divelab/Sys2Bench huggingface dataset:
Question: What is the number of integers from 1 to 500 (inclusive) that are divisible by neither 10 nor by 15?
Options:
A)170
B)250
C)300
D)560
E)420
Rationale: In 500 consecutive numbers, number of multiples of 10 = 500/10 = 50 (Ignore decimals)
In 500 consecutive numbers, number of multiples of 15 = 500/15 = 33
Number of multiples of 10*15 i.e. 150 = 500/150 = 3
Number of integers from 1 to 500 that are divisible by neither 10 nor by 15 = 500 - (50 + 33 - 3) {Using the concept of sets here) = 420
Answer is E
Answer: E
Question: In how many different number of ways a Committee of 3 person of can be selected from 5 men and 3 women such that at least 1 women is included in the committee
Options:
A)40
B)46
C)52
D)54
E)56
Rationale: 1W 2M 2W 1M 3W
= 3C1 × 5C2 + 3C2 × 5C1 + 3C3s
= 3 × (5 × 4)/2 + 3 × 5 + 1
= 30 + 15 + 1 = 46
Total 5M 3W
8C3 = 56
5C3 = 10
At least one women = total - with out women
At least one women = 56 - 10 = 46
B)
Answer: B
Question: For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 60?
Options:
A)10
B)15
C)8
D)12
E)20
Rationale: 4n+7 > 1
4n> -6
n > -(3/2)
n> -1.5 (n = -1, 0, 1 ,2 3........ upto infinity)
From second constraint
4n+7 < 60
4n< 53
n < 13. 25
n = (-infinity, .......-3, -2, -1, 0, 1, 2, .........upto 13)
Combining the two
-1.5 < n<13.25
n = 1 to 13 (48 integers)
and n = -1 and 0
so 15 integers.
B
Answer: B
Question: The average (arithmetic mean) of four different positive integers is 13. If the first of these integers in 3 times the second integer and the second integer is 2 less than the third integer, what is the least possible value of the fourth integer?
Options:
A)4
B)3
C)2
D)1
E)0
Rationale: Let the second integer be x and the fourth be a.
Then [3x + x + (x+2) + a]/4 = 13
=> 5x + 2 + a = 52
=> 5x + a = 50
=> a = 50 - 5x
From the above equation we can see that a is minimum when x is maximum, provided both are positive
The maximum value that x can take in the above equation while still keeping a positive is x=10
This gives us a=50 - 50 = 0
Therefore the minimum value that the fourth integer can have is 0. Option E
Answer: E
Question: Alok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 6 ice-cream cups. The cost of each chapati is Rs.6, that of each plate of rice is Rs.45 and that of mixed vegetable is Rs.70. The amount that Alok paid the cashier was Rs.1111. Find the cost of each ice-cream cup?
Options:
A)25
B)66
C)77
D)50
E)91
Rationale: Let the cost of each ice-cream cup be Rs.x
16(6) + 5(45) + 7(70) + 6(x) = 1111
96 + 225 + 490 + 6x = 1111
6x = 300 => x = 50.
Answer: D
Answer: D
Question: Which of the following integers doesn't have a divisor greater than 1 that is the square of an integer?
Options:
A)12
B)36
C)100
D)61
E)72
Rationale: Prime Factorization
12=2*2*3=2^2*3. Includes a perfect square of 4.
36=2*2*3*3=2^2*3^2. Includes perfect squares of 4 and 9.
100=2*2*5*5=2^2*5^2. Includes the perfect squares 4 and 25.
61=61*1. 61 is prime, no perfect squares so a possibility.
72= 2*3*2*3*2=6^2*3. Includes perfect square of 36.
28=2*2*7=2^2*7. Includes a perfect square of 4.
All but 61 have a perfect square as a factor so the answer is D.
12=4*3. Perfect square of 4.
36=4*9. Perfect squares of 4 and 9.
100=4*25. Perfect squares 4 and 25.
61=61*1. No perfect squares.
72= 36*2. Perfect square of 36.
Answer: D
Question: A card shop contains 10 birthday cards, 10 holiday cards, and 9 graduation cards. If three cards are purchased at random from the shop, what is the probability that the three cards will be of the same type?
Options:
A)3/29
B)12/58
C)12/840
D)7/841
E)12/841
Rationale: It doesn't matter which type of card you choose, so:
Probability of choosing 1st card: 1
Probability of choosing 2nd card of the same type: 4/29
Probability of choosing 3rd card of the same type: 3/29
Multiply and you get 12/841
Answer E.
Answer: E
Question: Money invested at x%, compounded annually, triples in value in approximately every 112/x years. If $1500 is invested at a rate of 8%, compounded annually, what will be its approximate worth in 28 years?
Options:
A)$3,750
B)$5,600
C)$13,500
D)$15,000
E)$22,500
Rationale: x=8%
112/x years=112/8=14 years
Now, money triples every 14 years
Therefore, in 14 yrs , if $1500 triples to $4500, in 28 years, it will again triple to $4500*3=$13,500
Answer C
Answer: C
Question: One-fifth of Ramu’s expenditure is equal to one-half of his savings. If his monthly income is Rs.6300 how much amount does he save?
Options:
A)Rs.1550
B)Rs.1800
C)Rs.2000
D)Rs.2350
E)Rs.2450
Rationale: Let the saving be Rs. x
Therefore, Expenditure = Rs. (6300-x)
then, (6300-x)* 1/5 = x* 1/2
=> 1260- x/5 = x/2
=> 1260= x/2 + x/5
=> 7x/10 = 1260
x= 1800
ANSWER:B
Answer: B
Question: If 1⁄8 of 2⁄3 of 4⁄5 of a number is 12 then 30 per cent of the number will be
Options:
A)48
B)64
C)54
D)42
E)None of these
Rationale: Let the number be x.
and 1⁄8 of 2⁄3 of 4⁄5 × x = 12
∴ 3x⁄10 = 54
Answer C
Answer: C
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
Options:
A)33 1/9%
B)33 1/6%
C)33 1/3%
D)33 8/3%
E)31 1/3%
Rationale: 675 ---- 225
100 ---- ? => 33 1/3%
Answer: C
Answer: C
Question: How many numbers between 0 and 1370 have a prime tens digit and a prime units digit?
Options:
A)204
B)212
C)220
D)228
E)236
Rationale: From 1-9 there are 4 prime numbers {2, 3, 5, 7}. The 10s and 1s of the number must be made with these numbers. The total number of combinations is 4*4 = 16. Thus every set of 100 consecutive positive integers has 16 such numbers.
From 0 to 1300, there 16*13 = 208 such numbers.
From 1301 to 1370, the 10s units can only use 3 numbers {2, 3, 5}. 3*4 =12.
The total number is then 208+12 = 220
The answer is C.
Answer: C
Question: A dishonest person wants to make a profit on the selling of milk. He would like to mix water (costing nothing) with milk costing 33 $ per litre so as to make a profit of 50% on cost when he sells the resulting milk and water mixture for 36$. In what ratio should he mix the water and milk?
Options:
A)1:20
B)1:10
C)3:8
D)3:4
E)3:2
Rationale: First of all, let's consider 1 liter of the stuff he is going to sell --- naive customers think it's pure milk, but we know it's some milk-water mixture. He is going to sell this liter of milk-water for $36.
This $36 should be a 50% increase over cost. Here, we need to think about percentage increases as multipliers.
Using multipliers
(cost)*1.50 = $36
cost = 36/1.5 = 360/12 = $24
If he wants a 20% increase over cost on the sale of one liter of his milk-water, the cost has to be $24.
Well, a liter of milk costs $33, so if he is going to use just $30 of milk in his mixture, that's 24/33 = 8/11 of a liter. If milk is 8/11 of the liter, then water is 3/11 of the liter, and the ratio of water to milk is 3:8. Answer choice(C)
Answer: C
Question: What percentage of numbers from 1 to 50 have squares that end in the digit 5?
Options:
A)1
B)14
C)10
D)21
E)22
Rationale: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 5. Such numbers from 1 to 50 are 5,15,25,35,45.
Number of such numbers = 14.
Required percentage = (5/50 * 100) = 10%
ANSWER:C
Answer: C
Question: A polygon has 35 diagonals. How many sides does it have?
Self made
Options:
A) 10
B) 13
C) 14
D) 15
E) 16
Rationale: The best way to solve this problem is to use the formula: An n sided polygon can have n*(n - 3)/2 diagonals
n*(n - 3)/2 = 35
n*(n - 3) = 70
Substitute n from the answer choices. n = 10
Answer: A
Answer: A
Question: Find the one which does not belong to that group ?
Options:
A)233
B)288
C)608
D)287
E)112
Rationale: Explanation:
The sum of the digits in 508, 328, 706 and 148 is 13, but not in 608.
Answer:C
Answer: C
Question: A, B, and C were to be paid in proportion to the part of work they did while working on the same piece of work. A and B individually can finish the piece of work in 12 days and 15 days respectively. They worked together for five days and then C completed the remaining work all alone. If $1350 was the net sum to be paid for the entire work, what was the average daily wage of B?
Options:
A)$144
B)$90
C)$60
D)$54
E)$48
Rationale: The correct answer is B.
Answer: B
Question: For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 105 units raises the average to 55 units per day, what is the value of n?
Options:
A)8
B)10
C)12
D)14
E)16
Rationale: The daily production was raised by 5 units for n days, which has a weighting of 5n.
5n = 105-55 = 50
n = 10
The answer is B.
Answer: B
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 Rs. 900 more than D, what is B's share?
Options:
A)Rs. 500
B)Rs. 1800
C)Rs. 2000
D)Rs. 2500
E)none of the above
Rationale: Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.
Then, 4x - 3x = 900
x = 900.
B's share = Rs. 2x = Rs. (2 x 900) = Rs. 1800.
Answer = B
Answer: B
Question: A man can row downstream at 20 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
Options:
A)15,2
B)15, 4
C)15, 8
D)15, 5
E)15,7
Rationale: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 20 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 30 => x = 15, y = 5.
Answer:D
Answer: D
Question: A man travels 100km by train at 40km/hr, 200km by ship at 20km/hr, 300km by aeroplane at 100km/hr and 100km by car at 50km/hr. What is the average speed for the entire distance?
Options:
A)35.3km/hr
B)40km/hr
C)48.9km/hr
D)52.6km/hr
E)27.6km/hr
Rationale: Total distance traveled = 100+200+300+100 = 700km
Total time taken = 100/40 + 200/20 + 300/100 + 100/50 = 17.5 hrs
Average speed = 700/17.5 = 40km/hr approximately ;
Answer is B
Answer: B
Question: A baker filled with a measuring cup with 3/4 cup water. He poured 1/2 of the water into the batter. How much water will the baker needed to add what is left in the cup to have 50% more than what he started with?
Options:
A)1/8 cup
B)3/8 cup
C)1/4 cup
D)1/2 cup
E)6/8 cup
Rationale: 3/4 is the original water in cup .half in batter.So left is 3/8.
so 50% more than what he started was = 3/4+1/2*(3/4)=9/8
Amount of water needed to add = 9/8 - 3/8=6/8
ANSWER:E
Answer: E
Question: How many Kg of sugar must be added to 30 Kg of 2% solution of sugar and water to increase it to a 10% solution?
Options:
A)2.6Kg
B)4Kg
C)3.4Kg
D)1.8Kg
E)None of these
Rationale: Explanation :
Solution: Amount of sugar in 30 Kg solution = (2/100 * 30) Kg = 0.6 Kg.
Let x Kg of sugar be added. Then, (0.6+x)/(30+x) = 10/100
60+100x = 300+10x
x = 240/90 = 8/3 = 2.6
Answer : A
Answer: A
Question: A train of length L is traveling at a constant velocity and passes a pole in t seconds. If the same train travelling at the same velocity passes a platform in 6t seconds, then what is the length of the platform?
Options:
A)L
B)3L
C)5L
D)7L
E)9L
Rationale: The train passes a pole in t seconds, so velocity v = L/t
(L+P)/v = 6t
(L+P) / (L/t) = 6t
P = 5L
The answer is C.
Answer: C
Question: How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 20-percent solution?
Options:
A)45
B)33 1/3
C)27
D)16 2/3
E)15
Rationale: How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 20-percent solution?
3% of a 50 liter solution is 1.5L. So you are trying to determine how many liters must a solution be for the 1.5L to represent 20% of the solution. Set up an inequality and solve for x:
1.5/x = 1/20
x = 30
Since you need a 15L solution, you must evaporate 45 of the original 50L solution to get a 20% solution.
Answer is A.
Answer: A
Question: By selling 50 meters of dress. I gain the selling price of 15 meters. Find the gain percent?
Options:
A)52 6/9%
B)45 8/7%
C)42 6/7%
D)12 8/3%
E)56 6/7%
Rationale: C
SP = CP + g
50 SP = 50 CP + 15 SP
35 SP = 50 CP
35 --- 15 CP gain
100 --- ? => 42 6/7%
Answer: C
Question: In an exam, Amar scored 64 percent, Bhavan scored 36 percent and Chetan 44 percent. The maximum score awarded in the exam is 800. Find the average mark scored by all the three boys?
Options:
A)384
B)127
C)276
D)998
E)267
Rationale: Average mark scored by all the three boys =
[64/100 (800) + 36/100 (800) + 44/100 (800)] / 3 = 384.Answer: A
Answer: A
Question: √{(8.2)(10^9)} is closest to which of the following?
Options:
A)6,000
B)12,000
C)30,000
D)50,000
E)90,000
Rationale: √{(8.2)(10^9)} = √{(82)(10^8)} = √(82)√(10^8) = (√82) * 10,000 which is about 90,000.
The answer is E.
Answer: E
Question: A bank offers 5% C.I. calculated on half-yearly basis . A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is?
Options:
A)126
B)121
C)165
D)134
E)123
Rationale: Amount = [1600 * (1 + 5/(2 * 100)2 + 1600 * (1 + 5/(2 * 100)]
= [1600 * 41/40(41/40 + 1)
= [(1600 * 41 * 81)/(40 * 40)]
= Rs. 3321.
C.I. = 3321 - 3200 = Rs.121.
Answer:B
Answer: B
Question: If 9 is added to thrice a number and this sum is multiplied by 6, the result is the same as if the number is multiplied by 7 and 10 is added to the product. What is the number?
Options:
A)-7
B)-8
C)-9
D)-10
E)-11
Rationale: let the number be x;
6(9+3x)=7x+10;
x=-11
ANSWER:E
Answer: E
Question: At a company, the average wage of male employees is $6 per hour, and the average wage of female employees is $8 per hour. If the average wage of all employees is $7.5 per hour, what is the ratio of the number of male employees to the number of female employees?
Options:
A)1 to 3
B)2 to 3
C)3 to 2
D)5 to 3
E)2 to 1
Rationale: Average hourly wage of male employees = 6 $
Average hourly wage of female employees = 8 $
Average hourly wage of all employees = 7.5 $
Let number of male employees = m
number of female employees = f
7.5 = (6m + 8f ) / m+f
=>7.5m + 7.5f = 6m + 8f
=> .15m = .5f
=> m/f = .5/.15 = 1/3
Answer A
Answer: A
Question: There is food for 760 men for 22 days. How many more men should join after two days so that the same food may last for 19 days more?
Options:
A)11
B)40
C)66
D)55
E)44
Rationale: 760 ---- 22
760 ---- 20
x ----- 19
x*19 = 760*20
x = 800
760
-------
40
Answer:B
Answer: B
Question: Find the odd pair of numbers
1) 55 - 42
2) 69 - 56
3) 48 - 34
4) 95 - 82
5) 45 - 32
Options:
A)55-42
B)69-56
C)48-34
D)95-82
E)45-32
Rationale: minus the numbers
55-42=13
69-56=13
48-34=14
95-82=13
45-32=13
here 48-34 = 14 which is not similar to the other, so 48 - 34 is the odd pair of numbers. correct answer (C)
Answer: C
Question: An article costing rs.160 is sold at 20% discount on a mark-up price. What is the selling price after
discount?
Options:
A)106
B)116
C)128
D)136
E)146
Rationale: 160*80/100=128
ANSWER:C
Answer: C
Question: Evaluate: 37 - 18÷3×2 =
Options:
A)20
B)25
C)27
D)22
E)17
Rationale: According to order of operations, 18÷3×2(division and multiplication) is done first from left to right
18÷3×2 = 6 × 2 = 12
Hence
37 - 18÷3×2 = 37 - 12 = 25
correct answer B)25
Answer: B
Question: Three dice are thrown together, Find the probability of getting a total of 5?
Options:
A)1/2
B)1/5
C)3/8
D)3/14
E)1/36
Rationale: Three different dice are thrown at the same time.
Therefore, total number of possible outcomes will be 63 = (6 × 6 × 6) = 216.
Number of events of getting a total of 5 = 6
i.e. (1, 1, 3), (1, 3, 1), (3, 1, 1), (2, 2, 1), (2, 1, 2) and (1, 2, 2)
Therefore, probability of getting a total of 5
P(E1) = Number of favorable outcomes/Total number of possible outcome
= 6/216
= 1/36
Answer: E
Question: The average marks in mathematics scored by the pupils of a school at the public examination were 39. If four of these pupils who actually scored 5, 12, 15 and 19 marks at the examination had not been sent up, the average marks for the school would have been 44. Find the number of pupils sent up for examination from the school?
Options:
A)25
B)20
C)30
D)35
E)40
Rationale: 39x = 5 + 12 + 15 + 19 + (x â€“ 4)44
x = 25
ANSWER A
Answer: A
Question: If xy > 0, 1/x + 1/y = 6, and 1/xy = 5, then (x+y)/6 = ?
Options:
A)1/25
B)1/6
C)1/5
D)5
E)6
Rationale: (1/X+1/Y)=6 canbe solved as {(x+y)/xy}=5. Substituting for 1/xy=5, we get
x+y=6/5
==> (x+y)/6= 6/(5*6)=1/5.
C
Answer: C
Question: A function g(n), where n is an integer, is defined as the product of all integers from 1 to n. How many of the followings must be a prime number?
g(12) + 2; g(12) + 3; g(12) + 4; and g(12) + 5?
Options:
A)1
B)2
C)3
D)4
E)none
Rationale: g(12) is the product of all integers from 1 to 12, so g(12) = 12!
Thus g(12) is a multiple of all the integers from 1 to 12.
Then g(12) is a multiple of 2, 3, 4, and 5.
2 divides g(12)+2
3 divides g(12)+3
4 divides g(12)+4
5 divides g(12)+5
The answer is E.
Answer: E
Question: A man sells a house for Rs.5,00,000 and loses something, if he had sold it for Rs.6,00,000, his gain would have been trible the former loss. Find the cost price of the horse?
Options:
A)5,50,000
B)5,25,000
C)5,20,000
D)5,02,000
E)6,00,200
Rationale: CP = SP + 1CP = SP - g
5,00,000 + x = 6,00,000 - 3x
4x = 1,00,000=> x = 2000
CP = 5,00,000 +2000 = 5,02,,000
Answer: D
Answer: D
Question: Set J consists of the terms {a, b, c, d, e}, where e > d > c > b > a > 2. Which of the following operations would decrease the standard deviation of Set J?
Options:
A)Divide each term by 2.2
B)Divide each term by b/c
C)Multiply each term by −1
D)Divide each term by d/e
E)Multiply each term by c
Rationale: CONCEPT: Standard Deviation is Defined as Average Deviation of Terms in the set from the Mean value of the set. i.e.
1) It depends on the separation between the successive terms of the set
2) If a Constant Value is Added/Subtracted in every terms of set then the Separation between successive terms does NOT change Hence S.D. remains Constant
3) If a Constant Value is Multiplied in every terms then the Separation between succesive terms gets multiplied by the constant Hence S.D. remains gets multiplied by same Number
A
Answer: A
Question: Alan bought 180 packets of chocolate. He was able to sell 1/3 of them at a 5% profit, another 1/3 of them at zero profit and the remainder was sold at a 10% loss. Find the total profit or loss made by Alan after selling those 150 packets. A packet sold at a loss had a price of $9.
It's a bit confusing to say 5% of profit. Please provide an intuitive answer if possible. Thanks!!
Options:
A)0
B)Profit of $20
C)Loss of $25
D)Profit of $30
E)Loss of $30
Rationale: A packet sold at a 10% loss had a price of $9, thus the cost of a packet is $10.
60 packets was sold at a 5% profit --> gives profit of 10*0.05*60 = $30.
60 packets was sold at a 10% loss --> gives loss of 10*0.1*60 = $60.
The overall loss is $30 - $60 = $30.
Answer: E.
Answer: E
Question: Each of the positive integers a, b, and c is a three-digit integer. If each of the digits 0 through 8 appears in one of these three integers, what is the minimum possible value of the sum of a, b, and c?
Options:
A)45
B)666
C)711
D)801
E)1368
Rationale: According to the stem we should use the digits 0 through 7 to construct 3 three-digit integers, so that their sum is as small as possible.
To minimize the sum, minimize the hundreds digits of a, b, and c, so make them 1, 2, and 3.
Next, minimize tens digits. Make them 0, 4, and 5.
Use the remaining digits (6, 7, and 8) for units digits.
So, a would be 106, b would be 247 and c would be 358.
106 + 247 + 358 = 711.
Answer: C.
Answer: C
Question: what is sum of fist 10 prime numbers?
Options:
A)128
B)129
C)117
D)123
E)121
Rationale: primes are of the form 6n+1 or 6n-1
1st 10 prime numbers are = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
sum of above numbers = 129
B
Answer: B
Question: Rahim bought 65 books for Rs.6500 from one shop and 35 books for Rs.2000 from another. What is the average price he paid per book ?
Options:
A)80
B)138
C)100
D)129
E)85
Rationale: Average price per book
= (6500+ 2000) / (65 + 35)
= 8500 / 100
= Rs.85
Answer:E
Answer: E
Question: My brother is 3 years elder to me. My father was 28 years of age when my sister was born while my mother was 26 years of age when I was born. If my sister was 4 years of age of when my brother was born, then, what was the age of my father and mother respectively when my brother was born?
Options:
A)32 yrs, 23 yrs
B)32 yrs, 29 yrs
C)35 yrs, 29 yrs
D)35 yrs, 33 yrs
E)none
Rationale: Sol.
Clearly, my brother was born 3 years before I was born and 4 years after my sister was born.
So, father's age when brother was born = (28 + 4) = 32 years.
mother's age when was born = (26 - 3) years = 23 years.
Answer A
Answer: A
Question: Jane and Thomas are among the 8 people from which a committee of 3 people is to be selected. How many different possible committees of 3 people can be selected from these 8 people if at least one of either Jane or Thomas is to be selected?
Options:
A)24
B)28
C)32
D)36
E)40
Rationale: The total number of ways to choose 3 people from 8 is 8C3 = 56.
The number of committees without Jane or Thomas is 6C3 = 20.
There are 56-20 = 36 possible committees which include Jane and/or Thomas.
The answer is D.
Answer: D
Question: An amount of money is to be distributed among Faruk, Vasim and Ranjith in the ratio 3 : 5 : 8. If Vasims share is Rs. 1500, what is the difference between Faruk's and Ranjith's shares?
Options:
A)s 1200
B)s 1500
C)s 1600
D)s 1900
E)s 1700
Rationale: Explanation :
Let P = Faruk, Q = Vasim, R = Ranjith
Let P = 3x, Q = 5x and R = 8x.
Then, 5x = 1500 ? x = 300. P=900,Q=1500 and R = 2400.
Hence, (R - p) = (2400 - 900) = 1500
Answer : B
Answer: B
Question: If (1+k)l=l, which of the following must be true?
Options:
A)k=-1 or l=0
B)k=0 or l=0
C)k=1 or l=1
D)k=-1 or l=-1
E)k=0 or l=1
Rationale: By only having kl=0, we cannot say answer is B as A and E options also satisfy the condition kl=0. ans B
Answer: B
Question: The surface area of a sphere is 4πR2, where R is the radius of the sphere. If the area of the base of a hemisphere is 3, what is the surface area T of that hemisphere?
Options:
A) 6/π
B) 9/π
C) 6
D) 9
E) 12
Rationale: Given Area of the base of a hemisphere is 3 = PI * R^2
Thus R = Sqrt ( 3 / PI ) .
Surface area of whole sphere = 4*PI*R^2 .
= 4 * PI * 3 / PI
= 12 .
Since the hemisphere is half of a sphere the Surface area of the hemisphere = 12 / 2
= 6 ( curved part , not including the flat rounded base ) .
But the total surface area = 6 + Area of the base of a hemisphere .
= 6 + 3
= 9.
Answer is D !!
Answer: D
Question: A group of 4 investment bankers and 5 clients recently frequented the Bonbon Ribs Restaurant. The total bill for the meal, including 20% gratuity, came to $756. On average, how much did the meal of each individual cost before gratuity?
Options:
A)$160
B)$70
C)$90
D)$80
E)$55
Rationale: 4 IBs and 5 clients - so total 9 people
The bill $756 includes 20% gratuity... so the actual cost of dinner was $630
Now, the cost per person will be $630/9 which is $70
Option B
Answer: B
Question: Two water pumps, working simultaneously at their respective constant rates, took exactly six hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at its constant rate?
Options:
A)8
B)10
C)12
D)14
E)16
Rationale: Let x be the rate of the slower pump. Then 1.5x is the rate of the faster pump.
Both pumps together can fill 1/6 of the pool each hour.
2.5x = 1/6
x = 1/15
1.5x = 1.5/15 = 1/10
The faster pump could fill the pool in 10 hours.
The answer is B.
Answer: B
Question: A boat having a length 4 m and breadth 3 m is floating on a lake. The boat sinks by 1cm when a man gets on it. The mass of the man is:
Options:
A)12 kg
B)120 kg
C)72 kg
D)96 kg
E)None of these
Rationale: Explanation:
Volume of water displaced = (4 x 3 x 0.01) m3
= 0.12 m3.
∴ Mass of man = Volume of Water displaced x Density of water
= (0.12 x 1000)kg
= 120 kg.
Answer: B
Answer: B
Question: A sum of money lent out at S.I. amounts to Rs. 850 after 2 years and to Rs. 1020 after a further period of 5 years. The sum is?
Options:
A)s.440
B)s. 500
C)s. 540
D)s. 782
E)s. 840
Rationale: S.I for 5 years = (1020 - 850) = Rs. 170.
S.I. for 2 years = 170/5 * 2 = Rs. 68.
Principal = (850 - 68) = Rs. 782.
ANSWER:D
Answer: D