
E)22073
Rationale: 200 + 130 = 330
800 - 330 = 470
200 ---- 4000
470 ---- ? => 9400
Answer: A
Answer: A
Question: How many odd, positive divisors does 500 have?
Options:
A)6
B)5
C)12
D)15
E)24
Rationale: Make a prime factorization of a number: 540=2^2*3^3*5 --> get rid of powers of 2 as they give even factors --> you'll have 3^3*5 which has (3+1)(1+1)=5 factors.
Another example: 60=2^2*3*5 it has (2+1)(1+1)(1+1)=12 factors out of which (1+1)(1+1)=4 are odd: 1, 3, 5 and 15 the same # of odd factors as 60/2^2=15 has.
Answer: B.
Answer: B
Question: A vessel of capacity 3 litre has 25% of alcohol and another vessel of capacity 5 litre had 40% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. What is the new concentration of Mixture?
Options:
A)31%.
B)71%.
C)27.5%.
D)29%.
E)51%.
Rationale: 25% of 3 litres = 0.75 litres
40% of 5 litres = 2 litres
Therefore, total quantity of alcohol is 2.75 litres.
This mixture is in a 10 litre vessel. Hence, the concentration of alcohol in this 10 litre vessel is 27.5%
C
Answer: C
Question: A train consists of 12 boggies, each boggy 15 metres long. The train crosses a telegraph post in 18 seconds. Due to some problem, one boggies were detached. The train now crosses a telegraph post in
Options:
A)16.5 sec
B)12 sec
C)15 sec
D)20 sec
E)None of these
Rationale: Length of train = 12 Ã— 15 = 180 m.
Then, speed of train = 180â„18 = 10 m/s
Now, length of train = 11 Ã— 15 = 165m
âˆ´ Required time = 165â„10 = 16.5 sec.
Answer A
Answer: A
Question: The ratio of the ages of three people is 4:6:7. Eight years ago, the sum of their ages was 44. Find their present ages.
Options:
A)28,42,49
B)24,36,42
C)20, 30,35
D)16,24,28
E)12,18,21
Rationale: Let the present ages be 4x, 6x, 7x.
(4x-8) + (6x-8) + (7x-8) = 44
17x = 68
x = 4
Their present ages are 16, 24, and 28.
The answer is D.
Answer: D
Question: On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction W of the total distance did he cover while the sun was shining on him?
Options:
A)1/4
B)4/5
C)1/5
D)1/6
E)1/7
Rationale: If s is an integer and we know that the average speed is 2.8, s must be = 2. That meanss+1= 3. This implies that the ratio of time for s=2 is 1/4 of the total time. The formula for distance/rate is D=Rt...so the distance travelled when s=2 is 2t. The distance travelled for s+1=3 is 3*4t or 12t. Therefore, total distance covered while the sun was shining over him is W=2/14 = 1/7. Answer: E
Answer: E
Question: ACME’s manufacturing costs for sets of horseshoes include a $12,450 initial outlay, and $20.75 per set. They can sell the sets $50. If profit is revenue from sales minus manufacturing costs, and the company producessells 950 sets of horseshoes, what was their profit?
Options:
A)$15300
B)$14300
C)$15337.50
D)$16300
E)$15800
Rationale: Total Manufacturing cost = 12,450+950*20.75 = 32162.5
Total Selling cost = 950*50 = 47500
Profit = 47500-32162.50 = 15337.50
Answer : C
Answer: C
Question: During a trip on an expressway, Don drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 40 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip?
Options:
A)400/x%
B)50%
C)x/12%
D)60/x%
E)500/x%
Rationale: Say x = 5 miles (so no remainder of the trip).
Time to cover x = 5 miles at 30 miles per hour = (time) = (distance)/(rate) = 5/30 = 1/6 hours = 10 minutes.
Time to cover x = 5 miles at 60 miles per hour = (time) = (distance)/(rate) = 5/40 = 1/8 hours = 5 minutes.
(Or simply, half rate will result in doubling the time.)
So, we can see that the time to cover x = 4 miles at 30 miles per hour (10 minutes) is 100% greater than the time to cover x = 4 miles at 60 miles per hour (5 minutes).
Now, plug x = 4 miles into the answer choices to see which one yields 100%. Only answer E works.
Answer: A.
Answer: A
Question: The area of a parallelogram is 98sq m and its altitude is twice the corresponding base. Then the length of the base is?
Options:
A)8
B)9
C)7
D)6
E)5
Rationale: 2x * x = 98 => x= 7
Answer: C
Answer: C
Question: A train 630 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
A)35
B)36
C)37
D)38
E)39
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 630 * 2/35 = 36 sec
Answer: Option B
Answer: B
Question: Buses A and B start from a common bus stop X. Bus A begins to travel in a straight line away from bus B at a constant rate of 30 miles per hour. One hour later, bus B begins to travel in a straight line in the exact opposite direction at a constant rate of 70 miles per hour. If both buses travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes bus B to cover the exact distance that bus A has covered and the amount of time it takes bus B to cover twice the distance that bus A has covered?
Options:
A)36
B)72
C)122
D)144
E)180
Rationale: 1st part: - In 1hr, Bus A covers 30 miles.
Relative speed of bus ABus B is (80-30) = 50mph.
So time required for Bus B to cover the exact distance as A is
50*t = 30
t=3/5 = 36min
2nd part
80*t=2d - B has to cover twice the distance
30*(t+1) = d - A traveled 1hr more and has to travel only only d
so
d/30 - 2d/80 = 1
D=120
T= 3hrs = 180 min
Question asks for +ve difference between part 1 and part 2 in minutes
= 180-36 = 122min
C
Answer: C
Question: total no. of players is 99 other than me.50 plays soccer,45 plays basket ball,50 play valley ball.15 play all three. How many will play only 2 games?
Options:
A)40
B)50
C)60
D)70
E)80
Rationale: let A=soccer players..B=basket ball players..C=vollyball players
n(A U B U C)=n(A) + n(B) + n(C) - n(A INTERSECTION B) - n(A INTERSECTION C) - n(C INTERSECTION B) + n(A INTERSECTION B - INTERSECTION C)
therefore..
100=50+45+50-intersections+15
hence..intersections=145-100+15=60 play only 2 games..
ANSWER:C
Answer: C
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)16 km/hr
B)50 km/hr
C)19 km/hr
D)15 km/hr
E)87 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: The speed of a car is 80 km in the first hour and 60 km in the second hour. What is the average speed of the car?
Options:
A)50 kmph
B)60 kmph
C)70 kmph
D)80 kmph
E)85 kmph
Rationale: S = (80 + 60)/2 = 70 kmph
ANSWER:C
Answer: C