mathewhe/aqua_rat huggingface dataset:
Question: If 5400 mn = k^4, where m, n, and k are positive integers, what is the least possible value of 4m + n?
(A) 11
(B) 18
(C) 55
(D) 25
(E) 33
Rationale: k^4=5400∗mn
k^4=3^3.2^3.5^2.mn
In order to make RHS a perfect power of 4, we require it to be multiplied by 3, 2 & 5^2
mn=3.2.5^2
mn = 150 = 10 * 15 (Least possible)
Answer = 4*10 + 15 = 55
ANSWER:C
Answer: (C) 55
Question: If xerox paper costs 5 cents a sheet and a buyer gets 10% discount on all xerox paper one buys after the first 2000 papers and 20% discount after first 10000 papers, how much will it cost to buy 15000 sheets of xerox paper?
(A) $1250
(B) $700
(C) $1350
(D) $900
(E) $1000
Rationale: 30 sec approach - solve it using approximation
15000 sheet at full price, 5 cent = 750
15000 sheet at max discount price, 4 cent = 600
Your ans got to be between these two.
Ans B it is.
Answer: (B) $700
Question: A tank can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tank from empty state if B is used for the first half time and then A and B fill it together for the other half.
(A) 15 mins
(B) 20 mins
(C) 25 mins
(D) 30 mins
(E) 35 mins
Rationale: Explanation:
Let the total time be x mins.
Part filled in first half means in x/2 = 1/40
Part filled in second half means in x/2 =1/60 +1/40 =1/24
Total =X/2 X 1/40 + X/2 X 1/24 =1
x=30mins
ANSWER IS D
Answer: (D) 30 mins
Question: How many five-digit numbers satisfy this property.: The last digit (unit's digit) of the square of the two-digit number is 3 ?
(A) 33
(B) 66
(C) 0
(D) 99
(E) 132
Rationale: A number ending with 3 can never be a perfect square.
Answer: C
Answer: (C) 0
Question: A total of 24 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?
(A)  32.2
(B)  31.5
(C)  32
(D)  32.5
(E)  33
Rationale: Let Aw = average age of women
Average = (Number of men X average age of men + Number of women X average age of women)/total number of people
35 * 50 = 24 * 38 + 26 * Aw
=>1750 = 912 + 26 Aw
=> 26 Aw = 838
=>Aw = 32.2
Answer A
Answer: (A)  32.2
Question: How many different values of positive integer x, for which |x+7|<x, are there?
(A) 0
(B) 2
(C) 3
(D) 8
(E) 16
Rationale: Answer A
I opted to put the random value option.
i used 0 , 7 , -7 and the the extreme of 30 and -30..
i was able to solve it in 1:09
B
Answer: (B) 2
Question: The annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years Q in which the population would be doubled assuming there is no emigration or immigration is
(A) Q=20
(B) Q=25
(C) Q=30
(D) Q=35
(E) 40
Rationale: Suppose the population of the country in current year is 1000.
So annual increase is 1000 + 39.4 - 19.4=1020
Hence every year there is an increase of 2%.
2000=1000(1+(2/100))^n
n=35 Answer is D
Answer: (D) Q=35
Question: What is the greatest power that 2 can be raised to so that the resulting number is a factor of 20!?
(A) 4
(B) 8
(C) 10
(D) 20
(E)  15
Rationale: the number of 2s in 20!= 20/2=10..
ans C
Answer: (C) 10
Question: Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.54000 after completion of one year. What will be Jose's share of profit?
(A) 10000
(B) 20000
(C) 22000
(D) 24000
(E) 30000
Rationale: SoL = ~s- So Anju’s share = [5/9] x 54000 = 30000
E
Answer: (E) 30000
Question: Q-1: How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 5?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 6
Two digit numbers divisible by 5 must end in either 0 or 5. Since there is no 0, all correct answers are a combination of the other digits and 5. There are six other numbers plus the 5 so there are 6 correct answers.
Correct answer is D.
Answer: (D) 6
Question: 8,13,23,43,83, (...)
(A) 123
(B) 223
(C) 143
(D) 163
(E) 113
Rationale: 8
8Ã— 2 - 3 = 13
13 Ã— 2 - 3= 23
23 Ã— 2 - 3 = 43
43 Ã— 2 - 3 = 83
83 Ã— 2 - 3 = 163
Answer is D
Answer: (D) 163
Question: 225 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees
(A) 10
(B) 12
(C) 14
(D) 16
(E) 17
Rationale: 26 trees have 25 gaps between them,
Required distance (225/25) = 10
A
Answer: (A) 10
Question: The original price of a suit is $160. The price increased 25%, and after this increase, the store published a 25% off coupon for a one-day sale. Given that the consumers who used the coupon on sale day were getting 25% off the increased price, how much did these consumers pay for the suit?
(A) $140
(B) $145
(C) $150
(D) $155
(E) $160
Rationale: 0.75*(1.25*160) = $150
The answer is C.
Answer: (C) $150
Question: There are 600 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school?
(A) 320
(B) 345
(C) 375
(D) 380
(E) 400
Rationale: In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 600. Hence
3x + 5x = 600
Solve for x
8x = 600
x = 75
Number of boys
3x = 3 × 75 = 225
Number of girls
5x = 5 × 75 = 375
C
Answer: (C) 375
Question: A fortune teller has a unique way of predicting his customer’s prognosis. He has three parrots kept in three different cages. Each cage has three cards with a one digit non-zero number inscribed on every card. No two cards have the same number and no cage contains two cards with the number totaling ten. Further the total of numbers on the three cards in the first cage is greater by two than that in the second and by four than that in the third. When a customer asks for his prognosis, the fortune teller lets out the three parrots, which randomly pick one card out of their respective cages. Before the prognosis is made, the fortune teller totals the numbers on the three cards picked out by the parrots and charges the customer the same number of rupees as the total of the numbers on the cards. One day a customer paid seven rupees for his prognosis.
Which of the following combinations of cards may be picked for prognosis?
(A) 5, 7, 8
(B) 7, 9, 4
(C) 2, 6, 3
(D) 1, 3, 8
(E) None of these
Rationale: considering the cages named as A B and C
according to the given conditon A=2B and A=4C
the customer paid the amount as the sum of three cards ,i,e card A,card B and card C=7
A+B+C=7 so, A+(A/2)+(A/4)=7
Solving, we get A=4
therefore a,b,c=4,2,1
ANSWER:E
Answer: (E) None of these
Question: How many liters of pure alcohol must be added to a 100-liter solution that is 20 percent alcohol in order to produce a solution that is 30 percent alcohol?
(A)  100/7
(B)  5
(C)  20/3
(D)  8
(E)  39/4
Rationale: 20% Alcohol solution means; in the 100 liter solution, 20 liters of solution is alcohol and 80 liters other solvents.
If we addxliters of alcohol to the solution, the solution becomes100+xliters and alcohol, which was 20 liters, becomes 20+x liters.
According to the statement;
20+x = 30% of (100+x)
OR
20+x=(100+x)3/10
200+10x=300+3x
7x=100
x=100/7
Ans:A
Answer: (A)  100/7
Question: Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
(A) 4 years
(B) 8 years
(C) 2 years
(D) 4 years
(E) 6 years
Rationale: Mother's age when Ayesha's brother was born = 36 years.
Father's age when Ayesha's brother was born = (38 + 4) years = 42 years.
Required difference = (42 - 36) years = 6 years.
ANSWER E
Answer: (E) 6 years
Question: A, Band C enter into partnership. A invests 3 times as much as B and B invests two-third of what C invests. At the end of the year, the profit earned is Rs. 5500. What is the share of B ?
(A) 1000
(B) 800
(C) 1400
(D) 1200
(E) None of them
Rationale: Let C's capital = Rs. x. Then, B's capital = Rs. (2/3)x
A’s capital = Rs. (3 x (2/3).x) = Rs. 2x.
Ratio of their capitals = 2x : (2/3)x :x = 6 : 2 : 3.
Hence, B's share = Rs. ( 5500 x (2/11))= Rs. 1000.
Answer is A
Answer: (A) 1000
Question: When two dice are rolled, what is the probability that the difference between the two numbers is 3?
(A)  1/9
(B)  2/9
(C)  1/3
(D)  2/3
(E)  None of the above
Rationale: We have 6 outcomes that satisfy the question:
1-4
2-5
3-6
4-1
5-2
6-3
the probability is (1/6*1/6)*6= 1/6.
I think the answer is E
Answer: (E)  None of the above
Question: n is a positive integer and k is the product of all integers from 1 to n inclusive. If k is a multiple of 3360, then what is the smallest possible value of n?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: 3360=2^5*3*5*7
2^5 means that n must be at least 8. That is, We need 2, 4, 6, and 8.
The answer is C.
Answer: (C) 8
Question: Amy's sells kale at x dollar per pound for the first 30 pounds and .8x for every subsequent pound. Lucia's price is x per pound for the first 14 pounds and .9x for subsequent pounds. What is the minimum number of pounds over 15 for which Amy's becomes an equal or better deal?
(A) 24
(B) 25
(C) 26
(D) 27
(E) 46
Rationale: For Amy's deal to be better, the cost has to be less or equal to Lucia's
Assuming 'n' is the number of pounds of kale, the equation is
30x + (n-30) (0.8x) <= 14x + (n-14)(0.9x)
Resolve it:
==> 30x + 0.8nx - 24x <= 14x + 0.9nx - 12.6x
==> 4.6x <=0.1nx
==> 46x < =nx
==> x (n-46) > = 0
as x cannot be 0,
==> n - 46 >=0
==> n > = 46
so the minimum value is 46
'E' would be the correct answer
Answer: (E) 46
Question: When m is divided by 9, the remainder is 3. When m is divided by 13, the remainder is 9. If 1 < m < 200, what is the greatest possible value of m?
(A) 47
(B) 65
(C) 103
(D) 117
(E) 165
Rationale: Looking at the choices, options BD can be eliminated as they are divisible by 13
Starting from the highest number 164;
165 = 162 + 3 (162 divisible by 9)
165 = 156 + 9 (156 divisible by 13)
it fits the result
Answer = E
Answer: (E) 165
Question: Indu gave Bindu Rs.1250 on compound interest for 2 years at 8% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
(A) 1
(B) 2
(C) 8
(D) 4
(E) 5
Rationale: 1250 = D(100/4)8
D = 8
Answer: C
Answer: (C) 8
Question: Bill bought 100 packets of candy. He was able to sell 1/2 of them at a 20% profit, another 1/4 of them at zero profit and the remainder was sold at a 5% loss. Find the total profit or loss made by Bill after selling those 100 packets. A packet sold at a loss had a price of $9.
Please provide an intuitive answer if possible. Thanks!!
(A) 0
(B) Profit of $87.5
(C) Loss of $25
(D) Profit of $80
(E) Profit of $85
Rationale: A packet sold at a 10% loss had a price of $9, thus the cost of a packet is $10.
50 packets was sold at a 20% profit --> gives profit of 10*0.2*50 = $100.
25 packets was sold at a 5% loss --> gives loss of 10*0.05*25 = $12.5.
The overall Profit is $100 - $12.5 = $87.5.
Answer: B.
Answer: (B) Profit of $87.5
Question: When E is divided by 9, the remainder is 4. All of the following are possible values of E, except for which of the following?
(A) 13
(B) 31
(C) 49
(D) 57
(E) 67
Rationale: The number can be expressed in the form of 9x+4 where x can 0,1,2,3,4....
by evaluating the answer choices carefully we can clearly observe that 57 is the only number which can't be expressed E in the form of 9x+4
In other words we can also say that the (answer - 4) will not be divisible by 9.57 is the number which doesn't follow this condition
Correct Answer - D
Answer: (D) 57
Question: In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole?
(A) 10
(B) 28
(C) 26
(D) 11
(E) 12
Rationale: Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps.
The distance to be covered is equal to the length of the train.
Required time t = d/s = 100/10
= 10 sec.
Answer:A
Answer: (A) 10
Question: A policeman noticed a criminal from a distance of 265 km. The criminal starts running and the policeman chases him. The criminal and the policeman run at the rate of 8 km and 9 km per hour respectively. What is the distance between them after 3 minutes ?
(A) 100 m
(B) 120 m
(C) 130 m
(D) 150 m
(E) None of these
Rationale: Explanation :
Solution: Relative speed = (9 - 8) = 1 km/hr.
Distance covered in 3 minutes = (1 * 3/60) km = 1/20 km = 50 m.
.'. Distance between the criminal and policeman = (265 - 50) m = 215 m.
Answer : E
Answer: (E) None of these
Question: The sum of the two digits of a number is 10. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number?
(A) 29
(B) 84
(C) 42
(D) 28
(E) 64
Rationale: Any two digit number can be written as (10P + Q), where P is the digit in the tens place and Q is the digit in the units place.
P + Q = 10 ----- (1)
(10Q + P) - (10P + Q) = 54
9(Q - P) = 54
(Q - P) = 6 ----- (2)
Solve (1) and (2) P = 2 and Q = 8
The required number is = 28
ANSWER: D
Answer: (D) 28
Question: P and Q can complete a work in 15 days and 10 days respectively. They started the work together and then Q left after 2 days. P alone completed the remaining work. The work was finished in --- days.
(A) 10
(B) 11
(C) 13
(D) 12
(E) 15
Rationale: Work done by P in 1 day = 1/15
Work done by Q in 1 day = 1/10
Work done by P and Q in 1 day = 1/15 + 1/10 = 1/6
Work done by P and Q in 2 days = 2 × (1/6) = 1/3
Remaining work = 1 – 1/3 = 2/3
Time taken by P to complete the remaining work 2/3 = (2/3) / (1/15) = 10 days
Total time taken = 2 + 10 = 12 days
Answer is D.
Answer: (D) 12
Question: A man sells 4000 common shares of a Company x (each of par value Rs. 10), which pays a dividend of 40% at Rs. 30 per share. He invests the sale proceeds in ordinary shares of Company Y (each of par value Rs. 25) that pays a dividend of 15%. If the market value of Company Y is Rs. 15, find the number of shares of Company Y purchased by the man
(A) 4000
(B) 8000
(C) 3000
(D) 6000
(E) 5000
Rationale: Just too much information is given in the question to confuse. This is a straight and simple question
Market Value of Company X (his selling price) = Rs.30
Total shares sold = 4000
Amount he gets = Rs.(4000 × 30)
He invests this amount in ordinary shares of Company Y
Market Value of Company Y(His purchasing price) = 15
Number of shares of company Y which he purchases = 4000×30/15=8000
Answer is B.
Answer: (B) 8000
Question: The sum of two positive integers multiplied by the larger number is 204. The difference multiplied by the smaller number is 35. The larger number is
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: let a and b be the 2 no.s , and a being the smaller
(a+b)*b=204
(b-a)*a=35
on solving
we get
b^2+a^2 = 169=13^2
remembering the pythagorean triplets of 5,12,13.
We get the values of a=5 and b=12
ANSWER:E
Answer: (E) 12
Question: Of all the homes on Gotham Street, 2/3 are termite-ridden, and 3/5 of these are collapsing. What fraction of the homes are termite-ridden, but NOT collapsing?
(A) a) 7/15
(B) b) 3/15
(C) c) 4/15
(D) d) 2/5
(E) e)1/5
Rationale: let total homes be 15
termite ridden= 2/3(15)= 10
termite ridden and collapsing = 3/5(10)=6
thus homes that are termite ridden, but not collapsing = 10-6=4
thus required ratio = 4/15
Answer C
Answer: (C) c) 4/15
Question: How many positive factors do 120 and 96 have in common?
(A) 8
(B) 12
(C) 16
(D) 18
(E) 24
Rationale: The number of common factors will be same as number of factors of the Highest Common Factor(HCF)
HCF of 120 and 96 is 24
Number of factors of 24 = 8
Answer :A
Answer: (A) 8
Question: Kiran received Rs. 6000 as his share out of the total profit of Rs.9000 which he and Arun earned at the end of one year. If Kiran invested Rs. 30,000 for 6 months, whereas Arun invested his amount for the whole year, what was the amount invested by Arun?
(A) Rs.5000
(B) Rs.6000
(C) Rs.7000
(D) Rs.7500
(E) Rs.6500
Rationale: Suppose Arun invested Rs.x. Then, Kiran : Arun = (30000 * 6) : (x * 12)
Therefore, 180000/ 12x = 6000/3000
or x = 18000/24
= 7500.
ANSWER:D
Answer: (D) Rs.7500
Question: In a cricket team, the average of eleven players is 28 years. Out of these, the average ages of three groups of three players each are 19 years, 28 years and 30 years respectively. If in these groups, the captain and the youngest player are not included, and the captain is eleven years older than the youngest player, what is the age of the captain ?
(A) 33 years
(B) 44 years
(C) 35 years
(D) 36 years
(E) 37 years
Rationale: Explanation :
Let the age of youngest player be x.
Then, age of the captain = (x + 11).
=> 3*19 + 3*28 + 3*30 + x + x + 11 = 11*28.
=> 57+84+90+2x+11=308
so 2x = 66
so x = 33.
Age of the captain = (x+11)
= 44 years.
Answer : B
Answer: (B) 44 years
Question: A highway is to be divided into 3 lanes. For this purpose, two yellow stripes are painted so that stripes divide the highway into 3 lanes. If 2 gallons of paint cover an area of 5P square feet of highway, how many gallons of paint are needed to paint two stripes x inches wide on a stretch of highway m miles long? (1 mile = 5280 feet and 1 feet = 12 inches)
(A) 880mx/P
(B) 440P/mx
(C) 352mx/P
(D) 1760mx/P
(E) 5P/352mx
Rationale: 1 square foot needs 2/5P gallons of paint.
The width of each stripe is x/12 feet.
The length of each stripe is 5280m feet.
The area of each stripe is (5280m)(x/12) = 440mx square feet.
For two stripes, the total area is 880mx square feet.
The number of gallons needed is (880mx)*(2/5P) = 352mx/P gallons.
The answer is C.
Answer: (C) 352mx/P
Question: If 2^98=256L+N , where Land N are integers and 0≤N≤4 , what is the value of N ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: If 2^98= 256L + N and 0<=N<=4, what is the value of N?
To solve this, note that 2^8 = 256, so 2^98 = 2^[(8*12)+2]=4*[256*256*......12 times]
As this is a multiple of 256, N can only be 0.
ANSWER:A
Answer: (A) 0
Question: If p and r are integers, and p^2 = 36r, then r must be divisible by which of the following?
(A) 2
(B) 4
(C) 9
(D) 7
(E) 14
Rationale: Ans: D
Solution: for p to be an int 36 r must be whole square of a number.
36r= 9*2*2*r
to make it whole square we need 9
so r can must be divisible by 9y where y is itself a whole square.
so C is the ans
Answer: (C) 9
Question: 99^n is such a number begin with 8, least value of n?
(A) 96157627
(B) 96157601
(C) 26779287
(D) 26876297
(E) 269181122
Rationale: Answer:
Explanation:
In a more traditional way, this problem can be solved like below.
99(100 - 1) = 9900-99= 9801
9801(100 - 1) = 980100-9801= 971299
971299(100 - 1) = 97129900 - 971299 = 96157601
Answer:B
Answer: (B) 96157601
Question: 44 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be :
(A) 56 m
(B) 88 m
(C) 120 m
(D) 137 m
(E) None
Rationale: Sol.
Let the length of the wire b h.
Radius = 1/2 mm = 1/20 cm. Then,
22/7 * 1/20 * 1/20 * h = 44 ⇔ = [44 * 20 * 20 * 7 / 22] = 5600cm = 56 m.
Answer A
Answer: (A) 56 m
Question: A is twice as good a work man as B and together they finish the work in 14 days. In how many days A alone can finish the work?
(A) 21 days
(B) 51 days
(C) 35 days
(D) 31 days
(E) 24 days
Rationale: A
21 days
WC = 2:1
2x + x = 1/14 => x = 1/42
2x = 1/21
A can do the work in 21 days.
Answer: (A) 21 days
Question: In how many ways can a cricket eleven be chosen out of a batch
of 15 players
(A) 1255
(B) 1355
(C) 1340
(D) 1365
(E) 1300
Rationale: Required number of ways
= 15C 11 = 15C (15-11)
= 15 C 4
15C4 = 15 * 14 * 13 * 12 / 4 * 3 * 2 *1
= 1365
ANSWER D 1365
Answer: (D) 1365
Question: Two dice are thrown simultaneously. What is the probability of geƫng two numbers whose product is
even ?
(A) 3/4
(B) 1/4
(C) 7/4
(D) 1/2
(E) None of these
Rationale: Explanation:
Total number of cases = 6*6 = 36
Favourable cases =
[(1,2),(1,4),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,2),(3,4),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,2),(5,4)
,(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)] = 27
So Probability = 27/36 = 3/4
Answer: A
Answer: (A) 3/4
Question: The price of commodity X increases by 30 cents every year, while the price of commodity Y increases by 20 cents every year. If in 2001, the price of commodity X was $4.20 and the price of commodity Y was $4.40, in which year will commodity X cost 40 cents more than the commodity Y?
(A) 2007
(B) 2008
(C) 2009
(D) 2010
(E) 2011
Rationale: The cost of commodity X increases by 10 cents per year relative to commodity Y.
The price of X must gain 20 + 40 = 60 cents on commodity Y, which will take 6 years.
The answer is A.
Answer: (A) 2007
Question: √0.0081 is equal to :
(A) 0.09
(B) 0.9
(C) ±0.08
(D) 0.81
(E) None of these
Rationale: √0.0081 = √0.0081/10000 = √81/10000 = 9/100 =0.09
Answer: A
Answer: (A) 0.09
Question: I bought two books; for Rs.490. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
(A) 337.83
(B) 285.83
(C) 284.83
(D) 266.83
(E) 299.83
Rationale: x*(85/100) = (490 - x)119/100
x = 285.83
Answer: B
Answer: (B) 285.83
Question: Oranges are bought at 11 for a rupee and an equal number more at 9 a rupee. If these are sold at 10 for a rupee, find the loss or gain percent?
(A) 22
(B) 87
(C) 65
(D) 20
(E) 28
Rationale: Speed Ratio = 1:4/5 = 5:4Time Ratio = 4:51 -------- 5 4 --------- ? è 20
Answer: D
Answer: (D) 20
Question: 37.	If the cost price of 15 tables be equal to the selling price of 20 tables, the loss per cent is ?
(A) 20%
(B) 30%
(C) 25%
(D) 37.5%
(E) 38 %
Rationale: Let C.P. of each table = Re. 1
C.P. of 20 tables = Rs. 20
S.P. of 20 table = C.P. of 15 tables = Rs. 15
loss = (5/20) x 100 % = 25%
answer :C
Answer: (C) 25%
Question: Souju's age is 130% of what it was 10 years ago, but 81% of what it will be after 10 years. What is her present age?
(A) 63 years
(B) 54 years
(C) 56 years
(D) 36 years
(E) 43years
Rationale: Let the age before 10 years =x. Then,
130x/100=x+10
â‡’130x=100x+1000
â‡’x=1000/30=33
Present age =x+10=33+10=43
ANSWER:E
Answer: (E) 43years
Question: (469 + 174)^2 - (469 - 174)^2 /(469 x 174)= ?
(A) 643
(B) 2
(C) 295
(D) 4
(E) 185
Rationale: Given exp. =(a + b)^2 - (a - b)^2/ab
=4ab/ab
= 4 (where a = 469, b = 174.)
Answer is D.
Answer: (D) 4
Question: Of the three-digit positive integers whose three digits are all different and nonzero, how many are odd integers greater than 700?
(A) 84
(B) 91
(C) 100
(D) 105
(E) 243
Rationale: Number of combinations for type 1 : 1*7*4 = 28
Number of combinations for type 2: 1*7*5 = 35
Number of combinations for type 3 : 1*7*4 = 28
Thus, total numbers possible = 28+35+28 = 91.
B is thus the correct answer
Answer: (B) 91
Question: In what ratio should a variety of rice costing Rs. 6.5 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg?
(A) 5/6
(B) 5/9
(C) 5/4
(D) 5/3
(E) 7/6
Rationale: Let us say the ratio of the quantities of cheaper and dearer varieties
= x : y
By the rule of allegation, x/y
= (8.75 - 7.50) / (7.50 - 6.5) =5/4
Answer: C
Answer: (C) 5/4
Question: Joe drives 360 miles at 60 miles per hour, and then he drives the next 120 miles at 40 miles per hour. What is his average speed for the entire trip in miles per hour?
(A) 42
(B) 53
(C) 50
(D) 54
(E) 56
Rationale: t1= 360/60=6 hours
t2=120/40=3 hours
T=t1+t2=9 hours
Avg speed = Total Distance/T
= 480/9 = 53mph=B
Answer: (B) 53
Question: If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:
(A) 2.87
(B) 2.965
(C) 3.876
(D) 3.9
(E) 4.526
Rationale: log5 512 = log 512/ log 5
= log 2^9/log(10/2)
=9 log 2 /log 10 - log 2
=(9*0.3010)/1-0.3010
=2.709/0.699 = 2709/699
= 3.876
ANSWER C
Answer: (C) 3.876
Question: John, Karen, and Luke collected cans of vegetables for a food drive. The number of cans that John collected was 1/2 the number of cans that Karen collected and 1/3 the number of cans that Luke collected. The number of cans that Karen collected was what fraction of the total number of cans that John, Karen, and Luke collected?
(A)  1/5
(B)  1/3
(C)  2/5
(D)  1/2
(E)  2/3
Rationale: John = (1/2)Karen --> Karen = 2(John)
John = 1/3(Luke) --> Luke = 3(John)
Total = 6(John)
Karen/Total = 2/6 = 1/3
Answer: B
Answer: (B)  1/3