mathewhe/aqua_rat huggingface dataset:
Question: If A,B,C are three integers and AB+C is even ; which of the following must be true? A)C is even B)B is Odd C)AB is Odd
(A) I only
(B) II only
(C) None of the above
(D) II,III only
(E) III only
Rationale: If AB is Odd then C will not even. O+E = O
If AB is even then C will not be odd.
If B is even AB is even always. But If C is Odd E+O = O
If B is Odd AB is even or odd depends on A
None of the above are true.
Answer : C
Answer: (C) None of the above
Question: The ratio of boys to girl in a school is 5:4. If there are 1500 boys in the school, how many girls are there?
(A) 300
(B) 1200
(C) 1500
(D) 1800
(E) 2000
Rationale: Think of the ratio as 5 parts: 4 parts.
Divide 1500 by 5 to find 1 "part" of the ratio.
1500/5 = 300
Multiply this by 4 to get 4 "parts" of the ratio.
300*4 = 1200
There are 1200 girls in the school.
The answer is B
Answer: (B) 1200
Question: A and B together can do a work in 3 days. If A alone can do it in 12 days. In how many days can B alone do it?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 25
Rationale: A
4
1/3 â€“ 1/12 = 1/4 => 4
Answer: (A) 4
Question: What is 25 % of 4/12 of 520?
(A) 49
(B) 56
(C) 60
(D) 43
(E) 70
Rationale: 25 % = 25 / 100 = 1/4 of 4/12 = 1/4 * 4/12 = 1 / 12 of 520 = 1/12 * 520 = 43.33 ==43 Ans - D
Answer: (D) 43
Question: The population of a town is 10000. It increases annually at the rate of 10% p.a. What will be its population after 2 years?
(A) 12100
(B) 14400
(C) 14500
(D) 14600
(E) 14700
Rationale: Formula :
10000 × 110/100 × 110/100 = 12100
Answer : A
Answer: (A) 12100
Question: Jim takes a seconds to swim z meters at a constant rate from point P to point Q in a pool. Roger, who is faster than Jim, can swim the same distance in b seconds at a constant rate. If Jim leaves point P the same time that Roger leaves point Q, how many fewer meters will Jim have swum than Roger when the two swimmers pass each other?
(A) c(b-a)/ a+b
(B) c(a-b)/a+b
(C) c(a+b)/a-b
(D) ab(a-b)/a+b
(E) z(a-b)/a+b
Rationale: Both JimRoger are travelling at constant speedin opposite direction:
So, speed of Jim = z/a speed of Roger = z/b
Let say Jim travelled distance x from P where it met Roger, it means that Roger travelled (z-x) from point Q
[x would be less than (z-x) as Jim is travelling slow]
From above, time taken by Jim to travel x = xa/z....................... (1)
Also, time taken by Roger to travel (z-x) = (z-x)b/z.....................(2)
Time taken by both JimRoger is same, so (1) = (2)
xa/z = (z-x)b/c,
Solving further, x = bz/(a+b).................... (3)
We require to find how many fewer meters will Jim have swum i.e
additional distance travelled by Roger = (z - x) - x
= z-2x
Substituting value of x from (3)solving the equation further, we get Answer = z(a-b)/a+b
Answer = (E)
Answer: (E) z(a-b)/a+b
Question: Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $8.91 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discount rates is 22 percent, what is the discount rate on Pony jeans?
(A) 9%
(B) 10%
(C) 11%
(D) 12%
(E) 15%
Rationale: Let x be the discount on Pony jeans. Then 0.22-x is the discount on Fox jeans.
3(0.22-x)(15) + 2x(18) = 8.91
9.9 - 45x + 36x = 8.91
9x = 0.99
x = 0.11
The answer is C.
Answer: (C) 11%
Question: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when m is even. What is [9]*[10] equivalent to?
(A) [25]
(B) [135]
(C) [30]
(D) [90]
(E) [45]
Rationale: [9]*[10] = 27*5 = 135 = 3*45 = [45]
The answer is E.
Answer: (E) [45]
Question: If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 27 more than n. What is y in terms of x ?
(A) x-3
(B) x+3
(C) x+5
(D) x-10
(E) x-7
Rationale: Original Digits=xy i.e. Number=10x+y
After reversing the digits:
Digits=yx i.e. Number=10y+x
10y+x is 27 more than 10x+y
10x+y+27=10y+x
10x-x+27=10y-y
9x+27=9y
x+3=y
OR
y=x+3
Answer : B
Answer: (B) x+3
Question: 6x + 2y = -4
4x + y = 1
In the system of equations above, what is the value of x?
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
Rationale: 6x + 2y = -4 can be written as 3x + y = -2
Let's subtract the second equation from this equation.
-x = -3
x = 3
The answer is C.
Answer: (C) 3
Question: One pump drains one-half of a pond in 7 hours, and then a second pump starts draining the pond. The two pumps working together finish emptying the pond in one-half hour. How long would it take the second pump to drain the pond if it had to do the job alone?
(A) 1 hour
(B) 1.1 hour
(C) 3 hours
(D) 5 hours
(E) 6 hours
Rationale: First pump drains 1/2 of the tank in 7 hours
so 14 hours it will take to drain the full tank.
Let, 2nd pump drains the full tank in a hours
so both together can drain (1/14+1/a) part in 1 hour
son in 1/2 hour they drain 1/2*(1/14+1/a) part of the tank
given that in 1/2 hour they drain 1/2 of the tank
hence we can say
1/2*(1/14+1/a) = 1/2
solving u get a = 14/13=1.1
Hence answer is B
Answer: (B) 1.1 hour
Question: A shopkeeper buys mangoes at the rate of 9 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?
(A) 33 4/3 %
(B) 33 1/7 %
(C) 200/3 %
(D) 32 1/3 %
(E) 33 2/3 %
Rationale: The total number of mangoes bought by the shopkeeper be 27.
If he buys 9 a rupee, his CP = 3
He selling at 3 a rupee, his SP = 9
Profit = SP - CP = 9 - 3 = 6
Profit Percent = 6/9 * 100 = 200/3 %
Answer:C
Answer: (C) 200/3 %
Question: The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:
(A) 17 kg
(B) 20 kg
(C) 26 kg
(D) 31 kg
(E) 35 kg
Rationale: Let A, B, C represent their respective weights. Then, we have:
A + B + C = (45 x 3) = 135 .... (i)
A + B = (40 x 2) = 80 .... (ii)
B + C = (43 x 2) = 86 ....(iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 .... (iv)
Subtracting (i) from (iv), we get : B = 31.
B's weight = 31 kg.
Answer: Option D
Answer: (D) 31 kg
Question: A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is?
(A) 3.34
(B) 3.349
(C) 3.348
(D) 3.37
(E) 3.248
Rationale: Area of the path = Area of the outer circle - Area of the inner circle = ∏{4/2 + 25/100}2 - ∏[4/2]2
= ∏[2.252 - 22] = ∏(0.25)(4.25) { (a2 - b2 = (a - b)(a + b) }
= (3.14)(1/4)(17/4) = 53.38/16 = 3.34 sq m
Answer: A
Answer: (A) 3.34
Question: [1/(1.2.3)] + [1/(2.3.4)] + [1/(3.4.5)] + [1/(4.5.6)] is equal to
(A) 7 / 30
(B) 11 / 30
(C) 13 / 30
(D) 17 / 30
(E) None
Rationale: Answer
Given Exp. = [(4 x 5 x 6) + (5 x 6) + (2 x 6) + (2 x 3)] / [(2 x 3 x 4 x 5 x 6)]
= 168 / (24 x 30)
= 7 / 30
Correct Option: A
Answer: (A) 7 / 30
Question: Luke purchased a used car for a price of H dollars, which he took to a garage where he bought a new windshield for L dollars, and four new wheels for J dollars per wheel. He then sold the car to a friend for K dollars.
How much profit did he make?
(A) (K+H)-(L-J)
(B) (K-H)-(L+J)
(C) (K-J)+(L+H)
(D) (K+H)-(L-4J)
(E) (K-H)-(L+4J)
Rationale: The cost for the new wheels= 4J dollars
Then the cost price=H+L+4J dollars
The selling price= K dollars
Hence, the profit= K-(H+L+4J)
= K-H-L-4J dollars
The correct answer is E!!
Answer: (E) (K-H)-(L+4J)
Question: A man purchased a fan and a tv for Rs. 5000 &Rs. 10000 respectively. He sold the fan at a loss of 6% and the tv at a profit of 12%. Overall how much he make a profit.
(A) 100
(B) 300
(C) 900
(D) 600
(E) 400
Rationale: Let the SP of the fan and the tv be Rs. r and Rs. m respectively.
r = 5000(1 - 6/100) = 5000 - 300
m = 10000(1 + 12/100) = 10000 + 1200
Total SP - Total CP = r + m - (15000 + 8000) = -300 + 1200 = Rs. 900
As this is positive, an overall profit of Rs. 900 was made.
C
Answer: (C) 900
Question: Java House charges $3.25 for a cup of coffee that costs a total of $2.85 to make. Cup'O'Joe charges $2.80 for a cup that costs $2.65 to make. If Java House sells 24,000 cups of coffee, how many must Cup'O'Joe sell to make at least as much in total gross profit as its competitor does?
(A) 7,858
(B) 8,301
(C) 14,667
(D) 64,000
(E) 146,667
Rationale: Java: Profit/Cup = 3.25-2.85 = 0.4
: No of Cups = 24,000
: Gross Profit = 24,000*0.4 = 9,600
Joe: Profit/Cup = 0.15
: Gross Profit = 9,600
: No of Cups = 9,600/0.15 = 64000
Answer D
Answer: (D) 64,000
Question: Tickets numbered from 1 to 27 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bears a number which is a multiple of 3?
(A) 1/3
(B) 2/5
(C) 3/10
(D) 3/7
(E) 1/7
Rationale: Here, S = [1, 2, 3, 4, …., 19, 20, 21, 22, 23, 24, 25, 26, 27]
Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18, 21, 24, 27]
P (E) = n (E) / n (S) = 9 / 27 = 1/3
The answer is A.
Answer: (A) 1/3
Question: If a man walks to his office at 5/4 of his usual rate, he reaches office 30 minutes early than usual. What is his usual time to reach office.
(A) 2 hrs
(B) 2 1⁄2 hrs
(C) 1 hr 50 min
(D) 2 hrs 15 min
(E) None of these
Rationale: usual time × (4⁄5 - 1) = -30⁄60
⇒ usual time = 1⁄2 × 5 = 21⁄2 hrs
Answer B
Answer: (B) 2 1⁄2 hrs
Question: A bag contains 4 white,5 red and 6 blue balls.Three balls are drawn at random from the bag.the probability that all of them are red are????
(A) 1/91
(B) 3/91
(C) 4/91
(D) 2/91
(E) 6/91
Rationale: 5c3/15c3=455/10=2/91
ANSWER:D
Answer: (D) 2/91
Question: The average of six numbers is 3.55. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers ?
(A) 4.7
(B) 4.6
(C) 4.2
(D) 3.4
(E) 4.9
Rationale: Explanation:
Sum of the remaining two numbers = (3.55 * 6) - [(3.4 * 2) + (3.85 * 2)]
= 21.30 - (6.8 + 7.7) = 21.30 - 14.5 = 6.8.
Required average = (6.8 / 2) = 3.4.
Answer: D) 3.4
Answer: (D) 3.4
Question: An army’s recruitment process included N rounds of selection tasks. For the first A rounds, the rejection percentage was 60 percent per round. For the next B rounds, the rejection percentage was 50 percent per round and for the remaining rounds, the selection percentage was 70 percent per round. If there were 100000 people who applied for the army and 245 were finally selected, what was the value of N?
(A) 4
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: fastly i reduce 60% till it gets closer to our required 2000 candidates
step(1) 40000 accepted.
step(2) another 40%of 40000=16000 accepted.
here it is quiet observable that if we further deduct candidate by 60% it would change our probablity of easy going 2000 candidate.
so i would get to second stage of recruitment where 50 % is accepted
step(3) 50% of 16000=8000
step(4) 50% of 8000=4000
Step(5) 50% of 4000=2000
Step(6) 50% of 2000=1000
Step(7) 50% of 1000=500
Step(8) 70% of 500=350
Step(9) 70% of 350=245(our target)
total 9 steps required.
Ans E
Answer: (E) 9
Question: The distance between two stars is 1.8 × 10^7 light years. What is the distance between the two stars in parsecs? (1 parsec = 3.26 light years)
(A) 1.1 x 10^2
(B) 2.2 x 10^3
(C) 3.3 x 10^4
(D) 4.4 x 10^5
(E) 5.5 x 10^6
Rationale: 1.8 × 10^7 ly / (3.26 ly/parsec) = (1.8/3.26) x 10^7 = 0.55 x 10^7 = 5.5 x 10^6 parsec
The answer is E.
Answer: (E) 5.5 x 10^6
Question: A group of five girls and three boys have tickets for seven adjacent seats in one row of a theater. If the three boys will not sit in three adjacent seats, how many possible different seating arrangements are there for these 8 theatre-goers?
(A) 8! – 2!3!2!
(B) 8! – 6!3!
(C) 8 × 2!3!2!
(D) 8! – 5!3!
(E) 2!3!2!
Rationale: There are 3 boys and 4 girls , we want to calculate the seating arrangements if three boys do not sit together, like MMM.
Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 8 persons without restriction. Thus we'll get the # of arrangements asked in the question.
1. Total # of arrangements of 8 is 8!.
2. # of arrangements when 3 boys are seated together, like MMM;
Among themselves these 3 boys can sit in 3! # of ways,
Now consider these 3 boys as one unit like this {MMM}. We'll have total of 6 units: {MMM}{W}{W}{W}{W}{W}. The # of arrangements of these 5 units is 5!.
Hence total # of arrangements when 3 men sit together is: 3!6!.
# of arrangements when 3 boys do not sit together would be: 8!-3!6!.
Answer: B).
Answer: (B) 8! – 6!3!
Question: 20 men can complete a piece of work in 30 days. In how many days can 25 men complete that piece of work?
(A) 23
(B) 27
(C) 24
(D) 27
(E) 11
Rationale: 20 * 30 = 25 * x => x = 24 days
Answer:C
Answer: (C) 24
Question: A number is doubled and 9 is added. If the resultant is trebled, it becomes 75. What is that number?
(A) 3.5
(B) 6
(C) 8
(D) 7
(E) 4
Rationale: Let the number be x. Then,
3(2x + 9) = 75
2x = 16 => x = 8
ANSWER:C
Answer: (C) 8
Question: If,
1 * 3 * 5 = 16
3 * 5 * 7 = 38
Then find,
5 * 2 * 9 =?
(A) 65
(B) 68
(C) 72
(D) 23
(E) 77
Rationale: (9 * 2) + 5 = 23
D
Answer: (D) 23
Question: On a certain road, 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 40% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on that road exceed the posted speed limit?
(A) 10.5%
(B) 12.5%
(C) 16.7%
(D) 25%
(E) 30%
Rationale: suppose there are X motorists.
10% of them exceeded the speed limit and received the ticket, i.e. X/10.
Again, suppose total no. of motorists who exceeded the speed limit are Y.
40% of Y exceeded the speed limit but didn't received the ticket, i.e. 2Y/5.
it means 3Y/5 received the ticket.
hence, 3Y/5 = X/10
or Y/X=1/6
or Y/X * 100= 1/6 * 100= 16.7%
C
Answer: (C) 16.7%
Question: Look at this series: V, VIII, XI, __, XVII, XX, ... What number should fill the blank?
(A) IX
(B) XXIII
(C) XV
(D) XIV
(E) None
Rationale: Explanation: This is a simple addition series; each number is 3 more than the previous number.
Answer: D
Answer: (D) XIV
Question: When the price of sugar was increased by 32%, a family reduced its consumption in such a way that the expenditure on sugar was only 10% more than before. If 30 kg were consumed per month before, find the new monthly consumption.
(A) 20 kg
(B) 25 kg
(C) 30 kg
(D) 35 kg
(E) None of these
Rationale: Since, expenditure = price × consumption
∴ 110% of 30 = 132⁄100 × new consumption
⇒ 110⁄100 × 30 = 132⁄100 × new consumption
⇒ New consumption = 25 kg
Answer B
Answer: (B) 25 kg
Question: An article is bought for Rs.805 and sold for Rs.900, find the gain percent?
(A) 12.8%
(B) 17.8%
(C) 15.8%
(D) 11.8%
(E) 14.8%
Rationale: 805 ---- 95
100 ---- ? => 11.8%
Answer:D
Answer: (D) 11.8%
Question: a person travels from his house to office from 11:10am to 12:10 am and covers a distence of 15.4km. find the average speed of the person.
(A) 20.1km/h
(B) 15.4km/h
(C) 21.1km/h
(D) 22.1km/h
(E) 20.9km/h
Rationale: time=12:10-11:10=1 hour
distance = 15.4 km
speed=15.4*1=15.4 km/h
ANSWER:B
Answer: (B) 15.4km/h
Question: Two trains of equal length, running with the speeds of 60 and 60 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
(A) 1.0
(B) 8.2
(C) 7.7
(D) 2.6
(E) 8.3
Rationale: RS = 60 -40 = 20 * 5/18 = 100/18
T = 50
D = 50 * 100/18 = 2500/9
RS = 60 + 60 = 120* 5/18
T = 2500/9 * 18/600 = 8.3 sec.Answer: E
Answer: (E) 8.3
Question: In a class, the average age of 45 boys is 10 years and the average of 15 girls is 10 years. what is the average age of the whole class?
(A) 12 Years
(B) 12.3 Years
(C) 10 Years
(D) 13 Years
(E) 15 Years
Rationale: Total age of 60 students
(45X 10+15 X 10) = 630
Average = 600/60 = 10 Years
C
Answer: (C) 10 Years
Question: If 2x + y = 7 and x + 2y = 8, then (x + y)/3 =
(A)  1
(B)  4/3
(C)  17/5
(D)  18/5
(E)  5/3
Rationale: We have two equations:
2x + y = 7
x + 2y = 8
Notice that something nice happens when we ADD them. We get:
3x + 3y = 15
Divide both sides by 3 to get:x + y = 5
So, (x + y)/3 =5/3
Answer: E
Answer: (E)  5/3
Question: Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 1000
(B) 1100
(C) 1230
(D) 1350
(E) 1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Large number = 270+1365 = 1635
E
Answer: (E) 1635
Question: Ten years ago, the age of Peter was one-third the age of Jacob at that time. The present age of Jacob is 12 years more than the present age of Peter. Find the present age of Peter?
(A) 15
(B) 11
(C) 18
(D) 16
(E) 20
Rationale: D
16
Let the present ages of Peter and Jacob be 'a' and 'b' respectively.
a - 10 = 1/3 (b - 10) --- (1)
b = a + 12
Substituting b = a + 12 in first equation,
a - 10 = 1/3 (a + 2) => 3a - 30 = a + 2
=> 2a = 32 => a = 16.
Answer: (D) 16
Question: There are 3 couples. If they will sit 6 chairs in a row such that each couple sits side by side, how many possible cases are there?
(A) 48
(B) 240
(C) 1,200
(D) 2,460
(E) 3,840
Rationale: Tie the couples. Then we have 3 persons that have to be arranged in 3 places. 3! ways.
Now the couples can change position with each other. 2! ways.
3! * (2!)^3 = 6*8= 48
Answer is A.
Answer: (A) 48
Question: The value of a scooter depreciates in such a way that its value of the end of each year is 3/4 of its value of the beginning of the same year. If the initial value of the scooter is Rs.40,000, what is the value at the end of 2 years ?
(A) 3277
(B) 2977
(C) 22500
(D) 6077
(E) 17112
Rationale: Explanation: 40,000*(3/4)^2
Answer:C
Answer: (C) 22500
Question: a dealer buys 4 varieties of rice costing rs. 40,rs.50,rs.60 and rs.70 per kg in the ratio 4:5:3:2 and mixes all the four varieties and sells at 40% profit. What is the selling price per kg of rice?
(A) 72
(B) 73
(C) 74
(D) 75
(E) 76
Rationale: CP = 40*4+50*5+60*3+70*2 = 730
SP = 1.4*730=1022
Total no.of kgs=4+5+3+2=14
SP per kg=1022/14 = 73
ANSWER:B
Answer: (B) 73
Question: If a quarter kg of carrots costs 60 paise, how many paise will 200 gms cost ?
(A) 78 paise
(B) 48 paise
(C) 54 paise
(D) 62 paise
(E) 65 paise
Rationale: Explanation:
Quarter of Kg means 250 gm
Less weight, less price (Direct Proportion)
So,
250 : 200 :: 60 : x => x = 48
So 200 gm will cost 48 paise.
Answer IS B
Answer: (B) 48 paise
Question: Q is an even integer greater than 300,000 and smaller than 1,000,000. How many numbers can Q be?
(A) 300,000
(B) 349,999
(C) 350,000
(D) 399,999
(E) 400,000
Rationale: Q 1,000,000-300,000=700,000 integers
700,000/2= 350,000 even integers.
350,000+1 inclusive. But since 1,000,000 and 300,000 are not included.
350,001-2=349,999
B
Answer: (B) 349,999
Question: Difference of two numbers is 1660. If 7.5% of the number is 12.5% of the other number , find the number ?
(A) 2660, 1000
(B) 3660, 2000
(C) 3000, 4160
(D) 2490, 4150
(E) 4660, 3000
Rationale: Let the numbers be x and y. Then, 7.5 % of x =12.5% of y
X = 125*y/75 = 5*y/3.
Now, x-y =1660
5*y/3 –y =1660
2*y/3= 1660
y =[ (1660*3)/2] =2490.
One number = 2490, Second number =5*y/3 =4150.
Answer D.
Answer: (D) 2490, 4150
Question: The present ages of three persons are in proportions 4:7:9. Six years ago, the sum of their ages was 122. Find their present ages.
(A) 20, 28
(B) 28, 36
(C) 35, 45
(D) 35, 55
(E) 49,63
Rationale: Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 6) + (7x - 6) + (9x - 6) = 122
20x = 140 => x = 7
Their present ages are 28, 49 and 63 years respectively.
ANSWER:E
Answer: (E) 49,63
Question: A bowl was filled with 10 ounces of milk, and 0.008 ounce of the milk evaporated each day during a 50-day period. What percent of the original amount of milk evaporated during this period?
(A) 0.004%
(B) 0.04%
(C) 4%
(D) 40%
(E) 42%
Rationale: Total amount of milk evaporated each day during a 50-day period = .008 * 50
=.008 * 100/2
= .8/2
= .4
percent of the original amount of milk evaporated during this period = (.4/10) * 100%
= 4 %
Answer C
Answer: (C) 4%
Question: The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?
(A) 300
(B) 800
(C) 500
(D) 600
(E) 700
Rationale: Area of the square = s * s = 5(125 * 64)
=> s = 25 * 8 = 200 cm
Perimeter of the square = 4 * 200 = 800 cm.
Answer: Option B
Answer: (B) 800
Question: A statue is being carved by a sculptor. The original piece of marble weighed 180 kg. In the first week 28 percent is cut away. In the second week 18 percent of the remainder is cut away. In the third week the statue is completed when 20 percent of the remainder is cut away. What is the weight of the final statue?
(A) 105 kg
(B) 85 kg
(C) 108 kg
(D) 125 kg
(E) 117 kg
Rationale: B
85 kg
180 Ã— 0.72Ã— 0.82Ã— 0.8 = 85 kg.
Answer: (B) 85 kg
Question: A hat company ships its hats, individually wrapped, in 8-inch by 10-inch by 12-inch boxes. Each hat is valued at $5.50. If the company’s latest order required a truck with at least 288,000 cubic inches of storage space in which to ship the hats in their boxes, what was the minimum value of the order?
(A) $960
(B) $1,350
(C) $1,650
(D) $2,050
(E) $2,250
Rationale: Total Volume is 288000
Given LBH = 8*10*12.
the number of hats inside it = 288000/10 * 8 * 12 = 300.
price of each hat is 5.5 $ then total value is 300 * 5.5 = 1650.
IMO option C is correct answer..
Answer: (C) $1,650
Question: A man invests Rs.5000 for 3 years at 5% p.a. compound interest reckoned yearly. Income tax at the rate of 20% on the interest earned is deducted at the end of each year. Find the amount at the end of the third year
(A) 5624.32
(B) 5624.39
(C) 5654.32
(D) 5624.38
(E) 5624.35
Rationale: Explanation:
5% is the rate of interest. 20% of the interest amount is paid as tax.
i.e 80% of the interest amount stays back.
if we compute the rate of interest as 80% of 5% = 4% p.a., we will get the same value.
The interest accrued for 3 years in compound interest = 3 x simple interest on principal + 3 x interest on simple interest + 1 x interest on interest on interest.
= 3 x (200) + 3 x (8) + 1 x 0.32 =600 + 24 + 0.32 = 624.32
The amount at the end of 3 years = 5000 + 624.32 = 5624.32
Answer: A) Rs.5624.32
Answer: (A) 5624.32
Question: If x is a positive integer with fewer than 3 digits, what is the probability that C x*(x + 1) is a multiple of either 4 or 5?
(A) 4/99
(B) 2/25
(C) 8/99
(D) 49/100
(E) 86/99
Rationale: Interesting question! Also one that we should be able to answer very quickly be keeping an eye on our best friends, the answer choices.
We know that x belongs to the set {1, 2, 3, ... , 99}. We want to know the probability C that x(x+1) is a multiple of either 4 or 5.
When will this happen? If either x OR (x+1) is a multiple of 4 or 5.
Since 4*5 is 20, let's look at the first 20 numbers to get a rough idea of how often this happens.
Out of the numbers from 1 to 20:
4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 20
So, 14 out of the first 20 numbers match our criteria. Since:
probability = (# of desired outcomes)/(total # of possibilities), we guesstimate the answer to be 14/20. Since (E) is the only answer greater than 1/2, we go with (E).
Answer: (E) 86/99
Question: In what time will Rs.1000 become Rs.1331 at 10% per annum compounded annually?
(A) 2 years
(B) 3 years
(C) 4 years
(D) 7 years
(E) None
Rationale: Solution
Principal	= Rs.1000;
Amount	= Rs.1331;
Rate	= Rs.10%p.a.
Let the time be n years.Then
[1000(1+10/100)Λn;]
= 1331.
= (1331/1000)
= (11/10)³
Therefore n = 3 years.
Answer B
Answer: (B) 3 years
Question: In how many ways can a group of 5 men and women be made out of a total of 7 men and 3 women?
(A) 63
(B) 90
(C) 126
(D) 45
(E) 135
Rationale: Required number of ways=7c5 x 3c2
=7c2 x 3c1
=63
ANSWER A 63
Answer: (A) 63
Question: When the positive integer x is divided by 9,the remainder is 5.What is the remainder when 7x is divided by 9?
(A) 0
(B) 1
(C) 3
(D) 4
(E) 8
Rationale: i tried plugging in numbers
x = 9q+5
x = 14
7x = 98
7x/9 = 9*10 + 8
remainder is 8
Answer is E.
Answer: (E) 8