mathewhe/aqua_rat huggingface dataset:
Question: Paul sold an item for Rs.3600/- and incurred a loss of 40%. At what price should he have sold the item to have gained a profit of 40%?
(A) 8000
(B) 8200
(C) 8400
(D) 8600
(E) 8800
Rationale: Explanation:
40% loss means SP = 60% of CP
:. CP = Rs.3600x100/60 = Rs.6000.
The SP for a gain of 40% = 6000+40% of 6000 = 6000+2400 =Rs8400.
Answer: Option C
Answer: (C) 8400
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) 4/8
(B) 9/2
(C) 7/6
(D) 9
(E) 2/21
Rationale: Explanation:
Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = Â³Câ‚‚/Â¹âµCâ‚‚ = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = Â²Câ‚‚/Â¹âµCâ‚‚ = (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow = (Â³Câ‚ * Â²Câ‚)/Â¹âµCâ‚‚ = (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: E
Answer: (E) 2/21
Question: There are 200 cats in Cat-City. Out of the 200, 70 are street cats and the rest are domestic cats. 110 cats are gray, 40 out of the gray cats are NOT domestic ones. How many domestic cats are there which are not gray in Cat-City?
(A) 90.
(B) 80.
(C) 60.
(D) 40.
(E) 25.
Rationale: STREET-CAT DOMESTIC-Cat
70 130
(40gray+30other) 70gray+60other
Answer:C
Answer: (C) 60.
Question: One-tenth of the students at a nursery school are 4 years old or older. If 20 students have not yet reached their third birthday, and a total of 25 students are not between 3 years old and 4 years old, how many children are in the nursery school?
(A) 51
(B) 20
(C) 40
(D) 50
(E) 55
Rationale: x/10 students are > 4 yrs
20 students are < 3 yrs
x/10+ 20 = 25
x/10 = 5
x = 50
Answer: D
Answer: (D) 50
Question: The product of all the prime numbers less than or equal to19 is closest to which of the following powers of 10 ?
(A)  10^9
(B)  10^8
(C)  10^6
(D)  10^7
(E)  10^5
Rationale: P = 2*3*5*7*11*13*17*19
= 21 * (11 * 19) (13*17) *10
~ 21 * (10 * 20) (10 *20) * 10
~ 8210 ^5
~ 10^ 7
Answer : D
Answer: (D)  10^7
Question: A shopkeeper sells 400 metres of cloth for Rs. 18000 at a loss of Rs.5 per metre. Find his cost price for one metre of cloth?
(A) Rs. 45
(B) Rs. 40
(C) Rs. 35
(D) Rs. 50
(E) None of these
Rationale: SP per metre = 18000/400 = Rs. 45 Loss per metre = Rs. 5 CP per metre = 45 + 5 = Rs. 50
ANSWER:D
Answer: (D) Rs. 50
Question: Exactly one of the following numbers cannot be written as a3 + b3 where a and b are integers.
Which number is it?
(A) 700056
(B) 707713
(C) 7000639
(D) 7077283
(E) 7077915
Rationale: If a is an integer, then a3 gives remainder 0, 1, or 6 when divided by 7 (just consider the
remainders of 03, 13, 23, 33, 43, 53, and 63 when divided by 7). Then a3 + b3 gives remainder
0, 1, 2, 5, or 6 when divided by 7. Well, 7077283 gives remainder 3 when divided by 7. (The
remaining numbers can be represented as a sum of two cubes of integers, 700056 = 403 + 863,
707713 = 143 + 893, 7000639 = 323 + 1913, and 7077915 = 33 + 1923.)
correct answer D
Answer: (D) 7077283
Question: A, B and C completed a piece of work, A worked for 6 days, B for 9 days and C for 4 days. Their daily wages were in the ratio of 3:4:5. Find the daily wages of C, if their total earning was $1480?
(A) $100
(B) $150
(C) $125
(D) $134
(E) $243
Rationale: A
$100
3x 4x 5x
6 9 4
18x + 36x + 20x = 1480
74x = 1480 => x = 20
5x = 100 Rs.
Answer: (A) $100
Question: A side of beef lost 35 percent of its weight in processing. If the side of beef weighed 545 pounds after processing, how many pounds did it weigh before processing?
(A)  191
(B)  355
(C)  737
(D)  838
(E)  1,560
Rationale: Let weight of side of beef before processing = x
(65/100)*x = 545
=> x = (545 * 100)/65 = 838
Answer D
Answer: (D)  838
Question: How many of the positive factors of 26 , 16 and how many common factors are there in numbers?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: factors of 26 - 1, 2, 13 and 26
factors of 16 - 1 , 2, 4, 8 and 16
Comparing both, we have three common factors of 45,16-2
Answer : B
Answer: (B) 2
Question: Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill cistern. How much time will be taken by A to fill the cistern separately?
(A) 7
(B) 8
(C) 6
(D) 54
(E) 3
Rationale: Let the cistern be filled by pipe A alone in x hours.
Then, pipe B will fill it in (x + 6) hours.
1/x + 1/(x + 6) = 1/4
x2 - 2x - 24 = 0
(x - 6)(x + 4) = 0 => x = 6.
Answer:C
Answer: (C) 6
Question: The Coen family consists of a father, a mother, two children and a dog. A photographer is about to take the family's picture. How many different arrangements (of standing in a row) does the photographer have, if it is known that the younger child insists of standing by his dog?
(A) 12
(B) 24
(C) 30
(D) 48
(E) 120
Rationale: We need to find the number of arrangements of Father, Mother, Child-1, Child-2, and a Dog, so that C2 and D are always together.
Consider F and M to be one unit, then we would have total of four units: {F}, {M}, {C1}, {C2D}. The number of arrangements of these four units is 4!, but C2 and D within their unit can be arranged in 2 ways: {C2D} or {DC2}, so total number of arrangements is 4!*2=48.
Answer: D
Answer: (D) 48
Question: If 2^2n + 2^2n + 2^2n + 2^2n = 4^18, then n =
(A) 3
(B) 6
(C) 17
(D) 23
(E) 24
Rationale: 2^2n + 2^2n + 2^2n + 2^2n = 4^18
=> 4 x 2^2n = 4^24 = 2^36
=> 2^2 x 2^2n = 2^36
=> 2^(2n+2) = 2^36
=> 2n+2 = 36=> n =17
So. Answer will be C.
Answer: (C) 17
Question: If x = 3^27 and x^x = 3^k, what is k?
(A) 3^9
(B) 3^12
(C) 3^27
(D) 3^30
(E) 3^33
Rationale: Solution:
We know that x=3^27
which implies x^x = (3^27)^(3^27) = 3^(27 * 3^27) [because (x^y)^z = x^(y*z))]
so 3^(3^3 * 3^27) = 3^(3^(3+27)) [because x^a * x^b = x^(a+b)]
therefore x^x = 3^(3^30)
Given that x^x=3^k
so 3^(3^30) = 3^k
Since the base is same the exponent will also be same
therefore k = 3^30
Answer: D
Answer: (D) 3^30
Question: Which of the following leads to the correct mathematical solution for the number of ways that the letters of the word BANANA could be arranged to create a six-letter code?
(A) 6!
(B) 6! − (3! + 2!)
(C) 6! − (3! × 2!)
(D) 6!/(3! + 2!)
(E) 6!/(3! × 2!)
Rationale: Number of letters in word 'BANANA' = 6.
The letters 'A' and 'N' appear 3 times and 2 times respectively in the word 'BANANA'.
Therefore the mathematical solution for number of ways that the letters of the word BANANA can be arranged to create six-letter code
= 6!/(3!*2!)
Answer: E
Answer: (E) 6!/(3! × 2!)
Question: A car takes 6 hours to cover a distance of 144 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
(A) 50 Kmph
(B) 60 Kmph
(C) 65 Kmph
(D) 16 Kmph
(E) None
Rationale: Time = 6
Distence = 144
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 144/9 = 16 Kmph
D)
Answer: (D) 16 Kmph
Question: A pair of prime numbers that can be expressed in the form {p, (p + 6)} is deﬁned as a pair of “sexy primes.” A “sexy triplet” is a group of three primes that can be expressed in the form {p, (p + 6), (p + 12)}. All of the following prime numbers are the middle term of a sexy triplet EXCEPT
(A) 11
(B) 13
(C) 17
(D) 19
(E) 23
Rationale: {x-6, x, x+6} all must be primes. Substitute options for x to check whether this will hold true. If x=19, then x+6=25, which is not a prime.
Answer: D
Answer: (D) 19
Question: Listed below are the mean temperatures measured in the Tokharian desert in a certain month. What is the median temperature W in that particular month?
Mean Temp (C°) No. of days
29 --------------------> 5
30 --------------------> 11
31 --------------------> 8
32 --------------------> 6
(A) 29
(B) 30
(C) 30.5
(D) 31
(E) 32
Rationale: to find out median===>they must be arranged in ascending order.
29 29 29...(5 times)30 30 30 30.....(11 times)31 31 31.....(8 times)32 32 32 .....(6 times)
total days=5+11+8+6=30
therefore 30 numbers ...median W will be==>mean of 15 and 16 th place temperature===>(30+30)/2=30
hence B
Answer: (B) 30
Question: A & B start a business jointly. A invests Rs 16000 for 8 month & B remains in a business for 4 months. Out of total profit, B claims 2/7 of the profit . How much money was contributed by B ?
(A) 11200
(B) 12000
(C) 12400
(D) 12800
(E) None of these
Rationale: Explanation :
B's share = 2/7 of the profit
=> A : B = 5 : 2
(We can easily find out A:B as given above by doing quick mental calculations
and it will be excellent if you can do as much as mental calculations possible.
Just for explanation, see below steps to systematically find out A : B
Let the total profit = x
B's share = 2x/7
A's share = x – 2x/7 = 5x/7
A:B = 5x/7 : 2x/7 = 5:2)
Let the money contributed by B = b
Then A:B = 16000*8 : b*4 = 5:2
=> (16000*8)/4b = 5/2
=> b = (16000*8*2)/ (4*5) = 800*8*2 = 12800. Answer : Option D
Answer: (D) 12800
Question: Mr. Thomas invested an amount of 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be 3508, what was the amount invested in Scheme B?
(A) 6400
(B) 6500
(C) 7200
(D) 7500
(E) None of these
Rationale: Let the sum invested in Scheme A be x and that in Scheme B be (13900 – x).
Then, (x×14×2/100)+[(13900−x)×11×2/100]=3508
⇒ 28x – 22x = 350800 – (13900 × 22) ⇒ 6x = 45000
⇒ x = 7500.
So, sum invested in Scheme B = (13900 – 7500) = 6400.
Answer A
Answer: (A) 6400
Question: A motorist knows eight different routes from Bristol to Birmingham. From Birmingham to Sheffield he knows three different routes and from Sheffield to Carlisle he knows two different routes. How many routes does he know from Bristol to Carlisle ?
(A) 4
(B) 8
(C) 12
(D) 24
(E) 48
Rationale: Explanation:
Total number of routes from Bristol to Carlisle = (8 x 3 x 2) = 48
Answer: E
Answer: (E) 48
Question: A windmill is taking advantage of strong air currents in order to produce electrical energy. On a typical day the wind speed is around 20 mph and in that speed the windmill produces 900 kw/h (kilowatts per hour). On a stormy day a windmill produces 20% more energy. How much kw/h can three windmills produce in two hours on a stormy day?
(A) 2880.
(B) 4860.
(C) 5780.
(D) 5760.
(E) 6480.
Rationale: Efficiency per machine = 900 watt/hr
Efficiency due to increase in wind speed = 900*120% => 1080 watt/hr
Production by each machine in 2 hours is 1080*2 => 2160 watt
Production by 3 machines => 2160 watt * 3 = 6480 watt
Answer will be (E)
Answer: (E) 6480.
Question: The radius of a circle is increased by 1%. Find how much % does its area increases?
(A) 2.07%
(B) 2.71%
(C) 2.09%
(D) 2.01%
(E) 1.01%
Rationale: r = 100 r = 101
r2 = 10000 r2 = 10201
10000 ---- 201
100 ---- ? => 2.01%
Answer:D
Answer: (D) 2.01%
Question: Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 90% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?
(A)  5%
(B)  10%
(C)  15%
(D)  55%
(E)  30%
Rationale: Total = n(A) + n(B) - n(Exactly 2 products) -2 (AnBnC) + Neither.
Neither is zero.
Hence 100 = 90 + 50 + 35 - n (Exactly 2 products) - 2*10
100 = 155 - n (Exactly 2 products) => n (Exactly 2 products) = 55.
Answer: D
Answer: (D)  55%
Question: When 2 no.'s divided by 17, leave remainders 13 and 11 respectively. If the sum of those 2 no.'s is divided by 17, the remainder will be
(A) 3
(B) 4
(C) 7
(D) 10
(E) 12
Rationale: (C)
Required remainder = remainder by (13 +11)/17 = 7
Answer: (C) 7
Question: In the xy-plane the point (-2 -3) is the centre of a circle, the point (-2, 2) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the circle r is an integer then r=
(A) 6
(B) 5.5
(C) 4
(D) 3
(E) 2
Rationale: Can be solved without much calculations.
You are given that (-2,-3) is the center of the circle. Point (4,-3) lies inside the circle ---> the radius is lesser than distance of (-2,-3) from (4,-3) ---> lesser than 6 units but the radius will also be greater than the distance of (-2,-3) from (-2,2) ----> greater than 5 units.
Thus the radius is >5 but <6 and as it is an integer, the only possible value of radius = 5. 5units.
B is the correct answer.
Answer: (B) 5.5
Question: A certain lab experiments with white and brown mice only. In one experiment, 2/3 of the mice are white. If there are 11 brown mice in the experiment, how many mice in total are in the experiment?
(A) 39
(B) 33
(C) 26
(D) 21
(E) 10
Rationale: Let total number of mice = M
Number of white mice = 2/3 M
Number of brown mice = 1/3 M = 11
=> M = 33
Answer B
Answer: (B) 33
Question: A room of 6m 44cm long and 3m 00cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor.
(A) 12076
(B) 12070
(C) 12077
(D) 12075
(E) 12074
Rationale: Explanation:
area of the room = 644 * 300sq cm
size of largest square tile = H.C.F of 644cm and 300cm= 4cm
area of 1 tile = 4*4 sq cm
no. of tiles required = (644*300) / (4 * 4) = 12075
Answer: D) 12075
Answer: (D) 12075
Question: In a Function, every person shakes hand with every other person. If there was a total of 28 handshakes in the function, how many persons were present in the Function?
(A) 8
(B) 7
(C) 2
(D) 6
(E) 5
Rationale: Suppose there are nn persons present in a function and every person shakes hand with every other person. Then, total number of handshakes
= nC2=n(n−1)/2
n(n−1)=28×2n(n−1)=56
n=8
ANSWER A 8
Answer: (A) 8
Question: Sekar started a business investing Rs.25,000 in 1999. In 2000, he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000. In 2001, Sekar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000. What will be Rajeev's share in the profit of Rs.1,80,000 earned at the end of 3 years from the start of the business in 1999?
(A) Rs.60,000
(B) Rs.50,000
(C) Rs.70,000
(D) Rs.75,000
(E) none
Rationale: Solution
Sekar:Rajeev:Jatin=	(25000×12+35000×12+45000×12):(35000×24) : (35000×12)
= 1260000 : 840000 : 420000
= 3 : 2 : 1.
Rajeev's share	=Rs.(180000×2/6)
= Rs.60000.
Answer A
Answer: (A) Rs.60,000
Question: When the positive integer y is divided by 9, the remainder is 5. What is the remainder when 3y is divided by 9?
(A) 0
(B) 1
(C) 3
(D) 4
(E) 6
Rationale: Lets take the number as y
when y is divided by 9 the remainder is 5 hence y can be written as
y=9k +5
Multiplying by 3 will give
3y = 27k + 15
we can also write
3y = 27k + 9 + 6
Now 27k and 9 are divisible by 9 leaving the remainder as 6 hence E is the answer.
Answer: (E) 6
Question: the price of a maruti car rises by 30% while the sales of the car came down by 20%. what is the percent change in the total revenue?
(A) -4
(B) 4
(C) -2
(D) 0
(E) none of these
Rationale: Assume that price is 100 and sales are also 100. Total revenue is 100*100=10000(100%). Now price increased by 30%. So new price is 130. Similarly new sales are 80. Now revenue is 130*80=10400(104%)= So total change is 4%
ANSWER:B
Answer: (B) 4
Question: The difference between C.I. and S.I. on an amount of $20,000 for 2 years is $72. What is the rate of interest per annum?
(A) 5%
(B) 6%
(C) 7%
(D) 8%
(E) 9%
Rationale: $72 is the interest on the first year of interest.
Let x be the interest rate.
The interest after the first year is 20000*x.
The interest on the first year's interest is 20000*x*x
20000*x^2 = 72
x = 0.06
The answer is B.
Answer: (B) 6%
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 30 years now, the son's age 2 years back was:
(A) 14 years
(B) 19 years
(C) 13 years
(D) 38 years
(E) 39years
Rationale: Let the son's present age be x years. Then, (30 - x) = x
2x = 30
x = 15
Son's age 5 years back (15- 2) = 13 years.
Answer: C
Answer: (C) 13 years
Question: Excluding stoppages, the average speed of a bus is 60 km/hr and including stoppages, the average speed of the bus is 35 km/hr. For how many minutes does the bus stop per hour?
(A) 22
(B) 88
(C) 24
(D) 20
(E) 99
Rationale: In 1hr, the bus covers 60 km without stoppages and 35 km with stoppages.
Stoppage time = time take to travel (60 - 35) km i.e 25 km at 60 km/hr.
stoppage time = 25/60 hrs = 24 min.
Answer: C
Answer: (C) 24
Question: There are 20 Kids in a classroom. 12 Kids are wearing socks and 8 are wearing Shoes. 6 Kids are wearing both.
How many are Bare Feet ?
(A) 1
(B) 2
(C) 4
(D) 5
(E) 6
Rationale: 12 kids wear socks
8 kids wear shoes
6 wear both.
12 â€“ 6 = 6 (wear only socks)
8 â€“ 6 = 2 (wear only shoes)
6 (wear both)
hence, 20 -14 = 6
6 kids are with bare feet.
E
Answer: (E) 6
Question: A train 220 m long is running with a speed of 59 kmph. In what time will it pass a man who is running at 7 kmph in the direction opposite to that in which the train is going?
(A) 15 seconds
(B) 10 seconds
(C) 11 seconds
(D) 12 seconds
(E) 14 seconds
Rationale: Relative speed=66kmph or 330/18m/s
Time taken to pass the man:
Length of the train/relative speed
220*18/330=12 seconds
ANSWER:D
Answer: (D) 12 seconds
Question: A table is bought for Rs.400/- and sold at Rs.600/- find gain or loss percentage
(A) 15%loss
(B) 10%gain
(C) 30%gain
(D) 20%loss
(E) 50% gain
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (600 - 400)/400 = 50% gain
E
Answer: (E) 50% gain
Question: a, b, c are three distinct integers from 2 to 10 (both inclusive). Exactly one of ab, bc and ca is odd. abc is a multiple of 4. The arithmetic mean of a and b is an integer and so is the arithmetic mean of a, b and c. How many such triplets are possible (unordered triplets)?
(A) 8
(B) 6
(C) 2
(D) 4
(E) 0
Rationale: DETAILED SOLUTION
Exactly one of ab, bc and ca is odd => Two are odd and one is even
abc is a multiple of 4 => the even number is a multiple of 4
The arithmetic mean of a and b is an integer => a and b are odd
and so is the arithmetic mean of a, b and c. => a+ b + c is a multiple of 3
c can be 4 or 8.
c = 4; a, b can be 3, 5 or 5, 9
c = 8; a, b can be 3, 7 or 7, 9
Four triplets are possible.
Correct Answer : D
Answer: (D) 4
Question: In one year, the population, of a village increased by 5% and in the next year, it decreased by 5%. If at the end of 2nd year, the population was 9975, what was it in the beginning?
(A) 7787
(B) 10000
(C) 1988
(D) 1277
(E) 2081
Rationale: x*105/100 * 95/100 = 9975
X*0.9975=9975
X=9975/0.9975
=> 10000
Answer:B
Answer: (B) 10000
Question: If a and b are positive integers of C such that a/b=2.86, which of the following must be a divisor of a?
(A) 10
(B) B.13
(C) 18
(D) 26
(E) 50
Rationale: The prompt gives us a couple of facts to work with:
1) A and B are positive INTEGERS
2) A/B = 2.86
We can use these facts to figure out POSSIBLE values of A and B. The prompt asks us for what MUST be a divisor of A. Since we're dealing with a fraction, A and B could be an infinite number of different integers, so we have to make both as SMALL as possible; in doing so, we'll be able to find the divisors that ALWAYS divide in (and eliminate the divisors that only SOMETIMES divide in).
The simplest place to start is with...
A = 286
B = 100
286/100 = 2.86
These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)...
A = 143
B = 50
143/50 = 2.86
There is no other way to reduce this fraction, so A must be a multiple of 143 and B must be an equivalent multiple of 50. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A....
Since A is a multiple of 143, we have to 'factor-down' 143. This gives us (11)(13). So BOTH of those integers MUST be factors of A. You'll find the match in the answer choices.
Final Answer:
B
Answer: (B) B.13
Question: The speed of a boat in still water is 60kmph and the speed of the current is 36kmph. Find the speed downstream and upstream?
A. 35, 25 kmph
(A) 76,24 kmph
(B) 40,24 kmph
(C) 96,24 kmph
(D) 26,24 kmph
(E) 12,36 kmph
Rationale: Speed downstream = 60 + 36
= 96 kmph
Speed upstream = 60 - 36
= 24 kmph
Answer: C
Answer: (C) 96,24 kmph
Question: Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 14,950, Deepak's share is:?
(A) s.8467
(B) s.9100
(C) s.8400
(D) s.8429
(E) s.8420
Rationale: Ratio of their shares
= 22500 : 35000
= 9:14
Deepak's share
= 14950 * 14/23
= Rs.9100.
Answer:B
Answer: (B) s.9100
Question: If the set S is composed of the following numbers {99, 100, 100, 105, 106, 114, 125}, which of the following is largest?
(A) The average (arithmetic mean) of set S
(B) The median of set S
(C) The mode of set S
(D) The range of set S
(E) The standard deviation of set S
Rationale: A) 99, 100, 100, 105, 106, 114, 125 = 749 and its mean is 749/7 = 107.
B) The list is of 7 numbers and median is 105.
C) Mode is number of repetition of a number in the list , here it is 100.
D) Range = Max value - min value = 125 -99 = 26.
E) SD = square root of (sum of ( mean of series - number)^2 ) / n =>< 100
IMO option A is correct answer..
Answer: (A) The average (arithmetic mean) of set S
Question: In X game of billiards, X can give Y 20 points in 60 and he can give Z 30 points in 60. How many points can Y give Z in X game of 120?
(A) 30
(B) 20
(C) 25
(D) 40
(E) 50
Rationale: X scores 60 while Y score 40 and Z scores 30.
The number of points that Z scores when Y scores 120 = (120 * 30)/40 = 90.
In X game of 100 points, Y gives (120 - 90) =30 points to C.
A
Answer: (A) 30
Question: The sum of the squares of the first 15 positive integers (1^2 + 2^2 + 3^2 + . . . + 15^2) is equal to 1260. What is the sum of the squares of the second 15 positive integers (16^2 + 17^2 + 18^2 + . . . + 30^2) ?
(A)  2480
(B)  3490
(C)  6785
(D)  8235
(E)  9255
Rationale: You'll never need a formula for the sums of squares on the actual GMAT. You don't need to use that formula here, though it's not all that straightforward to solve without one. Two different approaches:
16^2 + 17^2 + 18^2 + ... + 30^2 = (15 + 1)^2 + (15 + 2)^2 + (15 + 3)^2 + ... + (15 + 15)^2
Now we can expand each square; they are all in the (x + y)^2 = x^2 + 2xy + y^2 pattern.
= (15^2 + 2*15 + 1^2) + (15^2 + 4*15 + 2^2) + (15^2 + 6*15 + 3^2) + ... + (15^2 + 30*15 + 15^2)
Now we have fifteen 15^2 terms, so adding these gives 15*15^2 = 15^3 = 3375. We also have the entire sum 1^2 + 2^2 + ... + 15^2, which we know is equal to 1240. Finally adding the middle terms, we have:
2*15 + 4*15 + 6*15 + ... + 30*15 = 15(2 + 4 + 6 + .... + 30) = 15*2*(1 + 2 + 3 + ... + 15) = 15*2*8*15 = 3600
So the sum must be 3375 + 1240 + 3600 = 8215
Alternatively, we can use a different factoring pattern. We want to find the value of 30^2 + 29^2 + ... + 17^2 + 16^2. Well if we subtract 15^2 + 14^2 + .... + 2^2 + 1^2 from this, the answer will be 1240 less than what we want to find. So if we can find the value of
30^2 + 29^2 + ... + 17^2 + 16^2 - (15^2 + 14^2 + .... + 2^2 + 1^2)
then we can add 1240 to get the answer. Now grouping the terms above to get differences of squares, we have
= (30^2 - 15^2) + (29^2 - 14^2) + ... + (16^2 - 1^2)
and factoring each of these using x^2 - y^2 = (x + y)(x - y), we have
= 45*15 + 43*15 + 41*15 + ... + 17*15 = 15(45 + 43 + 41 + ... + 17)
In brackets we have an equally spaced sum with fifteen terms, which we can evaluate using the familiar formula. So the above equals
15*15*62/2 = 6975
and adding back the 1260, we get the answer of 8235. (ANS D)
Answer: (D)  8235
Question: 14, 23, 32, 41, 50, 59, …
In the sequence above, each term is 9 more than the previous term. What is the 41st term T of the sequence?
(A) 360
(B) 365
(C) 369
(D) 374
(E) 383
Rationale: First term , a= 14
Common difference , d = 9
nth term , tn = a + (n-1)d
41st term T , t41 = a+ 40*d = 14 + 40*9 = 374
Answer D
Answer: (D) 374