divelab/Sys2Bench huggingface dataset:
Question: 45 men working 8 hours per day dig 30 m deep. How many extra men should be put to dig to a depth of 50 m working 6 hours per day?
Options:
A)77
B)66
C)50
D)55
E)44
Rationale: (45 * 8)/30 = (x * 6)/50 => x =100
100 – 45 = 55
Answer: D
Answer: D
Question: John sells his laptop to Mark at a loss of 20% who subsequently sells it to Kevin at a profit of 25%. Kevin after finding some defect in the laptop, returns it to Mark but could recover only Rs.4.50 for every Rs. 5 he had paid. Find the amount of Kevin’s loss if John had paid Rs. 1,75,000 for the laptop.
Options:
A)Rs. 13,500
B)Rs. 2,500
C)Rs. 17,500
D)Rs. 18,500
E)None of these
Rationale: Let’s assume John bought the laptop for Rs. 100,
He then sells it to Mark for Rs. 80,
Who consequently sells it to Kevin for Rs. 100,
Then, Kevin sells it back to Mark for Rs. 90 (Rs.4.50 for every Rs. 5 that he had paid initially), so he suffers a loss of Rs. 10,
Therefore, for Rs 100 there is a loss of Rs. 10,
Then for Rs. 1,75,000 there will be a loss of Rs. 17,500
ANSWER:C
Answer: C
Question: A glass was filled with 10 ounces of water, and 0.05 ounce of the water evaporated each day during a 20-day period. What percent of the original amount of water evaporated during this period?
Options:
A)0.002%
B)0.02%
C)0.2%
D)2%
E)10%
Rationale: We are given that 0.05 ounces of water evaporated EACH DAY. Furthermore, we know that this process happened over a 20-DAY PERIOD. To calculate the total amount of water that evaporated during this time frame we need to multiply 0.05 by 20. This gives us:
0.05 x 20 = 1 ounces
Finally, we are asked for “What percent” of the original amount of water evaporated during this period. To determine this percentage, we have to make sure we translate the expression correctly. We can translate it to:
(Amount Evaporated/Original Amount) x 100%
(1/10) x 100%
(10/100) x 100% = 10%
Answer E
Answer: E
Question: A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets $500 more than D, what is C's share?
Options:
A)$1200
B)$1600
C)$1800
D)$2000
E)$2400
Rationale: Let the shares of A, B, C and D be 5x, 2x, 4x and 3x respectively.
Then, 4x - 3x = 500
x = $500
C's share = 4x = 4*$500 = $2000
The answer is D.
Answer: D
Question: In a sample of college students, 20 percent are third year students and 80 percent are not second-year students. What fraction of those students who are not third-year students are second-year students?
Options:
A) 1/4
B) 2/3
C) 4/7
D) 1/2
E) 3/7
Rationale: = 20/80. = 1/4
my answer is A too
Answer: A
Question: UBA Capital recently bought Brand new vehicles for office use. UBA capital only went for Toyota and Honda and bought more of Toyota than Honda at the ratio of 6:4. If 60% of the Toyota bought and 40% of the Honda bought were SUVÃ¢â‚¬â„¢s. How many SUVÃ¢â‚¬â„¢s did UBA capital buy in the aforementioned purchase?
Options:
A)66%
B)64%
C)68%
D)52%
E)72%
Rationale: let total no of Vehicles bought be 100, Toyota 60 and Honda 40, so total number of SUV's bought for Toyota and Honda respectively 60* 60/100=36 and 40* 40/100=16
so total 52 SUV's were bought out of 100 Vehicles bought..so required % is 52%
ANSWER:D
Answer: D
Question: A person decided to build a house in 100days. He employed 100men in the beginning and 100 more after 10 days and completed the construction in stipulated time. If he had not employed the additional men , how many days behind schedule would it have been finished?
Options:
A)40
B)80
C)70
D)60
E)90
Rationale: 200 men do the rest of the work in 100-10 = 90days
100 men can do the rest of the work in 90*200/100 = 180 days
Required number of days = 180-90 = 90 days
Answer is E
Answer: E
Question: By selling a watch for Rs.400/-, a man loses 20% what is that watch cost price
Options:
A)s. 700/-
B)s. 800/-
C)s. 880/-
D)s. 500/-
E)s. 990/-
Rationale: 80 % ------> 400 (80 * 5 = 400)
100 % ------>500 (100 * 5 = 500)
Cost price = Rs. 500/-
D
Answer: D
Question: The ratio of the present age of Viju to that of Aju is 7:2. Four years from now, the ratio of the ages of Viju to Aju will be 5:2. What was Viju age 10 years ago ? (RBI Assistant 2015)
Options:
A)11
B)18
C)12
D)15
E)13
Rationale: Let the present age of Viju be 7x years and that of Aju be 2x years.
Then, 4 years from now
7x + 4 / 2x + 4 = 5 / 2
or 4x = 12
or x = 3
Viju present age = 7 * 3 = 21 years
Viju age 10 years ago = 21 - 10 = 11 years
answer :A
Answer: A
Question: Find the principle on a certain sum of money at 5% per annum for 3 years if the amount being Rs.1120?
Options:
A)974
B)1067
C)1977
D)1056
E)1097
Rationale: 1120 = P [1 + (5*3)/100]
P= 974
Answer: A
Answer: A
Question: If x and y are integers and x divided by y is 19.15, then which of the following integers is a possible value for the remainder when x is divided by y? I. 15 II. 5 III. 3
Options:
A)I,III only
B)II only
C)I only
D)III only
E)II,III only
Rationale: x=19.15y from which x = 19y + 15y/100 or x = 19y + 3y/20.
Since x and y are integers, 3y/20 must also be an integer. 3 is not divisible by 20, then y must be divisible by 20, and therefore, y/20 is an integer and 3y/20 is an integer which is a multiple of 3. From the given answers, only 15 and 3 are divisible by 3.
Answer A
Answer: A
Question: At the beginning of the year, the ratio of juniors to seniors in high school X was 5 to 6. During the year, 10 juniors and twice as many seniors transferred to another high school, while no new students joined high school X. If, at the end of the year, the ratio of juniors to seniors was 6 TO 7, how many juniors were there in high school X at the beginning of the year?
Options:
A)250
B)100
C)260
D)110
E)120
Rationale: let the total number of juniors and seniors at the beginning of the year be 5x and 6x respectively.
now 10 juniors and 20 seniors are transferred to another school. thus no. of juniors and seniors students left in the school X are 5x-10 and 6x-20 respectively. the ratio of these juniors and seniors students = 6/7
thus we have (5x-10)/(6x-20) = 6/7
35x-70=36x-120
x=50
thus total no. of seniors at the beginning of the year =5(50)=250
Answer:option A
Answer: A
Question: Which of the following is closer to (6!+4!)-(6!-4!)?
Options:
A)28
B)38
C)48
D)58
E)68
Rationale: 6!+4!)-(6!-4!)=720+24-720+24
= 48
Answer: C
Answer: C
Question: A sum was put a simple interest at a certain rate for 5 years. Had it been put at 2% higher rate, it would have fetched Rs. 250 more. The sum is:
Options:
A)s.2000
B)s.2500
C)s.3000
D)s.3500
E)s.4000
Rationale: Explanation :
Let the sub be Rs.x and the initial rate be R%.Then
x Ã— (R+2) Ã— 5/100âˆ’xÃ—RÃ—5/100=250
â‡’x Ã— 2Ã—5/100=250
â‡’x Ã— 5 /100=125
â‡’5x=12500
â‡’x=2500
Answer : Option B
Answer: B
Question: The ratio of the radius of two circles is 2: 3, and then the ratio of their areas is?
Options:
A)1:7
B)2:9
C)4:9
D)3:7
E)3:4
Rationale: r1: r2 = 2: 3
Î r1^2: Î r2^2
r1^2: r2^2 = 4:9
Answer: C
Answer: C
Question: If a/x = 3 and a/y = 4, then (x + y) in terms of a
Options:
A)a/4
B)5a/7
C)7a/12
D)6a/13
E)11a/17
Rationale: Ratio 1:
x= a/3
Ratio 2:
y = a/4
x+y = a/3+a/4 = 7a/12
Answer is C
Answer: C
Question: Two taps can separately fill a cistern 10 minutes and 12 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?
Options:
A)7
B)7.8
C)6
D)9
E)5
Rationale: 1/10 + 1/12 - 1/x = 1/18
x = 180/23 = 7.8
Answer: B
Answer: B
Question: Ravi's brother is 3 years senior to him. His father was 28 years of age when his sister was born while his mother was 26 years of age when he was born. If his sister was 4 years of age when his brother was born, what were the ages of Ravi's father and mother respectively when his brother was born ?
Options:
A)32 years, 23 years
B)32 years, 29 years
C)35 years, 29 years
D)35 years, 33 years
E)36 years, 33 years
Rationale: Explanation:
When Ravi's brother was born, let Ravi's father's age = x years and mother's age = y years.
Then, sister's age = (x - 28) years. So, x - 28 = 4 or x = 32.
Ravi's age = (y - 26) years.
Age of Ravi's brother = (y - 26 + 3) years = (y - 23) years.
Now, when Ravi's brother was born, his age = 0 i.e. y - 23 = 0 or y = 23.
Answer: A) 32 years, 23 years
Answer: A
Question: If 40% of a certain number is 160, then what is 50% of that number?
Options:
A)270
B)380
C)200
D)360
E)290
Rationale: Explanation:
40% = 40*4 = 160
50% = 50*4 = 200
Answer: Option C
Answer: C
Question: Every student at Parcy School is in at least one of three clubs: horseback riding, embroidery, and country dancing, which are the only clubs in existence at the school. The ratio of the number of students in exactly two clubs to the number of students in exactly one club is 4:3, while the ratio of the number of students in exactly two clubs to the number of students in at least two clubs is 5:7. Which of the following could be the total number of students at Parcy School?
Options:
A)63
B)69
C)74
D)82
E)86
Rationale: the total number of students at Parcy School The answer is 86 or any multiple of 43.E
Answer: E
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 200 resolutions.
Options:
A)271.34 m
B)281.34 m
C)291.34 m
D)301.34 m
E)311.34 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 200 resolutions.
= 200 * 2 * 22/7 * 22.4
= 28134 cm
= 281.34 m
Answer: B
Answer: B
Question: Hanks Manufacturing recently conducted a survey of its employees. The results showed that of the n people who work at the company, 1/3 drink decaffeinated coffee, and the remainder drink regular coffee. Of those who do not drink decaf, 2/5 add cream to their coffee. Which of the expressions below accurately represents the number of employees who do not drink regular coffee with cream.
Options:
A)2n/3
B)n/8
C)4n/15
D)11n/15
E)13n/15
Rationale: Decaffeinated coffee = 1/3
Regular coffee = 2/3
"Of those who do not drink decaf, 2/5 add cream to their coffee."
means 'of the regular drinkers, i.e. of the 2/3, 2/5 add cream'
Regular coffee drinkers who add cream = 2/5 * 2/3 = 4/15
The fraction that drinks "regular coffee with cream" = 4/15
The fraction that does not drink "regular coffee with cream" is the rest = 1 - 4/15 = 11/15
Number of people = 11n/15
ANSWER:D
Answer: D
Question: The average (arithmetic mean) of all scores on a certain algebra test was 90. If the average of the 8 male students’ grades was 87, and the average of the female students’ grades was 92, how many female students took the test?
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: Total Marks of male = M
Total Marks of female = F
Number of males = 8
Number of females = f
Given: (M+F)/(8+f) = 90 -------------1
Also given, M/8 = 87 Thus M = 696 ---------2
Also, F/f = 92 thus F = 92 F - --------3
Put 2 and 3 in 1: we get
(696+92f)/(8+f) = 90
solving this we get f = 12
Answer: E
Answer: E
Question: If the sum of four consecutive positive integers is A, then the sum of the next four consecutive integers in terms of A is:
Options:
A)A+4
B)A+16
C)2A
D)2A + 4
E)4A
Rationale: In Case of Consecutive Integers or Integers in Arithmetic Progression Mean = Median
I.e. Median = A/4 = Mean = Average of Second and Third Integer
First Integer = A/4 - 1.5
Second Integer = A/4 - .5
Third Integer = A/4 + .5
Fourth Integer = A/4 + 1.5
i.e.
Fifth Integer = A/4 + 2.5
Sixth Integer = A/4 + 3.5
Seventh Integer = A/4 + 4.5
Eighth Integer = A/4 + 5.5
Now Mean of next 4 Integers = Median = A/4 + 4
i.e. Sum of Next 4 integers = (A/4 + 4)*4 = A+16
Answer: option B
Answer: B
Question: What is the area of a square field whose diagonal of length 12 m?
Options:
A)288
B)72
C)200
D)112
E)178
Rationale: d2/2 = (12 * 12)/2
= 72
Answer: B
Answer: B
Question: A boat goes 6 km up stream and 7 km down stream in 5 hours. It goes 3 km up stream and 6 km down stream in 3 hours. The speed of the boat in still water is:
Options:
A)2 km/hr
B)5.4 km/hr
C)4.8 km/hr
D)3.33 km/hr
E)None of these
Rationale: Explanation:
Let speed of the boat in still water be x km/hr
speed of the stream be y km/hr
then, speed of upstream = (x-y) km/hr
speed of down stream = (x+y) km/hr
6/(x-y) + 7/(x+y) = 5
3/(x-y) + 6/(x+y) = 3
Take 1/(x-y) = a & 1/(x+y) = b
6a + 7b = 5 ---(1)
3a + 6b = 3 ----(2)
(1) -------> 6a + 7b = 5
(2) x 2 ---> 6a + 12b = 6
------------------------
-5b = -1
b = 1/5
3a + (6/5) = 3
3a = 3 - 6/5
3a = (15 - 6)/5 = 9/5
a = 3/5
3/5 = 1/(x-y)
1/5 = 1/(x+y)
3x - 3y = 5 ---->(iii)
x + y = 5 ----> (iv)
(iv) x 3 ----> 3x + 3y = 15
(iii) -------> 3x - 3y = 5
-----------
6x = 20
x = 20/6 = 10/3 = 3.33
Answer: Option D
Answer: D
Question: 1, 6, 16, 31, 51, (....)
Options:
A)61
B)66
C)76
D)86
E)83
Rationale: Explanation:
The pattern is 5, 10, 15, 20, 25, etc
Hence 25=66
Answer : B
Answer: B
Question: (69842 x 69842 - 30158 x 30158) / (69842 - 30158) = ?
Options:
A)100000
B)69842
C)39684
D)30158
E)None
Rationale: Answer
Given expression = [(69842)2 - (30158)2] / [(69842 - 30158)]
= [ (69842 - 30158) (69842 + 30158) ] / (60842 - 30158)
= 100000
Correct Option: A
Answer: A
Question: (3x−4)⋅(3x+4)=?
Options:
A)3x2 - 4
B)9x2 - 16
C)-9x2 + 16
D)9x - 8
E)None
Rationale: Solution:
We use the product of the sum and the difference of the two terms:
(a+b)⋅(a−b)=a2−b2(a+b)⋅(a−b)=a2−b2
(3x−4)⋅(3x+4)=(3x)2−42=9x2−16
Answer B
Answer: B
Question: If x = 32 * 64 * 27 / 8, Find the tenth place of x,
Options:
A)1
B)2
C)5
D)4
E)3
Rationale: x = 32 * 64 * 27 / 8
x = 2^5 * 4^3 * 3*3 / 2^3
x = 2^2 * 12*3
x = 6912
Ans: A
Answer: A
Question: If p - q = 3 and
p2+q2=29
, find the value of pq.
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: Explanation:
We know
2ab=(a2+b2)−(a−b)2
2pq=29−9=20
=>pq=10
Option D
Answer: D
Question: Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.90 at the candy store. What is John’s weekly allowance?
Options:
A)$2.40
B)$3.00
C)$3.40
D)$3.60
E)$4.80
Rationale: Total allowance=X
Amount spent at the arcade=3/5X
Amount Remaining=2/5X
Amount Spent at the toy store=2/5*1/3X=2/15X
Amount Remaining=2/5X-2/15X=4/15X
Now, 4/15X=$0.9
Therefore, X=$3.40. Answer C
Answer: C
Question: If a and b are different positive integers and a + b = a(a + b), then which of the following must be true?
I. a = 1
II. b = 1
III. a < b
Options:
A)I only
B)II only
C)III only
D)I and II
E)I and III
Rationale: a+b=a(a+b)a+b=a(a+b) --> a(a+b)−(a+b)=0a(a+b)−(a+b)=0 --> (a+b)(a−1)=0(a+b)(a−1)=0 --> as aa and bb are positive the a+b≠0a+b≠0, so a−1=0a−1=0 --> a=1a=1. Also as aa and bb are different positive integers then bb must be more than a=1a=1 --> a<ba<b (bb can not be equal to aa as they are different and bb can not be less than aa as bb is positive integer and thus can not be less than 1).
So we have that: a=1a=1 and a<ba<b.
I. a = 1 --> true;
II. b = 1 --> not true;
III. a < b --> true.
Answer: E (I and II only).
Answer: E
Question: Find the area of trapezium whose parallel sides are 24 cm and 14 cm long, and the distance between them is 18 cm?
Options:
A)288 cm2
B)277 cm2
C)345 cm2
D)276 cm2
E)342 cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (24 + 14) * (18)
= 342 cm2
Answer: E
Answer: E
Question: The annual cost of owning and operating a car, C dollars, is a linear function of the distance, d kilometers, it is driven c = md + b
The cost is $4600 for 10 000 km and $9100 for 25 000 km.
(a) Determine the values of m and b.
(b) Write c as a function of d.
Options:
A)m = 0.3 and b = 1500
B)m = 0.3 and b = 1600
C)m = 0.3 and b = 1700
D)m = 0.3 and b = 1800
E)None
Rationale: Solution:
(a)
c = md + b
The cost is $ 4600 for 10 000 km
4600 = m (10 000) + b
10 000 m + b = 4600
b = -10 000 m + 4600 ------- (i)
The cost is $ 9100 for 25 000 km
9100 = m (25 000) + b
9100 = 25 000 m + b
25 000 m + b = 9100
b = -25 000 m + 9100 --------- (ii)
From equation (i) and (ii) we get;
-10 000 m + 4600 = -25 000 m + 9100
-10 000 m + 25 000 m = 9100 – 4600
15 000 m = 4500
m = 4500/15 000
m = 3/10
m = 0.3
Now, put the value of m = 0.3 in equation (i) we get;
b = -10 000 (0.3) + 4600
b = -3000 + 4600
b = 1600
Answer: m = 0.3 and b = 1600
(b) c = md + b
m = 0.3
b = 1600
c = 0.3d + 1600
Answer: c = 0.3d + 1600
Answer B
Answer: B
Question: A person incurs loss for by selling a watch for Rs1140.at what price should the watch be sold to earn a 5% profit ?
Options:
A)4560
B)2301
C)4512
D)3260
E)1260
Rationale: let the new sp be Rsx.then
(100-loss%) : (1st sp)=(100+gain%) (2nd sp)
{(100-5)/1400}={(100+5)/x}=> x={(105*1140)/95} =1260.
Ans: E
Answer: E
Question: The breath of a rectangle is three - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 2025 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the length is 10 units?
Options:
A)370 sq.units
B)270 sq.units
C)170 sq.units
D)470 sq.units
E)570 sq.units
Rationale: Given that the area of the square = 2025sq.units
=> Side of square = √2025 = 45 units
The radius of the circle = side of the square = 45 units breath of the rectangle = 3/5 * 45 = 27units
Given that length= 10 units
Area of the rectangle = lb = 27* 10 = 270 sq.units
Answer:B
Answer: B
Question: A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?`
Options:
A)10/21
B)11/21
C)2/7
D)5/7
E)3/7
Rationale: Total number of balls = (2 + 3 + 2) = 7.
Let S be the sample space.
Then, n(S)	= Number of ways of drawing 2 balls out of 7
= 7C2 `
=	(7 x 6)/(2 x 1)
= 21.
Let E = Event of drawing 2 balls, none of which is blue.
n(E)	= Number of ways of drawing 2 balls out of (2 + 3) balls.
= 5C2
=	(5 x 4)/(2 x 1)
= 10.
P(E) =	n(E)/n(S)	=	10/21.
Answer:A
Answer: A
Question: A departmental store has 2 managers and 10 associates. The 2 managers have an average salary of $5000. The 10 associates have an average salary of $20000. What is the average salary for the departmental store?
Options:
A)$15500
B)$16500
C)$17500
D)$14500
E)$19500
Rationale: Number of managers is 2
Their average salary is $5000
Number of associates is 10
Their average salary is $20,000
Total salary of managers is 2*5000=$10000
Total salary of associates is 10*20,000=$200,000
Total salary for the departmental store is 200,000+10000=210000
Average salary for the departmental store is 210000/10+2=17500
Answer is C
Answer: C
Question: One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill tank in 35 min, then the slower pipe alone will be able to fill the tank in?
Options:
A)229
B)787
C)144
D)128
E)140
Rationale: Let the slower pipe alone fill the tank in x min.
Then, faster pipe will fill it in x/3 min.
1/x + 3/x = 1/35
4/x = 1/35 => x = 140 min.
Answer: E
Answer: E
Question: A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 180 m long?
Options:
A)38 sec
B)35 sec
C)43.2 sec
D)40 sec
E)none of these
Rationale: Speed = 45 km/hr = 45 Ã— (5/18) m/s
= 150/12 = 50/4 = 25/2 m/s
Total distance = length of the train + length of the platform
= 360 + 180 = 540 meter
Time taken to cross the platform = 540/(25/2) = 540 Ã— 2/25 = 43.2 seconds
ANSWER:C
Answer: C
Question: A man buys s cycle for $100 and sells it at a loss of 20%. What is the selling price of the cycle?
Options:
A)$50
B)$60
C)$70
D)$80
E)$90
Rationale: S.P. = 80% of the $100 = 80/100 * 100 = $80
Answer is D
Answer: D
Question: One-third of Rahul’s savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 3,50,000 as total savings, how much has he saved in Public Provident Fund ?
Options:
A)Rs. 130,000
B)Rs. 150,000
C)Rs. 160,000
D)Rs. 140,000
E)None
Rationale: EXPLANATION
Let savings in N.S.C and P.P.F. be Rs. x and Rs. (350000 – x) respectively. Then,
1/3x=1/2(350000-x)
=> x/3 + x/2 = 175000
=> 5x/6 = 175000
=> x= 175000 x 6 /5= 210000
Savings in Public Provident Fund = Rs. (350000 – 210000) = Rs. 140000
Answer D
Answer: D
Question: In how many ways can a cricketer can score 200 runs with fours and sixes only?
Options:
A)13
B)17
C)19
D)16
E)15
Rationale: 200 runs can be scored by scoring only fours or through a combination of fours and sixes.
Possibilities are 50 x 4, 47 x 4 + 2 x 6, 44 x 4 + 4 x 6 ... A total of 17 ways
ANSWER:B
Answer: B
Question: What is the Mode of the following data set A- {1,2,4,6,4,9,4,10}
Options:
A)1
B)10
C)6
D)4
E)9
Rationale: Mode of a set is the data point that is repeated the most number of times. In the set given, 4 is repeated.
Answer : D
Answer: D
Question: If a man lost 7% by selling oranges at the rate of 21 a rupee at how many a rupee must he sell them to gain 42%?
Options:
A)12.75
B)11.75
C)8.75
D)15.75
E)13.75
Rationale: 93% ---- 21
142% ---- ?
93/142 * 21 = 13.75
Answer: E
Answer: E
Question: A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 7 inches wide on each side, the total area would have been (M + 264) square inches. What is the perimeter of the photograph, in inches?
Options:
A)8
B)12
C)16
D)20
E)24
Rationale: Let x and y be the width and length of the photograph.
(x+2)(y+2)=M and so (1) xy + 2x + 2y + 4 = M
(x+14)(y+14)=M and so (2) xy + 14x + 14y + 196 = M+264
Let's subtract equation (1) from equation (2).
12x + 12y + 192 = 264
2x + 2y = 12, which is the perimeter of the photograph.
The answer is B.
Answer: B
Question: Find the area of right angled triangle whose hypotenuse is 15 cm and one of the sides is 12 cm.
Options:
A)34 cm²
B)38 cm²
C)54 cm²
D)56 cm²
E)64 cm²
Rationale: AB² = AC² - BC²
= 15² - 12²
= 225 - 144
= 81
Therefore, AB = 9
Therefore, area of the triangle = ¹/₂ × base × height
= ¹/₂ × 12 × 9
= 54 cm²
ANSWER : C
Answer: C
Question: Six unbiased coin are tossed. What is the probability of getting atmost
one head?
Options:
A)61/2
B)61/4
C)63/64
D)63/5
E)61/6
Rationale: Here n(S)= 2^6
Let E=event of getting atmost one head =
n(E)= 63
P(E)=n(E)/n(S)=63/64
Answer option C)
Answer: C
Question: A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
Options:
A)7
B)6
C)5
D)4
E)3
Rationale: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 110 * 3/55 = 6 sec.
Answer:B
Answer: B
Question: The center of a circle is (5, -3). (5, 7) is outside the circle, and (1, -3) is inside the circle. If the radius, r, is an
integer, how many possible values are there for r?
Options:
A) 3
B) 5
C)11
D) 12
E) 13
Rationale: r must be greater than 4 and smaller than 10, hence r=5,6,7,8 or 9.
Answer B
Answer: B
Question: Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's salary?
Options:
A)Rs. 38,00
B)Rs. 38,000
C)Rs. 40,000
D)Rs. 57,000
E)Rs. 20,000
Rationale: Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.
Then, 2x + 4000/3x + 4000 = 40/57
57(2x + 4000) = 40(3x + 4000)
6x = 68,000
3x = 34,000
Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000.
Answer is B.
Answer: B
Question: Find the number of square tiles to cover the floor of a room measuring 4 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?
A. 425 B. 476 C. 450 D. 350
Options:
A)425
B)476
C)450
D)350
E)250
Rationale: 3 1/2 * 8 1/2 = 1/4 * 1/4 * x => x = 476
ANSWER:B
Answer: B