divelab/Sys2Bench huggingface dataset:
Question: The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, find his highest score.
Options:
A)179
B)367
C)269
D)177
E)191
Rationale: Explanation:
Total runs scored by the batsman = 60*46 = 2760 runs
Now excluding the two innings the runs scored = 58*44 = 2552 runs
Hence the runs scored in the two innings = 2760 – 2552 = 208 runs.
Let the highest score be x, hence the lowest score = x – 150
x + (x - 150) = 208
2x = 358
x = 179 runs
ANSWER: A
Answer: A
Question: In a coconut grove, (x + 1) trees yield 60 nuts per year, x trees yield 120 nuts per year and (x – 1) trees yield 180 nuts per year. If the average yield per year per tree be 100, find x.
Options:
A)2
B)4
C)5
D)6
E)None of the above
Rationale: (x+1)×60+x×120+(x−1)×180/(x+1)+x+(x−1)=100
⇒ 360x−120/3x = 100
⇒ 60x = 120 ⇒ x = 2
Answer A
Answer: A
Question: The total marks obtained by a student in Physics, Chemistry and Mathematics is 150 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics?
Options:
A)75
B)66
C)55
D)44
E)12
Rationale: Let the marks obtained by the student in Physics, Chemistry and Mathematics be P, C and M respectively.
P + C + M = 150 + P
C + M = 150
Average mark obtained by the student in Chemistry and Mathematics = (C + M)/2 = 150/2 = 75.
Answer:A
Answer: A
Question: a box contain 4 small bos, each small box again contain 3 box,again these box contain 2 box . total how many boxes
Options:
A)38
B)39
C)40
D)42
E)41
Rationale: a box contain 4 small box means 1+4 = 5 Boxes
each small box again contain 3 box means 4*3 = 12 boxes
Again these 12 boxes contain 2 boxes each... means 12*2 = 24
Total Boxes till now are 5 + 12 + 24 = 41
ANSWER:E
Answer: E
Question: Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 100. What is the value of x?
Options:
A)50
B)100
C)200
D)1,000
E)2,000
Rationale: y = 50% of 50% 0f x
= x/4
and
y/100 of x = 100
y /100 *4y =100
y = 50
and x= 200
Answer - C
Answer: C
Question: Eighteen years ago, a father was three times as old as his son. Now the father is only twice as old his son. Then the sum of the present ages of the son and the father is:
Options:
A)53
B)108
C)77
D)107
E)109
Rationale: Explanation:
Let the present ages of the father and son be 2x and x years respectively.
Then, (2x - 18) = 3(x - 18) => x = 36
Required sum = (2x + x) = 108 years.
Answer: Option D
Answer: D
Question: An outlet pipe empties a tank which is full in 10 hours. If the inlet pipe is kept open, which lets liquid in at the rate of 8 litres/min then outlet pipe would take 6 hours longer. Find the capacity of the tank.
Options:
A)8600 litres
B)12800 litres
C)12100 litres
D)11200 litres
E)13200 litres
Rationale: Let the rate of outlet pipe be x liters/hour;
Rate of inlet pipe is 8 litres/min, or 8*60 = 480 liters/hour;
Net outflow rate when both pipes operate would be x-480 liters/hour.
Capacity of the tank = x*10 hours = (x-480)*(10+6) hours
10x=(x-480)*16 --> x=1280 --> capacity = 10x = 12800 liters.
Answer: B
Answer: B
Question: Sakshi invests a part of Rs. 12,000 in 12% stock at Rs. 120 and the remainder in 15% stock at Rs. 125. If his total dividend per annum is Rs. 1360, how much does he invest in 12% stock at Rs. 120?
Options:
A)Rs. 4000
B)Rs. 4500
C)Rs. 5500
D)Rs. 6000
E)Rs. 7000
Rationale: Let investment in 12% stock be Rs. x.
Then, investment in 15% stock = Rs. (12000 - x).
12	x x +	15	x (12000 - x) = 1360.
120	125
x	+	3	(12000 - x) = 1360.
10	25
5x + 72000 - 6x = 1360 x 50
x = 4000.
ANSWER:A
Answer: A
Question: If a, b, and c are consecutive integers such that a < b < c and a is an even prime number, which of the following is true?
I. a + b + c > a^3
II. a × b × c < a^3
III. 5b < bc
Options:
A)I only
B)II only
C)III only
D)II and III
E)I, II, and III
Rationale: Only 'A' is possible solution. If a is even prime number i.e 2, b is 3 and c is 4
Putting the values in the answers only 'A' seems valid.
Answer: A
Question: If a real number x is chosen at random in the interval [0,3] and a real number y is chosen at random in the interval [0,5], what is the probability that x < y?
Options:
A)23/30
B)7/12
C)11/15
D)7/10
E)3/4
Rationale: Since x is in [0,3] and y is in [0,5] we can draw a rectangle in the coordinate plane with vertices (0, 0), (3, 0), (0, 5), and (3, 5).
The points above the line y=x satisfy x < y.
The part of the rectangle below y=x has an area of 4.5.
The whole rectangle has an area of 15.
P(x < y) = (15-4.5)/15 = 21/30 = 7/10
The answer is D.
Answer: D
Question: There are 3 sections with 4 questions each. If three questions are selected from each section, the chance of getting different questions is________
Options:
A)10
B)78
C)89
D)64
E)56
Rationale: we have to select three questions from each section so the chances are 4C3.4C3.4C3=64
ANSWER:D
Answer: D
Question: By weight, liquid X makes up 1.5 percent of solution P and 6.5 percent of solution Q. If 400 grams of solution P are mixed with 600 grams of solution Q, then liquid X accounts for what percent of the weight of the resulting solution?
Options:
A)3.6%
B)3.9%
C)4.2%
D)4.5%
E)4.8%
Rationale: The number of grams of liquid X is 1.5(400)/100 + 6.5(600)/100 = 6 + 39 = 45 grams.
45 / 1000 = 4.5%
The answer is D.
Answer: D
Question: Given distinct positive integers 1, 11,4, x, 2, and 10, which of the following could be the median?
Options:
A)3
B)4
C)7
D)8
E)9
Rationale: The median of a set with even number of terms is the average of two middle terms when arranged in ascending (or descending) order.
Arrange numbers in ascending order: 1, 2, 4, 9, 11, and x.
Now, x can not possibly be less than 4 as given that all integers are positive and distinct (and we already have 1, 2, and 4).
Next, if x is 4<x<10 then the median will be the average of 4 and x. As all answers for the median are integers, then try odd values for x:
If x=4, then median=(4+4)/2=4 --> OK;
Answer: B.
P.S. If x is more than 9 so 10 or more then the median will be the average of 4 and 9 so (4+10)/2=7 (the maximum median possible).
Answer: B
Question: What number comes next in the following series? 4, 14, 44, 134, 404, ____
Options:
A)1204
B)1208
C)1214
D)1216
E)1220
Rationale: 44 × 3 + 2 = 1414 × 3 + 2 = 4444 × 3 + 2 = 134134 × 3 + 2 = 404404 × 3 + 2 = 1214 C
Answer: C
Question: In a end-of-season sale, the prices at a store have been cut to 80%. How many dollars would a $50 item cost?
Options:
A)$15
B)$10
C)$21
D)$20
E)None of these
Rationale: Solution
Actual Cost of the item is $50
80%cut off on cost of the item = $50*80/100= $40
So Actual cost minus cut off percentage cost = $50- $40= $10
Answer B
Answer: B
Question: Two numbers are in the ratio of 5:7. If 33 is subtracted from each number, they are in the ratio of 1:2. What are the two numbers?
Options:
A)45, 63
B)50, 70
C)55, 77
D)60, 84
E)65, 91
Rationale: (5x-33):(7x-33) = 1y:2y
5x - 33 = y
7x - 33 = 2y
231-165 = 10y - 7y
66 = 3y
y = 22
5x-33 = 22
x = 11
The two numbers are 5x and 7x which are 55 and 77.
The answer is C.
Answer: C
Question: 7 people sit at the round table. In how many ways can we sit them so that ALI and BillI don't sit opposing each other?
Options:
A)A)400
B)B)420
C)C)440
D)D)460
E)E)480
Rationale: 7 People: ALI,BillI,Red, Blue,White,Pink,Purple
Round Table: T
7 Chairs: 1,2,3,4,5,6,7
Let chairs 1 and 4 be opposite each other;
ALI is sitting on 1 and Bill is sitting on 4;
The rest of the people on 2,3,5,6,7 - can rearrange themselves in 5! ways
Now, BillI and ALI swap their positions;
ALI is sitting on 4 and BILLI is sitting on 1;
The rest of the people on 2,3,5,6,7 - can rearrange themselves in 5! ways
Thus total number of ways in which ALI and BillI are sitting opposite each other = 2*5! = 120*2 = 240
We have to find in how many ways they are NOT sitting opposite; subtract 240 from the total number of possible arrangements;
In circular permutation, Total number of arrangements of n people = (n-1)!
Here number of people = 7
Arrangements = (7-1)! = 6!= 720
Number of ways ALI and BillI are NOT sitting opposite = 720-240 = 480.
Answer: E
Answer: E
Question: In the first 10 overs of a cricket game, the run rate was only 6.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
Options:
A)6.25
B)5.5
C)6.75
D)7
E)8
Rationale: 10 overs - run rate = 6.2
runs scored in first 10 overs = 62
remaining overs 40
total runs to be scored= 282
62 runs already scored 282-62=220
220 runs to be scored in 40 overs
let required runrate be x
40*x=220
x=220/40
x=5.5
the required runrate is 5.5
ANSWER:B
Answer: B
Question: The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:
Options:
A)1520 m2
B)2420 m2
C)2480 m2
D)2520 m2
E)2645 m2
Rationale: Explanation:
We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103.
Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m2.
Answer: D
Answer: D
Question: What least number should be subtracted from 13603 such that the remainder is divisible by 87 ?
Options:
A)27
B)29
C)28
D)30
E)31
Rationale: 13603 ÷ 87 = 156, remainder = 31
Hence 31 is the least number which can be subtracted from 13603 such that the remainder
is divisible by 87
Answer is E
Answer: E
Question: In Kaya's teacher's desk there are 6 pink highlighters, 2 yellow highlighters, and 4 blue highlighters. How many highlighters are there in all?
Options:
A)11
B)12
C)77
D)33
E)88
Rationale: Add the numbers of highlighters.
6 + 2 + 4 =12.
Answer is B.
Answer: B
Question: If C and D are positive integers, and the remainder obtained when C is divided by D is the same as the remainder obtained when D is divided by C, which of the following is a possible value of CD?
Options:
A) 62
B) 55
C) 48
D) 31
E) 25
Rationale: I am not too sure on this. I guess it is possible only when C and D are both same. If they are both same, CD must be a perfect square.
25 is a perfect square.
Ans:E
Answer: E
Question: Vijay sells a cupboard at 14% below cost price. Had he got Rs.2086 more, he would have made a profit of 14%. What is the cost price of the cupboard?
Options:
A)7450
B)14900
C)7400
D)7500
E)None of these
Rationale: Explanation:
Cost price = 2086/(0.14 + 0.14) = 2086/0.28
= Rs.7450
ANSWER A
Answer: A
Question: There are two bags A and B. A contains 6 red flowers and 3 pink flowers. where as bag B contains 2 red flowers and 7 pink flowers. One flower is chosen from a bag randomly. What is the probability that the flower chosen is pink?
Options:
A)5/8
B)5/6
C)5/1
D)5/9
E)5/2
Rationale: Bag A 6 red + 3 pink
Bag B 2 red + 7 pink
Probability of picking 1 pink from bag A is 3/9
Probability of picking 1 pink from bag B is 7/9
Total = 3/9 + 7/9 = 10/9
And probability of selecting a bag is 1/2
So finally probability of choosing a pink flower = 1/2(10/9) = 5/9
Answer : D
Answer: D
Question: The average weight of 6 person's increases by 1.8 kg when a new person comes in place of one of them weighing 69 kg. What might be the weight of the new person?
Options:
A)73 kg
B)79.8 kg
C)86 kg
D)Data inadequate
E)None of these
Rationale: Total weight increased = (6 x 1.8) kg = 10.8 kg.
Weight of new person = (69 + 10.8) kg = 79.8 kg.
Answer: Option B
Answer: B
Question: John and David work at a hospital with 8 other workers. For an internal review, 2 of the 8 workers will be randomly chosen to be interviewed. What is the probability that John and David will both be chosen?
Options:
A)1/30
B)1/25
C)1/20
D)1/28
E)1/30
Rationale: Probability that John and David will both be chosen out of 8 workers
= (2/8)*(1/7)
= 1/28
Answer D
Answer: D
Question: Three business people wish to invest in a new company. Each person is willing to pay one third of the total investment. After careful calculations, they realize that each of them would pay $5,200 less if they could find two more equal investors. How much is the total investment in the new business?
Options:
A)$64,000
B)$78,000
C)$39,000
D)$ 5,200
E)$ 3,800
Rationale: Total Investment between 5: (x/5)
Total investment including 5200 less between 3 people(x-(5200*3))/3
Set both eq. equal to eachother.
$39,000
Answer C)
Answer: C
Question: Given that G and H are events such that
G(Y)= 0.02
G(Z)=0.4
G(YnZ)=0.4
find G (Y|Z) and G(Y|Z)
Options:
A)1/22
B)1/20
C)1/25
D)1/10
E)1/50
Rationale: Here, Y and Z are events
G(Y|Z) = G(YnZ)/G(Z) = 0.4/0.4= 1
Q(G|H) = G(YnZ)/G(Y) = 0.4/0.20 = 1/20
Answer is B
Answer: B
Question: The product Z of two prime numbers is between 20 and 56. If one of the prime numbers is greater than 2 but less than 6 and the other is greater than 14 but less than 30 then what is Z?
Options:
A)26
B)35
C)39
D)51
E)55
Rationale: The smallest possible product is 51 which is 3*17.
All other products are too big.
The answer is D.
Answer: D
Question: A certain library assesses fines for overdue books as follows. On the first day that a book is overdue, the total fine is $0.09. For each additional day that the book is overdue, the total fine is either increased by $0.30 or doubled, whichever results in the lesser amount. What is the total for a book on the fourth day it is overdue?
Options:
A)$0.66
B)$0.70
C)$0.80
D)$0.90
E)$1.00
Rationale: 1st day fine - 0.09
2nd day fine - 0.09*2 = 0.18 (as doubling gives lower value)
3rd day fine - 0.18*2 = 0.36 (as doubling gives lower value)
4th day fine - 0.36 + 0.3 = 0.66 (as doubling gives higher value we add 0.3 this time)
Answer: A.
Answer: A
Question: Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 3:5, find his marks in Science?
Options:
A)18
B)99
C)77
D)66
E)43
Rationale: S:E = 1:3
E:M = 3:5
------------
S:E:M = 3:9:15
3/27 * 162 = 18
Answer:A
Answer: A
Question: Grace has 18 jellybeans in her pocket. She has 9 red ones, 5 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?
Options:
A)4
B)8
C)12
D)13
E)15
Rationale: The worst scenario is when she takes 9 red and 5 green, total of 14 jellybeans, and still doesn't have 3 distinct colors. But the next draw (15th) will surely be the third color jellybean (blue) as there is no other color jellybeans left in pocket.
Answer: E.
Answer: E
Question: If two of the four expressions x + y , x + 6y , x - y , and 6x - y are chosen at random, what is the probability that their product will be of the form of x^2-(by)^2, where b is an integer?
Options:
A)1/5
B)1/8
C)1/6
D)1/7
E)1/3
Rationale: Total number of expressions if 2 are multiplied = 4C2 = 4!/2!*2! = 6
now we have to find the expressions that are in form of x^2 - (by)^2
one is (x+y)(x-y) = x^2 - (1y)^2
If you see any other combination we are always going to have one term of xy since 6x and 6y are there, so there can be only one type of combination like this.
therefore, probablity is 1/6
Answer : C
Answer: C
Question: A wheel of a car of radius 21 cms is rotating at 500 RPM. What is the speed of the car in km/hr?
Options:
A)79.2 km/hr
B)47.52 km/hr
C)7.92 km/hr
D)39.6 km/hr
E)3.96 km/hr
Rationale: Explanatory Answer
The radius of the wheel measures 21 cm.
In one rotation, the wheel will cover a distance which is equal to the circumference of the wheel.
∴ in one rotation this wheel will cover 2 * π * 21 = 132 cm.
In a minute, the distance covered by the wheel = circumference of the wheel * rpm
∴ this wheel will cover a distance of 132 * 500 = 66000 cm in a minute.
In an hour, the wheel will cover a distance of 66000 * 60 = 3960000 cm.
Therefore, the speed of the car = 3960000 cm/hr = 39.6 km/hr
Choice D is the correct answer.
Answer: D
Question: The sum of two numbers is 44. Five times one number is equal to 6 times the other. The bigger of the two numbers is
Options:
A)10
B)12
C)16
D)22
E)24
Rationale: Sol.
Let the numbers be x and (44 - x).
Then, 5x = 6(44 - x)
⇔ 11x = 264⇔ x = 24.
So, the numbers are 24 and 20.
Answer E
Answer: E
Question: I have a huge bed-sheet of 1 meter long.
I want to cuts this role into pieces of 20 centimeter long cloth.
How long will it take me to cut the bed sheet if each 20 centimeter cut took me 5 minutes ?
Options:
A)245 minutes
B)345 minutes
C)445 minutes
D)545 minutes
E)None
Rationale: Solution:
245 minutes
It will take 49 cuts not 50.
so 49*5 => 245 minutes
Answer A
Answer: A
Question: In a forest 100 deer were caught, tagged with electronic markers, then released. A week later, 50 deer were captured in the same forest. Of these 50 deer, it was found that 5 had been tagged with the electronic markers. If the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest, and if no deer had either left or entered the forest over the preceding week, what is the approximate number of deer in the forest?
Options:
A)150
B)750
C)1,250
D)1,000
E)2,500
Rationale: The percentage of tagged deer in the second sample = 5/50*100=10%.
So, 100 tagged deers comprise 10% of total # of deers --> total # of deers = 100*10 = 1,000.
Answer: D.
Answer: D
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
Options:
A)11
B)27
C)20
D)21
E)24
Rationale: M = 15
S = 5
DS = 15 + 5 = 20
Answer: C
Answer: C
Question: A man while returning from his factory, travels 2/3 of the distance by bus, 3/4 of the rest partly by car and partly by foot. If he travels 2 km on foot, find the distance covered by him.
Options:
A)24 km
B)22 km
C)28 km
D)26 km
E)None of these
Rationale: D=2/3D+1/3x3/4D+2,
Therefore D = 24km
Answer: A
Answer: A
Question: A bag contains 6 red, 3 yellow and 4 green balls. 3 balls are drawn randomly. What is the probability that the balls drawn contain balls of different colours?
Options:
A)2/7
B)3/5
C)3/11
D)1/4
E)7/16
Rationale: Total number of balls = 6+3+4 = 13
n(S) = 13C3 = 286
n(E) = 6C1 * 3C1 * 4C1 = 72
Probability = 72/286 = 1/4
Answer is D
Answer: D
Question: Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is?
Options:
A)299
B)2767
C)120
D)287
E)261
Rationale: Work done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24) = - 1/40
Volume of 1/40 part = 3 gallons\
Volume of whole = 3 * 40 = 120 gallons.
Answer: C
Answer: C
Question: Six people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
Options:
A)7/8
B)1/8
C)1/3
D)1/5
E)1/9
Rationale: Original share of 1 person =1/6
New share of 1 person =1/5
Increase =1/5 -	1/6	=1/30
Required fraction =	(1/30)/(1/6)=1/5
Answer is D.
Answer: D
Question: In a triangle, one side is 6 Cm and another side is 12 Cm. which of the following can be the perimeter of the triangle?
Options:
A)18.
B)25.
C)30.
D)32.
E)34.
Rationale: Given : one side is 6 Cm and another side is 9 Cm. So the 3rd side will be > 3 and < 15. Thus the perimeter will be : 18 < perimeter < 30. Only option satisfying this condition is 32. Hence D.
Answer: D
Question: a,d,i,p,? what is next term
Options:
A)q
B)t
C)r
D)s
E)y
Rationale: a=1*1
d=2*2
i=3*3
p=4*4
next will be
5*5=25=Y
ANSWER:E
Answer: E
Question: 1850 men have provisions for 15 days. If 150 more men join them, for how many days will the provisions last now?
Options:
A)12.9
B)12.0
C)13.9
D)13.5
E)12.1
Rationale: 1850*15 = 2000*x
x = 13.9
Answer:C
Answer: C
Question: If grapes are 91% water and raisins are 19% water, then how many kilograms did a quantity of raisins, which currently weighs 9 kilograms, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.)
Options:
A)63
B)72
C)81
D)90
E)99
Rationale: Let x be the original weight.
The weight of the grape pulp was 0.09x.
Since the grape pulp is 81% of the raisins, 0.09x = 0.81(9 kg).
Then x = 9*9 = 81 kg.
The answer is C.
Answer: C
Question: How many ounces of a 60% salt solution must be added to 50 ounces of a 20 percent salt solution so that the resulting mixture is 40% salt?
Options:
A)16.67
B)30
C)50
D)60.33
E)70
Rationale: For 60% salt solution (X) and 20% salt solution (Y) to give 40%=(60+20)/2 salt solution, we should mix equal amounts of X and Y.
Answer: C.
Answer: C
Question: The banker's discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. What is the time?
Options:
A)3 months
B)4 months
C)5 months
D)6 months
E)None of these
Rationale: Explanation :
Bankers Discount, BD = Simple Interest on the face value of the bill for unexpired time.
True Discount, TD = Simple Interest on the present value for unexpired time.
Simple Interest on Rs. 1600 = True Discount on Rs.1680
=> Rs. 1600 is the Present Worth (PW) of Rs. 1680
=> Rs. 80 is the Simple Interest of Rs.1600 at 15%
⇒80=(1600×T×15)/100
⇒ 80 = 16 × T × 15
⇒ 5 = T × 15
⇒ 1 = T × 3
=> T = 1/3 year = 12/3 months = 4 months Answer : Option B
Answer: B
Question: An object thrown directly upward is at a height of h feet after t seconds, where h = -15 (t-2)^2 + 150. At what height, in feet, is the object 2 seconds after it reaches its maximum height?
Options:
A)72
B)90
C)124
D)132
E)140
Rationale: We see that h will be a maximum h=150 when t-2=0, that is when t=2.
At t=4, h = -15(4-2)^2 + 150 = -15(4) + 150 = 90
The answer is B.
Answer: B
Question: A batsman in his 12th innings makes a score of 115 and thereby increases his average by 3 runs. What is his average after the 12th innings if he had never been ‘not out’?
Options:
A)42
B)43
C)44
D)82
E)46
Rationale: Let ‘x’ be the average score after 12 th innings
⇒ 12x = 11 × (x – 4) + 115
∴ x = 82
Answer D
Answer: D
Question: A train crosses a platform of 110 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
Options:
A)A)310m
B)B)170m
C)C)180m
D)D)158m
E)E)350m
Rationale: Length of the train be ‘X’
X + 110/15 = X + 250/20
4X + 440 = 3X + 750
X = 310m
Answer: A
Answer: A
Question: What is the least number to be subtracted from 1300 to make it a perfect square?
Options:
A)80
B)25
C)75
D)63
E)90
Rationale: The numbers less than 1300 and are squares of certain number is 1225.
The least number that should be subtracted from 1300 to make it perfect square = 1300 - 1225 = 75.
ANSWER:C
Answer: C
Question: Find the LCM of 0.6, 9.6 and 0.36.
Options:
A)26.3
B)35.6
C)32.9
D)25.5
E)28.8
Rationale: The given numbers are equivalent to 0.60, 9.60 and 0.36.
Now, find the LCM of 60,960 and 36. Which is equal to 2880.
The required LCM =28.80.
Answer is E
Answer: E
Question: An error 3% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is
Options:
A)6.04%
B)6.14%
C)6.23%
D)6.26%
E)6.09%
Rationale: 100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (103 x 103) cm2.
(A2 - A1) = [(103)2 - (100)2]
= (103 + 100) x (103 - 100)
= 609 cm2.
Percentage error = 6.09
E
Answer: E
Question: The H.C.F. of two numbers is 32 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
Options:
A)448
B)299
C)421
D)460
E)365
Rationale: Clearly, the numbers are (32 x 13) and (32 x 14).
Larger number = (32 x 14) = 448. Answer: Option A
Answer: A
Question: The diagonals of a rhombus are 15 cm and 20 cm. Find its area?
Options:
A)329
B)288
C)150
D)238
E)31
Rationale: 1/2 * 15 * 20 = 150
Answer: C
Answer: C
Question: If x^2=x -1, then x^3=?
Options:
A)3x+2
B)3x-2
C)2x+1
D)-1
E)3x+4
Rationale: Given X^2 = X - 1
X^3 = X*X^2 = x*(X-1)-- Substituted from above.
= X^2 - X = X-1-X = -1.
Hence D.
Answer: D