RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: when W is divided by 13, the reminder is 0. if W is three more than it value and when divided by 11 its remainder is 0. what is the value of W ?
A.13
B.52
C.39
D.26
Answer: B.52
Explanation: W is divided by 13 so that is multiple of 14 as 13,26,39...
W+3 is divided by 11 the remainder is 0 so it is divisible by 11. Consider from option let us take the number is 13 it is divisible by 14 but 13+3 is not divisible by 11 so it is not answers so let us take 2nd option 52 which is divisible by 13 and 52+3=55 is divisible by 11 so ans is B
Question: Kunal walks 10 km towards North. From there he walks 6 Km towards South. Then, he walks 3 Km towards east. How far and in which direction is he with reference to his starting point ?
A.5 km north
B.5 km south
C.5 km east
D.5 km north-east
Answer: D.5 km north-east
Explanation: Clearly, Kunal moves from A 10 Km northwards upto B, then moves 6 Km southwards upto C, turns towards east and moves 3 km upto D.
Then AC = (AB-BC) = 4 Km
So AD is 5 Km also with reference to starting point Kunal's direction is North-East.
ANSWER D
Question: Find the fourth proportional to 22.8 , 36.2 and 40.8?
A.60.1
B.65.86
C.66.48
D.64.78
Answer: D.64.78
Explanation: Formula= Fourth proportional =(b x c)/a
a=22.8 , b=36.2 and c=40.8
(36.2 x 40.8)/22.8=64.78
D
Question: If x and y are integers, what is the least positive number of 24x+9y?
A.1
B.3
C.4
D.6
Answer: B.3
Explanation: 24x+9y = 3(8x+3y) which will be a minimum positive number when 8x+3y = 1.
8(-1) + 3(3) = 1
Then 3(8x+3y) can have a minimum positive value of 3.
The answer is B.
Question: A ship can travel with aspeed of 10km/hr in still water. If the speed of the stream is 10km/hr, find the time taken by the boat to go 60km downstream.
A.3 hrs
B.5 hrs
C.6 hrs
D.7 hrs
Answer: A.3 hrs
Explanation: Speed downstream = (10 + 10) km/hr = 45 km/hr.
Time taken to travel 68 km downstream = 60/20 hrs = 3 hrs.
A
Question: Two pipes A and B can fill a tank in 36 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
A.20 hrs
B.22 hrs
C.23 hrs
D.24 hrs
Answer: A.20 hrs
Explanation: 1/( 1/36 +1/45) = 180/9 = 20 hrs
ANSWER:A
Question: With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. If the second valve emits 50 cubic meters of water more than the first every minute, then what is the capacity R of the pool?
A.9000 cubic meters
B.10500 cubic meters
C.11750 cubic meters
D.12000 cubic meters
Answer: D.12000 cubic meters
Explanation: D. 12000 cubic meters.
If both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in (48*120)/(120-48) = 80 minutes.
Now, if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120x and also 80 (x+50).
or, 120x = 80 (x + 50).
or x = 100.
Hence, the capacity of pool = 120x = 12000 cubic meters.
Question: A boat can move upstream at 25 kmph and downstream at 45 kmph, then the speed of the current is?
A.10 kmph
B.7 kmph
C.8 kmph
D.9 kmph
Answer: A.10 kmph
Explanation: US = 25
DS = 45
M = (45 - 25)/2 = 10
Answer:A
Question: If f(x) = 2x + 3, & g(x) = (x - 3)/2, then what is the value of, fo(fo(go(go(fo(fo(go(go................(fo(fo(go(gof(x) )))).....)))))) ?
A.3
B.2
C.9
D.7
Answer: D.7
Explanation: f(x) = 2x + 3
g(x) = (x - 3)/2
gof(x) = 2x+3−32=x2x+3−32=x
gogof(x) = x−32x−32
fogogof(x) = 2(x−32)+32(x−32)+3 = 2x−6+622x−6+62 = x
fofogogof(x) = 2x + 3
This means, when we apply two times g(x) and two time f(x) on f(x) we get f(x). This pattern continues, Hence the answer is option (D).
Question: If the price of petrol increases by 30, by how much must a user cut down his consumption so that his expenditure on petrol remains constant?
A.25%
B.23%
C.16.67%
D.33.33%
Answer: B.23%
Explanation: Explanation :
let us assume before increase the petrol will be Rs. 100.
After increase it will be Rs (100+30) i.e 130.
Now, his consumption should be reduced to :-
=(130−100)/130 ∗ 100.
Hence, the consumption should be reduced to 23%.
Answer : B
Question: Sam buys 10 apples for $1. At what price should he sell a dozen apples if he wishes to make a profit of 25%?
A.$0.125
B.$1.25
C.$0.25
D.$1.5
Answer: D.$1.5
Explanation: Explanatory Answer
The cost price of 1 apple = $1/10 or $0.10.
As Sam wishes to make a profit of 25%, his selling price per apple should be 0.10 + 25% of 0.10 = 0.1 + 0.025 = $0.125.
If the selling price of 1 apple is $0.125, the selling price of a dozen apples = 12 * 0.125 = $1.5
Choice D
Question: The rate of a certain chemical reaction is directly proportional to the concentration of chemical A present and inversely proportional to the concentration of chemical B present. If the concentration of chemical B present is increased by 50 percent, which of the following is closest to the percent change in the the concentration of chemical A required to keep the reaction rate unchanged.
A.100 % decrease
B.50% decrease
C.40% decrease
D.30% increase
Answer: B.50% decrease
Explanation: Let's say here is the formula of how A and B affects the reaction speed:
rate = A/B
After the concentration B is increased by 50%, the percentage of B
become 1.5B, to keep 'rate' the same, need to have 1.5A.
Which means A increased by 50%
Answer : B
Question: Two numbers have a H.C.F of 11 and a product of two numbers is 1991. Find the L.C.M of the two numbers?
A.140
B.181
C.160
D.170
Answer: B.181
Explanation: L.C.M of two numbers is given by
(Product of the two numbers) / (H.C.F of the two numbers) = 1991/11 = 181.
ANSWER:B
Question: How many liters of water must be added to 14 liters of milk and water containing 10% water to make it 30% water?
A.1 liter
B.2 liters
C.3 liters
D.4 liters
Answer: D.4 liters
Explanation: By rule of alligation:
30% - 10% = 20%
100% - 30% = 70%
Quantity of pure water : Quantity of the mixture = 2 : 7
There are 14 liters of mixture, so we need to add 4 liters of pure water.
The answer is D.
Question: What is the units digit of (5!*4! + 6!*5!)/2?
A.4
B.3
C.0
D.1
Answer: C.0
Explanation: (5!*4! + 6!*5!)/2
=5!(4! + 6!)/2
=120 ( 24 + 720)/2
=(120 * 744)/2
= 120 * 372
Units digit of the above product will be equal to 0
Answer C
Question: In the kitchen of a busy restaurant, it takes M minutes to wash P pots. At this rate, how many hours does it take to wash 10P pots?
A.M/10
B.6/M
C.600M
D.M/6
Answer: D.M/6
Explanation: The time it takes to wash 10P pots is 10M minutes which is 10M / 60 = M/6 hours.
The answer is D.
Question: The amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 50,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 42 years later?
A.$ 280,000
B.$ 320,000
C.$ 360,000
D.$ 400,000
Answer: D.$ 400,000
Explanation: The amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 50,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 42 years later?
The investment gets doubled in 70/p years. Therefore, the investment gets doubled in 70/5= every 14 years. After 42 years, the investment will get doubled 42/14= 3 times.
So the amount invested will get doubled thrice.
So, 50000 *2^3 =400000
Hence, the answer is D.
Question: Linda and Angela contract to paint a neighbor's house. Even though Linda spends 30% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m ?
A.1/2 m
B.1/3 m
C.1/4 m
D.1/5 m
Answer: B.1/3 m
Explanation: After the final transaction:
Angela received $(m-n) for t hours;
Linda received $(m+n) for 1.5t hours;
We are told that after that transaction they received the same compensation per hour: (m-n)/t=(m+n)/1.5t --> 1.5m-1.5n=m+n -->m=5n --> n=m/3.
Answer: B.
Question: the distance between parallel sides of the hexagon is 9. determine the length of the hexagon
A.18*sqrt3
B.18*sqrt2
C.18*sqrt4
D.19*sqrt3
Answer: A.18*sqrt3
Explanation: Length of each side of regular hexagon will be 3*sqrt3. total length ( perimeter) of regular hexagon will be 18*sqrt3
ANSWER:A
Question: If the compound interest on a certain sum of money for 3 years at 10% per annum be Rs. 993, what would be the simple interest?
A.Rs. 880
B.Rs. 890
C.Rs. 895
D.Rs. 900
Answer: D.Rs. 900
Explanation: Let P = Principal
A - Amount
We have a = P(1 + R/100)3 and CI = A - P
ATQ 993 = P(1 + R/100)3 - P
? P = 3000/-
Now SI @ 10% on 3000/- for 3 yrs = (3000 x 10 x 3)/100
= 900/-
Answer: D.
Question: If 30% of a number is equal to one-third of another number, what is the ratio of first number to the second number ?
A.2:5
B.3:7
C.10:9
D.7:3
Answer: C.10:9
Explanation: Explanation :
Let 30% of A=1/3B
Then, 30A/100=1B/3
=> 3A/10=B/3
=> A:B= 10 : 9
Answer : C
Question: Mohan's salary was first increased by 20% and then decreased by 20%. If his present salary is Rs. 7200, then what was his original salary?
A.Rs. 8000
B.Rs. 7500
C.Rs. 7400
D.Rs. 7200
Answer: B.Rs. 7500
Explanation: Let Mohan's salary be Rs.100.
When increased by 20%, Mohan's salary = Rs.120
Again when decreased by 20%, Mohan's salary = 120 - 24 = Rs. 96.
But present salary is Rs. 7200
for, 96 ---> 100 ; 7200 ---> ?
Required salary is 7200/96 * 100 = Rs. 7500
ANSWER:B
Question: Find number which is 70% less than 60.
A.18
B.22
C.28
D.26
Answer: A.18
Explanation: Explanation:
70% less is 30% of the given number
Therefore, 30% of 60 is 18.
ANSWER: A
Question: Rani bought more apples than oranges. She sells apples at ₹23 apiece and makes 15% profit. She sells oranges at ₹10 apiece and makes 25% profit. If she gets ₹653 after selling all the apples and oranges, find her profit percentage W.
A.16.8%
B.17.4%
C.17.9%
D.18.5%
Answer: B.17.4%
Explanation: Given: Selling price of an Apple = 23 --> Cost price = 23/1.15 = 20
Selling price of an orange = 10 --> Cost price = 10/1.25 = 8
A > O
23*(A) + 10*(O) = 653
653 - 23*(A) has to be divisible by 10 --> Units digit has to be 0
Values of A can be 1, 11, 21, 31, .... --> 1 cannot be the value
Between 11 and 21, If A = 11, O = 30 --> Not possible
If A = 21, O = 17 --> Possible
Cost price = 20*21 + 8*17 = 420 + 136 = 556
Profit = 653 - 556 = 97
Profit% W= (97/556)*100 = 17.4%
Answer: B
Question: If rupee one produces rupees nine over a period of 45 years, find the rate of simple interest?
A.22 1/7 %
B.22 3/2 %
C.22 1/8 %
D.20 %
Answer: D.20 %
Explanation: 9 = (1*45*R)/100
R = 20 %
Answer:D
Question: 300 + 5 × 8 = ?
A.820
B.340
C.420
D.209
Answer: B.340
Explanation: 300 + 5 × 8 = ?
or, ? = 300 + 40 = 340
Answer B
Question: The first term in a sequence is 1 and the second term is 7. From the third term on each term is the average (arithmetic mean) of all preceding terms. What is the 25th term in the sequence?
A.2.5
B.3
C.4
D.25
Answer: C.4
Explanation: The third term is 4 since this is the average of 1 and 7.
Then the next terms will all be 4 since the average stays at 4.
The answer is C.
Question: The ratio between the number of sheep and the number of horses at the Stewar farm is 4 to 7. If each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day. what is number sheep in the form??
A.18
B.28
C.32
D.56
Answer: C.32
Explanation: et no of sheep and horses are 4k and 7k
no of horses= 12880/230=56
now 7K=56 and k=8
no of sheep=(4*8) =32
ANSWER:C
Question: There is a 20% chance that Ella will visit Finland this year, while there is a 70% chance that she will visit Mexico this year. What is the probability that Ella will visit either Finland or Mexico this year, but NOT both?
A.58%
B.60%
C.62%
D.64%
Answer: C.62%
Explanation: P(Finland but not Mexico)=0.2*0.3=0.06
P(Mexico but not Finland)=0.7*0.8=0.56
P(Finland or Mexico but not both)=0.06+0.56=0.62
The answer is C.
Question: Jaclyn buys $10 000 worth of debentures in a company. She earns 9.5% p.a. simple interest, paid to her quarterly (that is, every 3 months). If the agreed period of the debenture was 18 months: calculate the amount of interest Jaclyn will earn for each quarter
A.237.5
B.234
C.289.5
D.345
Answer: A.237.5
Explanation: Explanation:
I=(p x r x t)/100
= 10000*9.5/100*(18/12)^1/6 = 237.5
Answer: A
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
A.11:5
B.3 : 2
C.1:2
D.3:5
Answer: B.3 : 2
Explanation: Answer: Option B
Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2.
Question: What sum of money will produce Rs.90 as simple interest in 4 years at 3 1/2 percent?
A.263
B.500
C.367
D.642.9
Answer: D.642.9
Explanation: 90 = (P*4*7/2)/100
P = 642.9
Answer: D
Question: The distance between Delhi and Mathura is 150 kms. A starts from Delhi with a speed of 25 kmph at 5 a.m. for Mathura and B starts from Mathura with a speed of 40 kmph at 6 p.m. from Delhi. When will they meet?
A.11
B.77
C.8
D.10
Answer: C.8
Explanation: D = 150 – 25 = 125
RS = 40 + 25 = 65
T = 125/65 = 2 hours
6 a.m. + 2 = 8 a.m..Answer: C
Question: A paint crew gets a rush order to paint 80 houses in a new development. They paint the first y houses at a rate of x houses per week. Realizing that they'll be late at this rate, they bring in some more painters and paint the rest of the houses at the rate of 1.25x houses per week. The total time R it takes them to paint all the houses under this scenario is what fraction of the time it would have taken if they had painted all the houses at their original rate of x houses per week?
A. 0.8(80 – y)
B. 0.8 + 0.0025y
C. 80/y – 1.25
D. 80/1.25y
Answer: B. 0.8 + 0.0025y
Explanation: This may be a case of bad numberpicking but it worked for me.
80 houses. Let's say that y=40 houses are painted at the rate x=10 houses per week <=> 1/10 week per house. 40*1/10 = 4 houses per week will be painted at this rate.
80-y = 80-40 = 40 houses are to be painted at the faster rate. X*1,25=12,5 houses per week <=> 1/12,5 weeks per house * 40 houses = 40/12,5 = 80/25 = 320/100 = 3,2 weeks.
Which means finishing all houses at normal rate R=> 2*4 = 8 weeks. Faster rate = 4+3,2 = 7,2 weeks.
7,2/8 = 9/10 = 0,9. Insert y=40 in equations and it is clear that only (B) gives us 0,9.
Question: there is park of length 100 m and width 80m.there is path in middle of park across the length and breadth crossing each other.the breadth of path 3m.what % of park used for path?
A.5.53
B.6.63
C.4.43
D.8.61
Answer: B.6.63
Explanation: area of park=100*80=8000m2.
area of path=100*3+80*3-3*3=300+240-9=540-9=531m2.
%of path=531/8000*100=6.6375%
answer B
Question: Tina and Rebecca had the same number of candies. Tina gave Rebecca 20 candies so that now Rebecca has five times as many candies as Tina has. Rebecca has now how many candies initially?
A.36
B.48
C.50
D.55
Answer: A.36
Explanation: T = R
T - 24 ;R + 24
R + 24 = 5 ( T - 24 )
R + 24 =5T - 120
R - 5T = - 144
We knowR = T, so
R - 5T = - 144
Or, R - 5R = -144
Or, - 4R = - 144
Or, R = 36( This is the initital no of Candies Rebecca had)
Answer will be (A) 36
Question: One fast typist type some matter in 4hrs and another slow typist type the same matter in 6hrs. If both do combine in how much time they will take to finish.
A.10 hr
B.1 hr
C.2 hr 24 mins
D.3 hr 4 mins
Answer: C.2 hr 24 mins
Explanation: Fast's 1 hr work = 1/4
slow's 1 hr work = 1/6
1/4 + 1/6 = 5/12
they ll finish in 12/5hrs= 2 2/5 ==> 2 hr 24 mins
ANSWER:C
Question: Rs.4500 amounts to Rs.5544 in two years at compound interest, compounded annually. If the rate of the interest for the first year is 12%, find the rate of interest for the second year?
A.5544
B.2288
C.6776
D.1877
Answer: A.5544
Explanation: Let the rate of interest during the second year be R%. Given,
4500 * {(100 + 12)/100} * {(100 + R)/100} = 5544
R = 10%
Answer:A
Question: Current ages of Rahim and Thomas are in the ratio of 5 : 4 correspondingly. 0.5 decades hence, the ratio of their ages will become 11 : 9 correspondingly, What is Thomasâ€™s current age in years?
A.24 years
B.44 years
C.34 years
D.40 years
Answer: D.40 years
Explanation: 40 years
If current ages of Rahim and Thomas be 5A years and 4A years correspondingly
Then, 5A + 5 = 11
4A + 5 = 9
9(5A + 5)=11(4A + 5)
A = 10
Thomasâ€™s current age = 4A
= 40 years.
D
Question: 120 candies are distributed to children with the same number of candies for each child. What can’t be the range which includes the number of children?
A.1~10
B.10~20
C.20~30
D.45~55
Answer: D.45~55
Explanation: 120 = 2^3*3*5
There are factors in each range except for 45~55
The answer is D.
Question: A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?
A.30 minutes
B.45 minutes
C.1 hour
D.1 hour 15 min
Answer: D.1 hour 15 min
Explanation: Sol.
Rate downstream = [16/2] kmph = 8 kmph; Rate upstream = [16/4] kmph = 4 kmph.
∴ Speed in still water = 1/2(8+4) kmph = 6 kmph.
Answer D
Question: The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
A.249
B.247
C.245
D.2882
Answer: C.245
Explanation: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (130 + x)/30 = 25/2
x = 245 m.
Answer: C
Question: I. a2 - 7a + 12 = 0,
II. b2 - 3b + 2 = 0 to solve both the equations to find the values of a and b?
A.if a < b
B.if a ≤ b
C.if the relationship between a and b cannot be established
D.if a > b
Answer: D.if a > b
Explanation: I.(a - 3)(a - 4) = 0
=> a = 3, 4
II. (b - 2)(b - 1) = 0
=> b = 1, 2
=> a > b
ANSWER:D
Question: If 9 men working 6 hours a day can do a work in 88 days. Then 6 men working 8 hours a day can do it in how many days?
A.78 days.
B.99 days.
C.49 days.
D.48 days.
Answer: B.99 days.
Explanation: B
99 days.
From the above formula i.e (m1*t1/w1) = (m2*t2/w2)
so (9*6*88/1) = (6*8*d/1)
on solving, d = 99 days.
Question: The moon revolves around the earth at a speed of approximately 1.04 kilometers per second. This approximate speed is how many kilometers per hour?
A.60
B.61.2
C.3,744
D.3,600
Answer: C.3,744
Explanation: 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= 1.04*3600=3744kilometers per hour.
Option C is correct
Question: By selling an article at $800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?
A.$580
B.$450
C.$480
D.$400
Answer: C.$480
Explanation: C
$480
SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 25% = 25% of 640 = $160
SP = CP - Loss = 640 - 160 = $480
Question: In the Bargaining Bazar everyone purchase with a fair bargaining, so the traders markup the prices too much. A trader marked up an article at Rs. M expected huge profit if it is sold on marked price. But a customer purchased it at M/2 with his fine bargaining skills, so the expected profit of the trader diminished by 66.66%. What is the percentage discount fetched by the customer through bargaining?
A.33.33%
B.50%
C.60%
D.66.66%
Answer: B.50%
Explanation: Solution: MP = M
SP = M/2
% Discount = [(M/2) /M] *100 = 50%.
Answer: Option B
Question: If 4x + 3y = 8 and y − 3x = 2, then what is the value of x + 4y?
A.10
B.3
C.15
D.52/7
Answer: A.10
Explanation: 4x + 3y = 8
−3x + y = 2
Adding both the equations --> x + 4y = 10
Answer: A
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B?
A.8
B.9
C.10
D.11
Answer: C.10
Explanation: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 27
5x = 25
x = 5.
Hence, B's age = 2x = 10 years.
ANSWER C
Question: When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 39, what is the remainder when k is divided by 7?
A.4
B.5
C.6
D.3
Answer: D.3
Explanation: Cant think of a straight approach but here is how I solved it:
K is divided by 5 and remainder is 2. This means k = 5n + 2 (n is an integer)
so the possible values of K = {2, 7, 12, 17, 22, 27, 32, 37} (less than 39)
Secondly, if K is divided by 6, the remainder is 5 => k= 6m + 5
so the possible value set for k = {5, 11, 17, 23, 29,35} (less than 39)
17 is the only common number in both the sets. Hence k = 17
Answer : D
Question: The sum of three consecutive multiples of 3 is 72. What is the larget number?
A.26
B.27
C.46
D.57
Answer: B.27
Explanation: Sol.
Let the numbers be 3x, 3x + 3 and 3x + 6.
Then, 3x + (3x + 3) + (3x + 6) = 72 ⇔ 9x = 63 ⇔ x = 7.
∴ Largest number = 3x +6 = 27.
Answer B
Question: For how many integers pair (x,y) satisfies the result
(1/x)+((1/y)=1/12
A.12
B.6
C.29
D.16
Answer: C.29
Explanation: Now let’s look at this question from the perspective of number theory.
1/x + 1/y = 1/12
12x + 12y = xy
12x + 12y – xy =0
We need to factorize it and for that we subtract 144 from left and right parts.
12x – xy +12y – 144 = -144
(x-12)(12-y) = -144
(x-12)(y-12) = 144
Now we need to represent 144 as a product of 2 factors and find out our pairs of x and y.
(1*144) (2*72) (3*48) (4*36) (6*24) (8*18) (9*19) and 12*12.
All factor pairs (except 12*12) can be written in reverse order, so we have total 15 positive solutions.
Because we have product, x and y can also take negative values. Using same logic we got 15 negative solutions, but in this case we need to discard (-12)*(-12), because it will give us x=0, y=0. In this point the original equation is undetermined (we can’t divide by zero).
Hence we have total number of integer pairs 15 + 14 = 29
ANSWER:C
Question: The function f is defined for all positive integers s by the following rule. f(s) is the number of positive integers each of which is less than s and has no positive factor in common with s other than 1. If t is any prime, number then f(t)=
A.(t-1)/2
B.t-2
C.(t+1)/2
D.t-1
Answer: D.t-1
Explanation: If not the wording the question wouldn't be as tough as it is now. The GMAT often hides some simple concept in complicated way of delivering it.
This question for instance basically asks: how many positive integers are less than given prime number t which have no common factor with t except 1.
Well as t is a prime, all positive numbers less than t have no common factors with t (except common factor 1). So there would be t-1 such numbers (as we are looking number of integers less than t).
For example: if t=5 how many numbers are less than t having no common factors with 5: 1, 2, 3, 4, 5,--> 5-1=4.
Answer: D.
Question: In a class, the average age of 28 boys is 12 years and the average of 20 girls is 8 years. what is the average age of the whole class?
A.10.3 Years
B.12.3 Years
C.12.6 Years
D.13 Years
Answer: A.10.3 Years
Explanation: Total age of 48 students
(28X 12+20 X 8) = 496
Average = 496/48 = 10.3 Years
A
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
A.2/22
B.2/20
C.2/21
D.2/23
Answer: C.2/21
Explanation: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow = (2 * 3 * 2)/(15 * 14) = 2/35
Required probability = 1/35 + 1/105 + 2/35
= 3/35 + 1/105 = 1/35(3 + 1/3)
= 10/(3 * 35) = 2/21
Answer:C
Question: if the selling price of an object is rs.2300 and the profit percent is 15,what is the cost price?
A.1995
B.1945
C.2000
D.2645
Answer: C.2000
Explanation: cp=Sp/1.15=2300/1.15
=2000
ANSWER:C