divelab/Sys2Bench huggingface dataset:
Question: In the interior of a forest, a certain number of apes equal to the square of one-sixth of the total number are playing and having great fun. The remaining five apes are on a hill and the echo of their shrieks by the adjoining hills frightens them. They came and join the apes in the forest and play with enthusiasm. What is the total number of apes?
Options:
A)48
B)16
C)64
D)6 or 30
E)16 or 48
Rationale: Let total number be x
No in the interior = (x/6)^2
No outside = 5
So : x - (x/6)^2=5
x^2-36x+180=0
x^2-30x-6x+180=0
(x-6)(x-30)=0
So either x=6 or x=30
D
Answer: D
Question: Ajay and Vijay have some marbles with them. Ajay told Vijay "if you give me 'x' marbles, both of us will have equal number of marbles". Vijay then told Ajay "if you give me twice as many marbles, I will have 30 more marbles than you would". Find 'x'?
Options:
A)6
B)5
C)8
D)7
E)9
Rationale: Explanation:
If Vijay gives 'x' marbles to Ajay then Vijay and Ajay would have V - x and A + x marbles.
V - x = A + x --- (1)
If Ajay gives 2x marbles to Vijay then Ajay and Vijay would have A - 2x and V + 2x marbles.
V + 2x - (A - 2x) = 30 => V - A + 4x = 30 --- (2)
From (1) we have V - A = 2x
Substituting V - A = 2x in (2)
6x = 30 => x = 5.
Answer: B
Answer: B
Question: If x and y are integers and x^2*y is a negative odd integer, which of the following must be true?
I. xy^2 is odd.
II. xy is negative.
III. x + y is even.
Options:
A)I only
B)III only
C)I and II only
D)I and III only
E)I, II, and III
Rationale: x^2*y = negative odd integer
inference:
1. Odd * Odd = Odd
2. y is negative odd integer
3. x is odd (since its squared, the result is positive - so x could be either positive or negative).
Statement I - xy is odd, so is its sqaure - statement must be true
Statement II - xy may or may not be negative - statement may be true but NOT must
Statement III - x and y are odd, so Odd + Odd = Even - statement must be true
Answer is D
Answer: D
Question: Three friends-whose walking rates are 1 ft./sec., 3ft./sec.,and 6ft./sec. start together walking in the same direction around a circular track that is 240 feet in circumference.After how many minutes are the three of them together again?
Options:
A)4 mins
B)10 mins
C)15 mins
D)3 mins
E)7 mins
Rationale: Answer will be A
The time they take will be what the 1st friend takes to complete one circumference as he is the slowest and that is the point all 3 of them will be together at the end of 4 mins.
Answer: A
Question: A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
Options:
A)1 min
B)9 min
C)4 min
D)3 min
E)8 min
Rationale: C
4 min
S = 600/40 = 15 mps
S = 3600/15 = 240 sec = 4 min
Answer: C
Question: P is three times as fast as Q and working together, they can complete a work in 16 days. In how many days can Q alone complete the work?
Options:
A)11 days
B)16 days
C)13 days
D)64 days
E)19 days
Rationale: P = 3Q
P + Q = 3Q + Q = 4Q
These 4Q people can do the work in 16 days,
which means Q can alone do the work in 4*16=64 days.
Answer : D
Answer: D
Question: Set A: {1, 3, 6, 9, 12, 15,18}
If three numbers are randomly selected from set A without replacement, what is the probability that the sum of the three numbers is divisible by 3?
Options:
A)3/14
B)2/7
C)9/14
D)4/7
E)11/14
Rationale: probability : 6/7*5/6*4/5=4/7.
Ans D
Answer: D
Question: The numbers of pizza slices that are sold in Joey's Pizza are only in quantities of 5 and 8 slices per customer. How many slices cannot be bought?
Options:
A)42.
B)38.
C)33.
D)22.
E)20
Rationale: Let X pizzas of 5 slices and Y pizzas of 8 slices.
5X + 8Y.
Lets check options wise.
A. 42 => 5(2) + 8(4)
B. 38 => 5(6) + 8(1)
C. 33 => 5(5) + 8(1)
D. 22 = we can't write anything with 5 and 8 series..Lets try 5(1) + 8(2) = 21 , 5(3) + 8(1) = 23 , nothing works out.
E. 20 = 5(4) + 8(0)
Answer: correct option is D
Answer: D
Question: A room contains 240 people, 15 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?
Options:
A)02
B)04
C)06
D)08
E)10
Rationale: Say group of x people left the room.
# of women in the room was 0.15*240=36;
# of women in the group that left 0.3x;
# of women in the room after the group left it is 0.1(240-x);
So, 36-0.3x= 0.1(240-x) --> x=6.
Answer: C.
Answer: C
Question: If a and b are positive integers such that a/b = 9.32, which of the following must be a divisor of a
Options:
A)4
B)3
C)11
D)10
E)5
Rationale: a/b = 9.32
a/b = 932/100
a/b = 466/50
a = 466/50*b
We require to find from the available 5 options that must be a divisor of a"
This also means which of the following 5 options can divide 466 evenly
(Ignore b as its value unknown; Ignore 50 as in denominator)
Only option A = 4 best fits in
Answer = 4
ANSWER:A
Answer: A
Question: The cost price of an article is 64% of the marked price. Calculate the gain percent after allowing a discount of 12%?
Options:
A)37.5%
B)37.8%
C)38.5%
D)27.5%
E)37.1%
Rationale: Explanation:
Let marked price = Rs. 100.
Then, C.P. = RS. 64, S.P. = Rs. 88
Gain % = 24/64 * 100 = 37.5%.
Answer:A
Answer: A
Question: The average of 11numbers is 50. Out of 11numbers the average of first 6no. is 58, and last 6numbers is 65 then find 6th number?
Options:
A)A)188
B)B)65
C)C)58
D)D)62
E)E)48
Rationale: 6th number = sum of 1st 6no.s + sum of last 6no.s - sum of 11no.s
answer = 6*58+6*65-11*50= 188
Answer is A
Answer: A
Question: Points X, Y, and Z lie, in that order, on a straight railroad track. The distance from point X to point Y is twice the distance from point Y to point Z. A train traveled from point X to point Z without stopping. The train's average speed when traveling from point X to point Y was 300 miles per hour and the train's average speed when traveling from point Y to point Z was 100 miles per hour. What was the train's average speed, in miles per hour, when traveling from point X to point Z?
Options:
A)200
B)220
C)240
D)180
E)260
Rationale: Average speed = distance/time
Because we are looking for average speed we can pick a distance for the variable D.
Speed X-Y = 300
Speed Y-Z = 100
Average Speed = total distance/total rate
rate = distance/time
X====================Y==========Z
If X-Y is twice the length of Y-Z then let X-Y = 2d and let Y-Z= d
Average speed = 3d/(2d/300) + (d/100)
3d/(2d/300) + (3d/300)
3d/(5d/300)
900d/5d
Average speed = 180
ANSWER: D
Answer: D
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 80 metres?
Options:
A)16 seconds
B)76 seconds
C)26 seconds
D)12 seconds
E)18 seconds
Rationale: Speed of the boat downstream = 15 + 3
= 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 80 m
= 80/5
= 16 seconds.
Answer: A
Answer: A
Question: During a recent track meet, Peter ran x meters of the 100 meter dash in 8 seconds; running at the same rate, how many seconds will it take Peter to run z meters of the 200 meter dash?
Options:
A)xz/8
B)8zx
C)8x/z
D)8/xz
E)8z/x
Rationale: Speed of Peter = x/8 meters per second
Time needed to run z meters = DISTANCE/SPEED = z / (x/8) = 8z/x
Option E
The values 100m and 200m have no role to play here and are just given to confuse you.
Answer: E
Question: Average between two sets of numbers is closer to the set withmore numbers?
Options:
A)70
B)80
C)90
D)95
E)98
Rationale: If on a test three people answered 90% of the questions correctly and two people answered 80% correctly, then the average for the group is not 85% but rather 3×90+2×805=4305=86.3×90+2×805=4305=86.
Here, 90 has a weight of 3 => it occurs 3 times.
Whereas 80 has a weight of 2 => it occurs 2 times.
So the average is closer to 90 than to 80 as we have just calculated.
B
Answer: B
Question: Exactly one side of a certain 10-sided die are red. What is the probability that Kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll?
Options:
A)0.09
B)0.1
C)0.081
D)0.091
E)0.074
Rationale: Total no. of sides = 10
Side that are red = 1
Probability that the die lands with red side up = 1/10
Therefore, Probability that the die does not land with red side up = 1 - 1/10 = 9/10
Probability that Kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll
= (1st roll - non red face) X (2nd roll - non red face) X (3rd roll - red face)
= (9/10) X (9/10) X (1/10)
= 81/1000
= 0.081
C
Answer: C
Question: With out any halt a train travels a certain distance with an average speed of 75 km ph , and with halts it covers the same distance at an average speed of 60 kmph. When it is traveling with halts, how many minutes/per hour does the train halt on an average ?
Options:
A)48 min.
B)12min.
C)15min.
D)18min.
E)19min.
Rationale: With halt in 1 hour the train travels 60km
With out halt for traveling same distance it take 60/75 = 4/5 = 48 minutes
:. 12 minutes is the halting time per hour
ANSWER:B
Answer: B
Question: 20 percent of Andrea's living room floor is covered by a carpet that is 4 feet by 9 feet. What is the area of her living room floor?
Options:
A)14.4
B)180
C)50.4
D)60
E)90
Rationale: 20% of Area of the floor = 4*9 square feet = 36 square feet
i.e. 100% Area of Floor = (36/20)*100 = 180 square feet
Answer: Option B
Answer: B
Question: In a school 50% of the students are younger than 10, 1/20 are 10 years old and 1/10 are older than 10 but younger than 12, the remaining 70 students are 12 years or older. How many students are 10 years old?
Options:
A)50
B)60
C)10
D)20
E)30
Rationale: Let us write the fraction for each group of students
Group A: younger than 10: 50% = 50/100 = 1/2
Group B: 10 years old: 1/20
Group C: older that 10 but younger than 12: 1/10
Group D: 12 years or older: 70 students
The fraction for group A, B and C together is given by
1 / 2 + 1 / 20 + 1 / 10 = 10 / 20 + 1 / 20 + 2 / 20 , common denominator
= 13 / 20 , add numerators
The fraction for group D is given by
20 / 20 - 13 / 20 = 7 / 20 and corresponds to 70 students
If X is the total number of students, then
7 / 20 of X = 70
or (7 / 20) * X = 70
Solve for X
X = 70 * (20 / 7) = 200
Students who are 10 years old have a fraction of 1 / 20 of the total X and their number is equal to
(1 / 20) of 200 = 10 students
correct answer C
Answer: C
Question: A cricketer has certain average for 5 innings. In the 6 inning he scored 90 runs, there by increasing his average by 8 runs. His new average is
Options:
A)42
B)52
C)60
D)48
E)36
Rationale: Let the average for 5 innings be x
Then, (5x+90)/6 = x+8
x = 42
Answer is A
Answer: A
Question: The average salary of Raj and Roshan is Rs. 4000 but the average salary of Raj, Roshan and Thomas is Rs. 5000. What is the salary of Thomas?
Options:
A)4000
B)5000
C)6000
D)7000
E)8000
Rationale: Total salary of Raj and Roshan= 2x4000=8000
Total salary of Raj Roshan and Thomas= 3x5000=15000
Salary of Thomas= 15000-8000= Rs. 7000
Answer: D
Answer: D
Question: 300 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees
Options:
A)10
B)12
C)14
D)16
E)18
Rationale: 26 trees have 25 gaps between them,
Required distance (300/25) = 12
B
Answer: B
Question: A movie buff buys movies on DVD and on Blu-ray in a ratio of 17:4. If she returns 4 Blu-ray movies, that ratio would change to 9:2. If she buys movies on no other medium, what was the original number of movies purchased?
Options:
A)22
B)28
C)77
D)99
E)378
Rationale: if u can just keep an eye on the options
99 is the only multiple of 9 in options given .. SO you can mark it wid in seconds.
Now coming to the process m(D) = 17x and b(D) = 4x
now from the next line the new eqn becomes 17x/ (4x -4) = 9/2
Solving it 34x = 36x -36
x =18
which means m (d) = 306 and b(d) = 72
SO total initially is m(d) + b(d) = 378
E
Answer: E
Question: The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 20 per cent. The two reductions together are equal to a single reduction of
Options:
A)45%
B)40%
C)35%
D)32.5%
E)30%
Rationale: Price = p
initially price reduced by 25% which means new price is 3/4P
Now on this new price further 20 percent is reduced which means the new price is merely 80 percent of 3/4P
==> (3/4)x(4/5)P = 12/20P is the new price after both deduction which is 60 percent of the original value P. This implies this entire series of deduction is worth having discounted 40% of P. So answer is B = 40%
ANSWER:B
Answer: B
Question: In a certain mathematical activity, we have five cards with five different prime numbers on them. We will distribute these five cards among three envelope: all could go in any envelope, or they could be broken up in any way among the envelopes. Then in each envelop, we find the product of all the cards in that envelope: that is the “number” of the envelope. An envelope containing no cards has the number 1. We then put the three envelope numbers in order, from lowest to highest, and that is our set. How many different Q sets can be produced by this process?
Options:
A) 41
B) 89
C) 125
D) 243
E) 512
Rationale: Case 1: 1 used envelope => 1 way
Case 2: 2 used envelopes
- 4-1-0: Choose 4 from 5 cards: 5 ways
- 3-2-0: Choose 3 from 5 cards: 10 ways
Case 3: All envelopes used
- 3-1-1: Choose 3 from 5 andno need to choose 1 from 2: 10 ways
- 2-2-1: Choose 2 from 5 and choose 2 from 3, but two groups are the same => (10X3):2 = 15
Total Q: 1+5+10+10+15=41 => Answer: A
Answer: A
Question: It takes Avery 3 hours to build a brick wall while Tom can do it in 2.5 hours. If the two start working together and after an hour Avery leaves, how much time will it take Tom to complete the wall on his own?
Options:
A)25 minutes.
B)30 minutes.
C)40 minutes.
D)55 minutes
E)1 hour and 20 minutes
Rationale: Avery's efficiency is 100/3 = 33%
tom's = 100/2.5= 40%
they worked together for 1 hour and finished 73% of the job
remaining = 27 %
tom will complete 40% in 60 minutes , 20% in 30 minutes and ,
7% in 60*7/40 minutes = 10.5 minutes
time taken by tom to finish the remaining on his own = 30+10.5 = 40.5 minutes (adjusting for the 0.333) ~ 40 minutes
ANSWER:C
Answer: C
Question: A and B together have $1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have?
Options:
A)$310
B)$395
C)$484
D)$512
E)$542
Rationale: 4/15 A = 2/5 B
A = 2/5 * 15/4 B
A = 3/2 B
A/B = 3/2
A:B = 3:2
B's share = 1210*2/5 = $484
Answer is C
Answer: C
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:
Options:
A)44 years
B)40 years
C)50 years
D)60 years
E)None of these
Rationale: Lets assume fathers,mothers and child's age before 3 years is x,y,z respe.
therefore (x+y+z)/3=27
now x+y+z=27*3=81
and (y-2+z-2)/2=20
y+z=40
on calculating both equations x=37
hence present age x+3=40
ANSWER:B
Answer: B
Question: Tough and Tricky questions: Word Problems.
AC Car Company wants to manufacture a new car known as Model X, and it is trying to determine how many cars it needs to sell in order to make an annual profit of $30,500,000. The annual fixed costs for Model X total $50,200,000. In addition, each Model X car has an average cost of $5,000 per vehicle to manufacture. If the Company forecasts it will sell 20,000 Model X cars this year, at what price must the Company sell the car to achieve the desired annual profit?
Options:
A)$4,035
B)$4,036
C)$9,035
D)$16,140
E)$36,140
Rationale: The AC company plans to make a profit of $30,500,000 and it needs to earn the fixed costs of $50,200,000, so it needs to earn $80,700,000 on top of the costs for the production of the 20,000 cars.
Therefore, price of each car needs to be the unit costs plus $80,700,000/20,000. After removing the 0's, we end with the unit costs plus $8,070/2, which is $5,000 plus $4,035. Therefore, Answer C is correct.
Answer: C
Question: A goods train leaves a station at a certain time and at a fixed speed. After 6 hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph. This train catches up the goods train in 4 hours. Find the speed of the goods train.
Options:
A)36 kmph
B)40 kmph
C)30 kmph
D)42 kmph
E)None of these
Rationale: Let the speed of the goods train be x kmph.
Distance covered by goods train in 10 hours
= Distance covered by express train in 4 hours.
∴ 10x = 4 × 90 or x = 36.
So, speed of goods train = 36 kmph.
Answer A
Answer: A
Question: What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?
Options:
A)4%
B)13%
C)20%
D)23%
E)26%
Rationale: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.
Number of such number =14
Required % = (14/70)x100 % =20%
answer :C
Answer: C
Question: Find the value of X: 2a^2-7a+10 = 14
Options:
A)7
B)5
C)6
D)4
E)2
Rationale: Using the elimination method substitute options for x and find the correct option.
Answer: D
Answer: D
Question: If one type of tobacco costs Re.1/- per kg and other type costs Rs. 5/- per kg. What quantity of first type and second type are mixed so that 100 kg of mixture costs Rs. 100/-?
Options:
A)50 kg
B)100 kg
C)150 kg
D)200 kg
E)250 kg
Rationale: 100 kg of first type.
ANSWER:B
Answer: B
Question: The moon revolves around the earth at a speed of approximately 0.2 kilometers per second. This approximate speed is how many kilometers per hour?
Options:
A)60
B)720
C)62.5
D)3,600
E)3,672
Rationale: moon revolves around the earth at a speed of 1.02kilometers per second.
one hour equal to 60 minutes.
one minute equals to 60 seconds. so one hour equals to 3600seconds.
so one hour, speed= 0.2*3600=720kilometers per hour.
Option B is correct
Answer: B
Question: Find the odd man out. 1, 16, 81, 255, 625, 1296
Options:
A)255
B)1296
C)81
D)1
E)625
Rationale: Explanation :
The pattern is 1^4, 2^4, 3^4, 4^4, 5^4, 6^4
Hence, in place of 255, the right digit is 44 = 256
Answer : Option A
Answer: A
Question: Two trains for Delhi leave Jaipur at 8:30 am and 9:00 am and travel at 60 km/hr and 75 km/hr respectively. How many km from Jaipur will the two trains meet?
Options:
A)150 km
B)127 km
C)1717 km
D)166 km
E)177 km
Rationale: ANSWER: A
Answer: A
Question: How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 2 can be used only once?
Options:
A)20
B)150
C)225
D)300
E)320
Rationale: 4 options for the first digit: 2, 4, 6, 8;
5 options for the second digit: 1, 3, 5, 7, 9;
4 options for the third digit: 2, 3, 5, 7;
4 options for the fourth digit: 0, 3, 6, 9.
Four digit # possible without the restriction (about the digit 2): 4*5*4*4=320
Numbers with two 2-s, 2X2X 1*5*1*4=20.
Thus there are 320-20=300 such numbers.
Answer: D.
Answer: D
Question: There are two positive numbers in the ratio 3:11. If the larger number exceeds the smaller by 32, then what is the smaller number?
Options:
A)8
B)11
C)12
D)15
E)17
Rationale: Let the two positive numbers be 3x and 11x respectively.
11x - 3x = 32
8x = 32 => x = 4
Thus, the smaller number = 3x = 12.
Answer: C
Answer: C
Question: If two dice are thrown together, the probability of getting an even prime number on the dice is
Options:
A)1/36
B)1/18
C)1/13
D)1/9
E)5/36
Rationale: The number of exhaustive outcomes is 36.
Let E be the event of getting an even number prime number on the dice.
P(E) = 1/36
A)
Answer: A
Question: A trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg. In order to earn a profit of 30%, what should be the sale price of the mixed tea?
Options:
A)23.75
B)22
C)20.8
D)19.2
E)None of these
Rationale: C.P. of mixture = 80×15+20×20 /80+20=16
∴ S.P. = (100+30)/100×16=20.8
Answer C
Answer: C
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
Options:
A)298
B)180
C)289
D)177
E)123
Rationale: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer: B
Answer: B
Question: In how many ways 4 boys and 3 girls can be seated in a row so that they are alternate.
Options:
A)144
B)288
C)12
D)256
E)None
Rationale: Solution: Let the Arrangement be,
B G B G B G B
4 boys can be seated in 4! Ways.
Girl can be seated in 3! Ways.
Required number of ways,
= 4!*3! = 144.
Answer: Option A
Answer: A
Question: What is the remainder when 43^89 is divided by 5?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: The units digit of the exponents of 3 cycle in a group of 4: {3, 9, 7, 1}
89 has the form 4k+1 so the units digit of 43^89 is 3.
The remainder when dividing by 5 is 3.
The answer is D.
Answer: D
Question: The average (arithmetic mean) of the even integers from 0 to 40 inclusive is how much greater than the average (arithmetic mean) of the even integers from 0 to 20 inclusive?
Options:
A)5
B)8
C)10
D)15
E)20
Rationale: The sum of even numbers from 0 to N is 2 + 4 +...+ N
= 2(1 + 2 + ...+ N/2)
= 2(N/2)(N/2+1)/2 = (N/2)(N/2+1)
The average is (N/2)(N/2+1)/(N/2+1) = N/2
The average of the even numbers from 0 to 40 is 40/2 = 20
The average of the even numbers from 0 to 20 is 20/2 = 10
The answer is C.
Answer: C
Question: The HCF and LCM of two numbers m and n are respectively 5 and 210. If m + n = 75, then 1/m + 1/n is equal to
Options:
A)1/14
B)3/35
C)5/37
D)2/35
E)None
Rationale: Answer
We have, m x n = 5 x 210 = 1050
âˆ´ 1/m + 1/n = (m + n)/mn = 75/1050 = 1/14
Correct Option: A
Answer: A
Question: If x^2 − 2x − 15 = (x + r)( x + s) for all values of x, and if r and s are constants, then which of the following is a possible value of (r + s)^2?
Options:
A)8
B)2
C)− 2
D)− 3
E)4
Rationale: We know that given ax^2 + bx + c = 0, Sum of the roots = -b/a and product of the roots = c/a.
The roots here are -r and -s.
-r - s = -(-2)/1 = r + s = -2
(-r)*(-s) = -15/1 = rs
So one of r and s is -5 and the other is 3. So (r + s)^2 could be 4.
Answer (E)
Answer: E
Question: There are 3 income earning members in a family namely X,Y&Z. .Total monthly income of the family is $12200.Ratio of their income 12:15:16.Find out the income of Z?
Options:
A)$5681.45
B)$4539.54
C)$3556.25
D)$6528.98
E)$2926.38
Rationale: Ratio of their income 12+15+16=43. Income of Z = 16/43 *12200=$4539.54 Answer: B
Answer: B
Question: Out of 20 students studying in a class, 7 are from Maharashtra, 5 are from Karnataka and 3 are from Goa. Four students are to be selected at random. What are the chances that at least one is from Karnataka?
Options:
A)12â„13
B)11â„13
C)10â„15
D)1â„15
E)51/71
Rationale: Total possible ways of selecting 4 students out of 20 students =20C4 =4845
The no. of ways of selecting 4 students in which no student belongs to Karnataka = 15C4=1365
âˆ´ Hence no. of ways of selecting at least one student from Karnataka = 20C4 â€“ 15C4 =3480
âˆ´ Probability = 3480â„4845 = 51/71
Answer E
Answer: E
Question: A corporation that had $2 billion in profits for the year paid out $100 million in employee benefits. Approximately what percent of the profits were the employee benefits? (Note: 1 billion = 10^9)
Options:
A)50%
B)20%
C)5%
D)2%
E)0.2%
Rationale: required answer = [employee benefit/profit] *100
=[(100 million)/(2 billion)]*100
=[(100*10^6)/(2*10^9)]*100
=(50/1000)*100
=5%
So answer is (C)
Answer: C
Question: The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.72. Find the principal?
Options:
A)2277
B)2667
C)3600
D)2766
E)1800
Rationale: P = 72(100/5)^2 => P = 1800
Answer: E
Answer: E
Question: How many odd numbers between 10 and 1,300 are the squares of integers?
Options:
A)12
B)13
C)14
D)15
E)17
Rationale: The square of an odd number is an odd number:
10 < odd < 1,000
10 < odd^2 < 1,000
3.something < odd < 31.something (by taking the square root).
So, that odd number could be any odd number from 5 to 31, inclusive: 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, and 31.
17 numbers.
Answer: E.
Answer: E