mathewhe/aqua_rat huggingface dataset:
Question: A car averages 65 mph for the first 5 hours of a trip and averages 75 mph for each additional hour. The average speed for the entire trip was 60 mph. How many hours long is the trip?
(A) 9
(B) 8
(C) 7
(D) 6
(E) 5
Rationale: Let the time for which car averages 75 mph = t
60*(t+5)= 65*4 + 70 t
=>10t= 40
=> t = 4
Total duration of the trip = 5+4=9
Answer A
Answer: (A) 9
Question: A can do a certain work in 12 days. B is 60% more efficient than A. How many days does B alone take to do the same job?
(A) 15/2
(B) 14/2
(C) 15/4
(D) 14/4
(E) 13/4
Rationale: Let the total units of work done be 60.
Units of work done by A in one day = 5.
Given, B is 60% more efficient than A.
Thus, B will be able to finish 8 units of work in a day.
Therefore, time taken by B alone to complete the total work = 60/8 =15/2 days.
ANSWER:A
Answer: (A) 15/2
Question: If 4XZ + YW = 3 and XW + YZ = 6, what is the value of the expression (2X + Y)(2Z + W)?
(A) 9.
(B) 12.
(C) 15.
(D) 16
(E) 18.
Rationale: Expand this to get: (2X + Y)(2Z + W) = 4XZ + 2XW + 2YZ + YW
= 4 XZ + YW + 2XW + 2YZ [I rearranged the terms]
= 3 + 2XW + 2YZ [replaced 4XZ + YW with 3]
= 3 + 2(XW + YZ) factored out a 2
= 3 + 2(6)
= 3 + 12
= 15
ANSWER:C
Answer: (C) 15.
Question: A chemical supply company has 60 liters of a 40% HNO3 solution. How many liters of pure undiluted HNO3 must the chemists add so that the resultant solution is a 50% solution?
(A) 12
(B) 15
(C) 20
(D) 24
(E) 30
Rationale: 60 liters of a 40% HNO3 solution means HNO3 = 24 liters in 60 liters of the solution.
Now, let x be the pure HNO3 added.
As per question,
24 + x = 50% of (60 + x)
or x =12. Hence, A
Answer: (A) 12
Question: A producer of tea blends two varieties of tea from two tea gardens one costing Rs 18 per kg and another Rs 20 per kg in the ratio 5 : 3. If he sells the blended variety at Rs 22 per kg, then his gain percent is
(A) 12%
(B) 13%
(C) 14%
(D) 15%
(E) 17%
Rationale: Explanation:
Suppose he bought 5 kg and 3 kg of tea.
Cost Price = Rs. (5 x 18 + 3 x 20) = Rs. 150.
Selling price = Rs. (8 x 22) = Rs. 176.
Profit = 176 - 150 = 26
So, Profit % = (26/150) * 100 = 17%
Option E
Answer: (E) 17%
Question: A,B,C can complete a piece of work in 24,6,12 days. Working together, they complete the same work in how many days?
(A) 2
(B) 4/5
(C) 7/9
(D) 10
(E) 24/7
Rationale: A+B+C 1day work = 1/24 + 1/6 + 1/12 = 7/24
A,B,C together will complete the job in 24/7 days
Answer is E
Answer: (E) 24/7
Question: The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $60,000?
(A) $38,796.
(B) $40,000.
(C) $38,976.
(D) $58,464.
(E) $36,796.
Rationale: 60,000 *1.16*.84= Unit and tens digit of the expression is 6 and 7 respectively.
Only option D fulfills the condition and hence is the answer
Answer: (D) $58,464.
Question: A positive integer which when added to 100, gives a sum which is greater than when it is multiplied by 100. What is the number?
(A) 6
(B) 5
(C) 4
(D) 1
(E) 8
Rationale: Explanation:
The number is 1
ANSWER: D
Answer: (D) 1
Question: If the number is divided by 3, it reduced by 36. The number is
(A) A)51
(B) B)50
(C) C)45
(D) D)54
(E) E)36
Rationale: Explanation:
Let the number be x. Then,
x - (x/3) = 36 => 2x/3 = 36
=> x = 54
Answer: Option D
Answer: (D) D)54
Question: When n is divided by 32, the remainder is 5. What is the remainder when 4n is divided by 8?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Let n=5 (leaves a remainder of 5 when divided by 32)
4n = 4(5) =20, which leaves a remainder of 4 when divided by 8.
Answer B
Answer: (B) 4
Question: For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 920, what is the maximum possible sum of the length of x and the length of y?
(A) 14
(B) 12
(C) 10
(D) 16
(E) 18
Rationale: we know that : x > 1, y > 1, and x + 3y < 1000,
and it is given that length means no of factors.
for any value of x and y, the max no of factors can be obtained only if factor is smallest noall factors are equal.
hence, lets start with smallest no 2.
2^1 =2
2^2 =4
2^3=8
2^4=16
2^5=32
2^6=64
2^7=128
2^8=256
2^9=512
2^10 =1024 (it exceeds 920, so, x can't be 2^10)
so, max value that X can take is 2^9 , for which has length of integer is 9.
now, since x =512 ,x+3y<920
so, 3y<408
==> y<136
so, y can take any value which is less than 136. and to get the maximum no of factors of smallest integer, we can say y=2^7
for 2^7 has length of integer is 7.
SO, combined together : 9+7 = 16.
D
Answer: (D) 16
Question: A waiter's salary consists of his salary and tips. During one week his tips were 7/4 of his salary. What fraction of his income came from tips ?
(A) 4/9
(B) 5/4
(C) 5/8
(D) 5/9
(E) 7/11
Rationale: Income = salary (s) +tips = s + s*7/4 = s*11/4
Tips = s*7/4
fraction of his income came from tips = (s*7/4)/(s*11/4)= 7/11
ANSWER:E
Answer: (E) 7/11
Question: Complete the series
13, 9, 5, 1, -3,-7 ...
(A) -11
(B) 0
(C) 3
(D) -2
(E) 3
Rationale: In the above series clearly we know we can get the next term by subtract 4 from the previous term so the answer is Option A) -11
Answer: (A) -11
Question: Mark is playing poker at a casino. Mark starts playing with 150 chips, 20% of which are $100 chips and 80% of which are $20 chips. For his first bet, Mark places chips, 10% of which are $100 chips, in the center of the table. If 70% of Mark's remaining chips are $20 chips, how much money did Mark bet?
(A) $1,960
(B) $1,740
(C) $1,540
(D) $3,080
(E) $2,100
Rationale: Total chips 150
20% of $100 chips = 30 chips * $100 = $3,000
80% of $20 chips = 120 chips * $20 = $2,400
If x is the number of chips bet and y is the amount of chips remaining:
x + y = 150
y = 150 - x ~ (1)
[First round bet] + [Second round bet] = $3,000 + $2,400
[0.1x * $100 + 0.9x * $20] + [0.3y * $100 + 0.7y * $20] = $5,400
10x + 18x + 30y + 14y = 5400
28x + 44y = 5400 ~ (2)
Substitute (1) into (2) to solve for x:
28x + 44(150 - x) = 5400
28x + 6600 - 44x = 5400
16x = 1200
x = 75
Substituting x:
[First round bet] = [0.1x * $100 + 0.9x * $20] = 0.1(75)($100)+0.9(75)($20) = $750 + $1,350 = $2,100
Answer is E
Answer: (E) $2,100
Question: Given 2x + y + z = 3 and 5x + 3y + z = 14, what is the value of x + y - z?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: (1) 5x + 3y + z = 14
If 2x + y + z = 3, then (2) 4x + 2y + 2z = 6
Let's subtract equation (2) for equation (1).
x + y - z = 8
The answer is D.
Answer: (D) 14
Question: Departments A has 20 employees, B, and C have 20 employees each, and department D has 20 employees. Departments A, B, C, and D have no employees in common. A task force is to be formed by selecting 1 employee from each of departments A, B, and C and 2 employees from department D. How many different task forces are possible?
(A) 19,000
(B) 40,000
(C) 100,000
(D) 190,000
(E) 380,000
Rationale: 20c1 * 10c1* 10c1*20c2 = 20*10*10*190=380,000. Hence E is the correct answer.
Answer: (E) 380,000
Question: The length of a room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of Rs. 400 per sq. metre.
(A) Rs. 15000
(B) Rs. 8250
(C) Rs. 15600
(D) Rs. 16500
(E) None of these
Rationale: Solution
Area of the floor = (5.5 × 3.75) m2 = 20.625 m2
∴ Cost of paving = Rs. (400 × 20.625) = 8250. Answer B
Answer: (B) Rs. 8250
Question: City X has a population 3 times as great as the population of City Y, which has a population twice as great as the population of City Z. What is the ratio of the population of City X to the population of City Z?
(A) 1:8
(B) 1:4
(C) 2:1
(D) 6:1
(E) 8:1
Rationale: x= 3y, y= 2*z
X : Y , Y : Z
3 : 1 , 2 : 1
6 : 2 , 2 : 1
So, X : Z = 6 : 1
(D)
Answer: (D) 6:1
Question: Hector runs a one-product widget shop. Each month, his fixed costs, whether he produces anything or not, amount to x dollars. The marginal cost of producing and selling one widget is a constant y dollars, regardless of the number he produces. He generally can sell widgets for z dollars each. What is the minimum number of widgets he must produce, assuming he sells every widget he produces, to break even (neither make a profit nor incur a loss) in a given month?
(A) x/(y - z)
(B) x/(z - y)
(C) x
(D) x/z
(E) x/y
Rationale: Two ways...
1) let t be the total number, so cost = t*y+x and selling price=t*z..
No profit no loss....t*y+x=t*z.....T=x/(z-y)...
2) choices..
The answer has to use all 3 variables x,y and z....
Only A and B are left...
In A, y will be lesser than z, so A will become NEGATIVE..
ANSWER:B
Answer: (B) x/(z - y)
Question: Henry answered 4/5 of the questions he was given for homework in the first hour, 5/19 of the remaining questions in the second hour and the remaining x questions in the third hour where x is an integer. How many questions was Henry given for homework?
(A) x
(B) (95/7)*x
(C) (95/14)*x
(D) (95/21)*x
(E) (95/28)*x
Rationale: Let Q be the number of homework questions.
Q = 4Q/5 + (5/19)(Q/5) + x
Q = 76Q/95 + 5Q/95 + x
14Q/95 = x
Q = (95/14)*x
The answer is C.
Answer: (C) (95/14)*x
Question: Jagan went to the book shop and bought things worth Rs. 30, out of which 25 paise went on sales tax on taxable purchases. If the tax rate was 5%, then what was the cost of the tax free items?
(A) Rs 22.75
(B) Rs 25
(C) Rs 24.75
(D) Rs 26
(E) None of these
Rationale: Explanation :
Solution: let the amount of taxable purchases be Rs. X.
Then, 5% of x= 25/100
=> x= (25/100 *100/5) = Rs. 5
.'. Cost of tax free items = Rs.[30-(5+0.25)] = Rs. 24.75
Answer : C
Answer: (C) Rs 24.75
Question: A money lender lends Rs.2000 for six months at 20% p.a. rate. It the interest is reckoned quarterly than find the amount given after time limit.
(A) 2205
(B) 2201
(C) 2229
(D) 2289
(E) 2202
Rationale: A = 2000(21/20)2
= 2205
Answer:A
Answer: (A) 2205
Question: An inlet pipe fill a tank in 5 hrs and outlet pipe empty same tank in 36 hrs working indiviually.how many additional number of outlet pipes of same capacity required to be opened so that tank never over flows
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Inlet pipe fills the tank in 5 hr and outlet pipe empties the tank in 36 hr.
So inlet pipe is 36/5 = 7.2 times efficient than , ensure that the an outlet pipe.
Therefore , in order to tank never overflows , we will need total 8 outlet pipes.
Already we have 1 outlet pipe , thus we need only (8-1) = 7 outlet pipes
ANSWER:B
Answer: (B) 7
Question: In an apartment building that has 490 units, 4 out of every 7 units are currently rented, including 1/6 of the one-bedroom units. If, of the rented apartments, there is a 6:1 ratio of two-bedroom units to one-bedroom units, and the building only consists of two-bedroom and one-bedroom units, how many two-bedroom units are not rented?
(A) 50
(B) 70
(C) 100
(D) 105
(E) 10
Rationale: Rented = 4/7*490 = 280.
Rented two-bedroom = 6/7*280 = 240;
Rented one-bedroom = 1/7*280 = 40 (or 280-240=40).
Rented one-bedroom units are 1/5 of all one-bedroom: 1/6*{All one bedroom} = 40 --> {All one-bedroom} = 240.
{All two-bedroom} = 490 - 240 = 250.
Two-bedroom not rented = 250 - 240 = 10
Answer: E
Answer: (E) 10
Question: Sony and Johnny caught 80 fishes. Sony caught four times as many as Johnny. How many fishes did Johnny catch?
(A) 12
(B) 16
(C) 34
(D) 38
(E) 42
Rationale: s+j=80
s=4*j
j=16
ANSWER:B
Answer: (B) 16
Question: A train passes a station platform in 48 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 420 m
(B) 200 m
(C) 240 m
(D) 320 m
(E) None
Rationale: Sol.
Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x metres.
Then, x + 300 / 48 = 15 ⇔ x + 300 = 720 ⇔ x = 440 m.
Answer A
Answer: (A) 420 m
Question: If 9 pumps can raise 1085 tonnes of water in 10 days, working 7 hours a day; in how many days will 8 pumps raise 868 tonnes of water, working 9 hours a day?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Explanation :
Let the required number of days be x. Then,
Less pumps, More days (Indirect Proportion)
Less water, Less days (Direct Proportion)
More hours / day, Less days (Indirect Proportion)
Pumps 8 : 9
Weight 1085 : 868
Hours/day 9 : 7 :: 10 : x
(8 x 1085 x 9 x x) = (9 x 868 x 7 x 10)
x = 9 x 868 x 7 x 10/ (8 x 1085 x 9)
x = 7
Answer : B
Answer: (B) 7
Question: Starting from 1 if you are asked to write first 172 digits of the natural numbers , which digit you stop at?
(A) 4
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: 12345678910=11digits
11-20=20digits
21-90=140 digits
total 171digits are completed
next number is 91 9is 172th digit & 1 is 173rd digit
ANSWER:D
Answer: (D) 9
Question: when n divided by 3, the remainder is 2.
when n divided by 4, the remainder is 1
what is the the remainder when divided by 11
(A) 1
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: case1
N=5,8,11,14,17,20
case 2
M=5,9,13,17,21
Therefore n=17
Remainder of 17/11 will be 6
E 6 correct
Answer: (E) 6
Question: At the end of year X, automobile installment credit accounted for 20% of all outstanding consumer installment credit. At that time automobile finance companies extended $57 billion of credit, or 1/3 of the automobile installment credit. How many billion dollars of consumer installment credit was outstanding at that time?
(A) 171
(B) 855
(C) 870
(D) 788
(E) 684
Rationale: System of Equations
a = (20/100) c
(1/3) a = 57 --> a = 171
Substitution
171 = (20100) c
c = (100/20) 171
- Calculate 171/20 * 100
The Correct answer B. The answer is 855.
Answer: (B) 855
Question: A man can row with a speed of 20 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
(A) 27
(B) 27
(C) 20
(D) 25
(E) 2
Rationale: M = 20
S = 5
DS = 20 + 5 = 25
Answer:D
Answer: (D) 25
Question: A positive number x is multiplied by 7, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x ?
(A)  7/3
(B)  3/2
(C)  4/3
(D)  2/3
(E)  1/2
Rationale: sq rt(7x/3) = x
=> 7x/3 = x^2
=> x = 7/3
Ans - A
Answer: (A)  7/3
Question: One fast typist type some matter in 3 hrs and another slow typist type the same matter in 5hrs. If both do combine in how much time they will take to finish.
(A) 1 hr 5 mins
(B) 1 hr 10 mins
(C) 1 hr 12 mins
(D) 3 hr 10 mins
(E) 4 hr 5 mins
Rationale: Fast's 1 hr work = 1/3
slow's 1 hr work = 1/5
1/3 + 1/5 = 8/15
they ll finish in 15/8hrs= 1 7/8 ==> 1 hr 12 mins
ANSWER:C
Answer: (C) 1 hr 12 mins
Question: A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?
(A) 3 hrs 45 min
(B) 3 hrs 15 min
(C) 4 hrs
(D) 4 hrs 15 min
(E) 5 hrs 15 min
Rationale: time taken by one tap in hr = (4*1/6)=2/3
remaining part = (1-1/2)=1/2
x=3/4 hrs => 3hrs 45 min
ANSWER A
Answer: (A) 3 hrs 45 min
Question: Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.40 at the candy store. What is John’s weekly allowance?
(A) $1.50
(B) $2.00
(C) $2.50
(D) $3.00
(E) $3.50
Rationale: x = 3x/5 + 1/3*2x/5 + 40
4x/15 = 40
x = 150 = $1.50
The answer is A.
Answer: (A) $1.50
Question: 10x + 2y = -4
4x + y = 1
In the system of equations above, what is the value of x?
(A) -5
(B) -3
(C) -1
(D) 1
(E) 3
Rationale: 10x + 2y = -4 can be written as 5x + y = -2
Let's subtract the second equation from this equation.
x = -3
The answer is B.
Answer: (B) -3
Question: If p and r are positive integers such that p > r > 1, what is the remainder when 92p × 5p+r + 11r × 6pr is divided by 10?
(A) A.0
(B) B.1
(C) C.3
(D) D.4
(E) E.5
Rationale: 92p × 5p+r + 11r × 6pr--1=B
Answer: (B) B.1
Question: There are 750 male and female participants in a meeting. Half the female participants and one-quarterof the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?
(A) 75
(B) 100
(C) 125
(D) 175
(E) 225
Rationale: Let m be the number of male participants and f be the number of female articipants in the meeting. Thetotal number of participants is given as 750.
Hence, we have m+f= 750
Now, we have that half the female participants and one-quarter of the male participants are Democrats.
Let d equal the number of the Democrats.
Then we have the equation f/2 + m/4 =d
Now, we have that one-third of the total participants are Democrats. Hence, we have the equation
d = 750/3 = 250
Solving the three equations yields the solution
f = 250,m= 500, and d= 250.
The number of female democratic participants equals half the female participants equals
250/2 = 125.
ANSWER:C
Answer: (C) 125
Question: If a - b = 3 and a2 + b2 = 29, find the value of ab.
(A) 10
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: 2ab = (a2 + b2) - (a - b)2
= 29 - 9 = 20
ab = 10.
A
Answer: (A) 10
Question: The average weight of three boys M, N and P is 54 1/3 kg, while the Average weight of three boys N, Q and R is 53 kg. What is the average weight of M, N, P, Q and R?
(A) 52.4 kg
(B) 53.2 kg
(C) 53.8 kg
(D) Data Inadequate
(E) None of these
Rationale: Explanation :
Total weight of (M + N + P) = 54 1/3 x 3 kg = 163 kg.
Total weight of (N + Q + R) = (53 x 3) kg = 159 kg.
Adding both, we : M + 2N + P + Q + R = (163 + 159) kg = 322 kg.
So, to find the average weight of M, N, P, Q and R, we ought to know Ns weight, which is not given. So, the data is inadequate.
Answer : D
Answer: (D) Data Inadequate
Question: City A and City B are 140 miles apart. Train C departs City A, heading towards City B, at 4:00 and travels at 40 miles per hour. Train D departs City B, heading towards City A, at 4:40 and travels at 20 miles per hour. The trains travel on parallel tracks. At what time do the two trains meet?
(A) 5:00
(B) 5:30
(C) 6:40
(D) 6:30
(E) 7:00
Rationale: Train C has traveled 20 mi in the half hour before Train D has started its journey.
140-20=120
40+20 =60 mph
120 mi/ 60 mph = 2 hrs
4:40pm + 2 hrs = 6:40pm
Answer:
C. 6:40
Answer: (C) 6:40
Question: If a2 - b2 = 8 and a*b = 2, find a4 + b4.
(A) 62
(B) 72
(C) 82
(D) 92
(E) 62
Rationale: a2 - b2 = 8 : given
a4 + b4 - 2a2b2 = 82 : square both sides and expand.
a*b = 2 : given
a2b2 = 22 : square both sides.
a4 + b4 - 2(4) = 82 : substitute
a4 + b4 = 72
correct answer B
Answer: (B) 72
Question: 3 OUT OF 1500 PARTS OF EARTH IS SULPHUR. WHAT IS THE PERCENTAGE OF SULPHUR IN EARTH
(A) 1/5
(B) 2/9
(C) 1/45
(D) 2/45
(E) NONE OF THESE
Rationale: REQUIRED PERCENTAGE=(3/1500*100)%=1/5%
CORRECT OPTIONS: A
Answer: (A) 1/5
Question: A train 200 m long can cross an electric pole in 5 sec and then find the speed of the train?
(A) 114
(B) 124
(C) 134
(D) 144
(E) 154
Rationale: Length = Speed * time
Speed = L/T
S = 200/5
S = 40 M/Sec
Speed= 40*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 144 Kmph
Answer:D
Answer: (D) 144
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
(A) 170 m
(B) 177 m
(C) 278 m
(D) 150 m
(E) 271 m
Rationale: Speed=(60 * 5/18) m/sec
= (50/3) m/sec Length of the train
= (Speed x Time) = (50/3 * 9) m
= 150 m.
Answer:D
Answer: (D) 150 m
Question: In 1 hour, a boat goes 10 km along the stream and 12 km against the stream. The speed of the boat in still water (in km/hr) is :
(A) 3 km/hr.
(B) 2 km/hr.
(C) 11 km/hr.
(D) 8 km/hr.
(E) 5 km/hr.
Rationale: Speed in still water = 1/2(10 + 12) km/hr
= 11 km/hr. ANSWER :C
Answer: (C) 11 km/hr.
Question: Three people are playing cards. What is the probability that a card drawn from a pack of 52 cards will be a diamond or a king?
(A) 1/3
(B) 2/11
(C) 4/13
(D) 5/13
(E) 5/14
Rationale: Here, n(S) = 52
There are 13 cards of diamond (including one king) and there are 3 more kings.
Let E = event of getting a diamond or a king.
Then, n(E) = (13 + 3) = 16
P (E) = 16 / 52 = 4/13
C
Answer: (C) 4/13
Question: If a computer program generates three-digit odd numbers using the numbers 9, 7, 0, 8, and 1, and the digits can be repeated, what is the probability that the number formed from the program is a multiple of three?
(A) 1/3
(B) 1/4
(C) 1/5
(D) 1/6
(E) 1/7
Rationale: A
Answer: (A) 1/3
Question: Miguel is 46 years old. He is 6 years older than twice his son’s age. Find the age of his son.
(A) 11years
(B) 12years
(C) 13years
(D) 14years
(E) 20years
Rationale: sons age=x
46-2x=6
x=20years
ANSWER:E
Answer: (E) 20years
Question: if integer N has p factors ; how many factors will 5N have ?
(A) p
(B) 2p
(C) P+1
(D) 2p+1
(E) Cannot be determined
Rationale: Case 1:
Let N = 6 => 2 x 3 (prime factorization) => p = 4;
5N =30 => no. of factors = 8; (p+2)
Case 2:
Let N = 7 => p = 2;
5N = 35 => no of factors = 4; (p+2)
For different N different results are observed. So, shouldn't E be the right answer?
Answer: (E) Cannot be determined
Question: There are 42 distinct numbers in set M, there are 28 distinct numbers in set N, and there are 12 distinct numbers that are in both sets M and N. Set H is the set containing the elements that are in at least one of sets M and N. How many elements are in set H?
(A) 39
(B) 40
(C) 51
(D) 58
(E) 63
Rationale: {Total} = {M} + {N} - {Both}
{Total} = 42 + 28 - 12 = 58.
Answer: D.
Answer: (D) 58
Question: If a and b are positive integers and (2^a)^b = 2^5, what is the value of 2^a*2^b?
(A) 8
(B) 64
(C) 16
(D) 32
(E) 4
Rationale: 2^ab =2^5 therefore ab=5 either a=1or5 or b=5 or 1
therefore 2^a* 2^b = 2^(a+b)= 2^6 =64
B
Answer: (B) 64
Question: If population of certain city increases at the rate of 5%. If population in 1981 was 138915, then population in 1978 was?
(A) 120000
(B) 298991
(C) 299992
(D) 188611
(E) 122111
Rationale: X * (105/100) * (105/100) * (105/100) = 138915
X = 138915/1.157625
X = 120000
Answer: A
Answer: (A) 120000
Question: What percent is 6 gm of 1 kg?
(A) 1.5 %
(B) 0.5 %
(C) 0.6 %
(D) 3.5 %
(E) 4 %
Rationale: 1 kg = 1000 gm
6/1000 × 100 = 600/1000
=3/5 = 0.6 %
C)
Answer: (C) 0.6 %
Question: A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 45
(B) 60
(C) 75
(D) 90
(E) 95
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
16x = 480
x = 30.
Hence, total number of notes = 3x = 90.
Answer: Option D
Answer: (D) 90
Question: What is the average of first 21 multiples of 5 ?
(A) A)70
(B) B)77
(C) C)55
(D) D)81
(E) E)82
Rationale: Required average = 7(1+2+....+21) / 21
(5/21)X ( (21x22) / 2 ) (because sum of first 21 natural numbers)
= 55
C
Answer: (C) C)55
Question: Jamshid can paint a fence in 50 percent less time than Taimour can when each works alone. When they work together, they can paint the fence in 6 hours. How long would it take Taimour to paint the fence alone?
(A) 6 hours
(B) 8 hours
(C) 18 hours
(D) 24 hours
(E) 32 hours
Rationale: I believe the answer is C. Please see below for explanation.
if Jamshid can paint a dence in 50 percent less time then Taimour we can infer the following rate J = 2T
if working together they can do the job in 8 hours we can infer 1 = 2T+T * 6 => 1/18
Working alone Taimour can do the job in 1 = 1/18* hours => 18
Answer C
Answer: (C) 18 hours
Question: A is faster than B. A and B each walk 24 km. The sum of their speeds is 7 km/hr and the sum of times taken by them is 14 hours. Then, A's speed is equal to?
(A) 12 km/hr
(B) 3 km/hr
(C) 17km/hr
(D) 16km/hr
(E) 19km/hr
Rationale: Let A's speed = x km/hr. Then, B's speed = (7 - x) km/ hr.
So, 24/x + 24/(7 - x) = 14
x2 - 98x + 168 = 0
(x - 3)(x - 4) = 0 => x = 3 or 4.
Since, A is faster than B, so A's speed = 4 km/hr and B's speed
= 3 km/hr.
Answer:B
Answer: (B) 3 km/hr