mathewhe/aqua_rat huggingface dataset:
Question: Boy purchased two flats for Rs.5,00,000. On one he gains 15 % while on the other he losses 15%. How much does he gain or lose?
(A) 2.05%
(B) 2.10%
(C) 2.25%
(D) 2.30%
(E) 2.34%
Rationale: Generally in such cases, there is always loss.
So always remember, when two materials are sold and if one material gets profit and the other gets a loss, then use the trick shown below to calculate the loss.
Loss% = Common loss and gain% 2	= x 2
10 10
Therefore, here common loss and gain % = 15%
Hence,
Loss% = 15 2	= 2.25%
C
Answer: (C) 2.25%
Question: A person is traveling at 35km/hr and reached his destiny in 5hr find the distance?
(A) A)100km
(B) B)95km
(C) C)175km
(D) D)80km
(E) E)125km
Rationale: speed = 35km/hr
time = 5hr
distance = 35*5 = 175km
Answer is C
Answer: (C) C)175km
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 36 kmph and 72 kmph. In how much time will the trains cross each other?
(A) 70/3 sec
(B) 80/3 sec
(C) 40/3 sec
(D) 60/3 sec
(E) 90/3 sec
Rationale: C
Relative speed = (36 + 72)* 5/18 = 6 * 5 = 30 mps.
The time required = d/s = (100 + 100 + 200)/35
= 400/30 = 40/3 sec.
Answer: (C) 40/3 sec
Question: Find the value of x from the below equation? : 3x^2+5x+2 = 0
(A) -1
(B) 1
(C) -2
(D) 2
(E) -3
Rationale: a = 3, b = 5, c = 2
x1,2 = (-5 ± √(52 - 4×3×2)) / (2×3) = (-5 ± √(25-24)) / 6 = (-5 ± 1) / 6
x1 = (-5 + 1)/6 = -4/6 = -2/3
x2 = (-5 - 1)/6 = -6/6 = -1
A
Answer: (A) -1
Question: A sum of money place at compound interest doubles itself in 5 years. In how many years will it amount to eight times itself?
(A) 15 years
(B) 11 years
(C) 12 years
(D) 18 years
(E) 19 years
Rationale: 100 ---- 200 ---- 5
400 ---- 5
800 ---- 5
------
15 years
Answer: A
Answer: (A) 15 years
Question: A software programmer does 10% of the work in 80% of the time, and 80% of the work in the remaining 20% of the time. If the code he writes is X lines long and he was given one month (30 days) to accomplish the task, then, assuming that the programmer works at a constant rate in each of the two stages, How many lines of code were written in the last two weeks, in terms of X?
(A) 13x /15
(B) 15x/15
(C) 7x/15
(D) 2x/30
(E) 13x/30
Rationale: Take X=30 lines
80% of 30 = 24 lines
20% of 30 = 6 lines
W - R - T
6 lines - r1 - 24 (first 80% of the 30 days)
24 lines - r2 - 6 ( last 20% of the 20 days)
r1 = 1/4r2 = 4
Now Work in last 14 days = 6 days programmer worked at r2 + 8days programmer worked at r1
=> 6 * 4 + 8 * 1/4 = 24 + 2 = 26
Insert, X=30 in all options => C is the answer.
Answer: (C) 7x/15
Question: On flipping 3 coins together what is the outcomes for exactly one head and one tail?
(A) {HHH, HTH, THH, TTH, THT, HTT}
(B) {HHT, HTH, THH, TTH, THT, TTT}
(C) {HHT, HTH, THH, TTH, THT, HTT}
(D) {HHT, HTH, THH, TTH, THT, TTT}
(E) None
Rationale: Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
Favorable outcomes for at least two heads
= favorable outcomes for one head and one tail and favorable outcomes for more than one head and one tail.
= {HHT, HTH, THH, TTH, THT, HTT}
C
Answer: (C) {HHT, HTH, THH, TTH, THT, HTT}
Question: What is the lowest possible common multiple of 2 distinct integers, each greater than 67?
(A) 68
(B) 69
(C) 136
(D) 68^2
(E) 68·69
Rationale: In order to get the lowest LCM, we have to take the first number as 68 and the next number as its multiple.
So, I can take 68 and 136 as two distinct numbers, such that Lowest LCM = 136.
Answer should be C.
Answer: (C) 136
Question: A work which could be finished in 11 days was finished 3 days earlier after 10 more men joined. The number of men employed was?
(A) 22
(B) 20
(C) 88
(D) 71
(E) 12
Rationale: x ------- 11
(x + 10) ---- 6
x * 11 = (x + 10)6
x = 12
\Answer: E
Answer: (E) 12
Question: A sum of money becomes triple itself in 5 years at simple interest. How many years will it become six times at the same rate?
(A) 12 1/2 years
(B) 2 1/2 years
(C) 12 1/5 years
(D) 12 6/2 years
(E) 13 1/2 years
Rationale: 100 ---- 200 ---- 5
200 ---- 5
100 ---- 2 1/2
------------------
600 ---- 12 1/2 years
Answer: A
Answer: (A) 12 1/2 years
Question: In a group of ducks and cows, the total number of legs are 24 more than twice the no. of heads. Find the total no.of buffaloes.
(A) 11
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 24
=> 2x = 24 => x = 12
B
Answer: (B) 12
Question: A shoe store sells Adidas shoes for $60 each and Puma shoes for $50 each. On every Adidas shoe the restaurant makes a profit of $10 while on every Puma shoe it makes a profit of $8. If on a given day the storest's sales amounted to $1600, which of the following cannot be the profit made on that day?
(A) 262
(B) 260
(C) 258
(D) 256
(E) 254
Rationale: $254 is the only option that does not fit into a combination of Adidas and Puma sales profits, given the total sales of the day. Answer: E
Answer: (E) 254
Question: The price of 357 mangoes is Rs. 1517.25. What will be the approximate price of 49 dozens of such mangoes?
(A) Rs. 3000
(B) Rs.2500
(C) Rs 2700
(D) Rs 2900
(E) None of these
Rationale: Explanation :
More mangoes, more cost (Direct)357 : 49 * 12 :: 1517.25 : xor 375 * x= 49 * 12 * 1517.25.49 * 12 * 15l7.25 / 357 = 2499Approximate cost = Rs. 2500.
Answer : B
Answer: (B) Rs.2500
Question: Suraj has a certain average of runs for 16 innings. In the 17th innings he scores 92 runs thereby increasing his average by 4 runs. What is his average after the 17th innings?
(A) 48
(B) 64
(C) 28
(D) 72
(E) 27
Rationale: To improve his average by 4 runs per innings he has to contribute 16 x 4 = 64 runs for the previous 16 innings.
Thus, the average after the 17th innings
= 92 - 64 = 28.
ANSWER:C
Answer: (C) 28
Question: The length of a fabric needed for a dress is cut into two pieces. If the total length of the fabric is 200 inches and the shorter side is 10 inches less than half the length of the other fabric, what is the length of the shorter fabric?
(A) 60
(B) 140
(C) 400
(D) 200
(E) 80
Rationale: length one as L1, and length two as L2.
L1=(L2/2)-10 as eq.a
L1+L2=200 as eq.b
Substitute equation a into equation b, (L1/2)-10 +L1=200
Transpose like terms, (L1/2) + L1= 200 + 10
Get rid of fraction, L1+ L1*2= 400+20
reduces to 3*L1= 40, L1 results to 140.
Shorter fabric is (140/2)-10=60
Answer is A.
Answer: (A) 60
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) 10 years
(B) 12 years
(C) 14 years
(D) 16 years
(E) 18 years
Rationale: 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.
A)
Answer: (A) 10 years
Question: Cecilia, Robbie, and Briony all bought stamps. The number of stamps Cecilia purchased was equal to a single digit. The number of stamps only one of them purchased was divisible by 6. The number of stamps one of them bought was an even number. Which of the following could represent the numbers of stamps each purchased?
(A) 3, 8, 24
(B) 7, 9, 17
(C) 6, 9, 12
(D) 5, 15, 18
(E) 9, 10, 13
Rationale: I didnt get your point on eliminating A.
The number of stamps only one purchased was divisible by 6.Could that not be Cecilia with 9 stamps.
I choose this and marked A.
Answer: (A) 3, 8, 24
Question: A hiker walked for 3 days. She walked 21 miles on the first day, walking 3 miles per hour. On the second day she walked for one less hour but she walked one mile per hour, faster than on the first day. On the third day she walked the same number of hours as on the first day, but at the same speed as on the second day. How many miles in total did she walk?
(A) 73
(B) 44
(C) 58
(D) 60
(E) 62
Rationale: She walked 21 miles on the first day, walking 3 miles per hour i.e. total time of walk on Day-1 = 21/3 = 7 Hours
Second day time of walk = 7-1 = 6 hours and Speed = 3+1=4 miles per hour i.e. Distance walked on second day = 6*4 = 24 miles
Third day time of walk = 7 hours and Speed = 4 miles per hour i.e. Distance walked on second day = 7*4 = 28 miles
Total Distance travelled on three days = 21+24+28 = 73
Answer: Option A
Answer: (A) 73
Question: A shopkeeper purchased 85 kg of potatoes for Rs. 1105 and sold the whole lot at the rate of Rs. 15 per kg. What will be his gain percent?
(A) 18 1/9 %
(B) 16 9/3 %
(C) 14 1/3 %
(D) 12 1/3 %
(E) 15 5/13 %
Rationale: C.P. of 1 kg = 1105/85 = Rs. 13S.P. of 1 kg = Rs. 15Gain % = 2/13 * 100 = 200/13 = 15 5/13 %Answer: E
Answer: (E) 15 5/13 %
Question: The old lady who lived in a shoe was having some real trouble buying Christmas presentsfor her enormous family. Although she bought the least expensive stocking stuffers she couldfind, the bill was high. Of course, both a 15 percent sales tax and a 5 percent luxury tax wereadded to the original price. She paid a total of Rs.100. What was the cost of the stuffers before taxes?
(A) 82.333rupees
(B) 83.333rupees
(C) 84.333rupees
(D) 85.333rupees
(E) 86.333rupees
Rationale: let the cost before taxes=x
x+15x/100+5x/100=100
120x/100=100
x=83.333rupees
ANSWER:B
Answer: (B) 83.333rupees
Question: The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 9 years hence?
(A) 22
(B) 77
(C) 78
(D) 98
(E) 71
Rationale: A + B = 60, A = 2B
2B + B = 60 => B = 20 then A = 40.
9 years, their ages will be 49 and 29.
Sum of their ages = 49 + 29 = 78.
Answer: C
Answer: (C) 78
Question: x and y are positive integers of h. If 1/x + 1/y < 2, which of the following must be true?
(A)  x + y > 4
(B)  xy>1
(C)  x/y + y/x < 1
(D)  (x - y)^2 > 0
(E)  None of the above
Rationale: Answer is B:
1/X + 1/Y < 2
The maximum value of 1/X is 1 because if X equals any other number greater than one it will be a fraction. The same is true with 1/Y.
So 1/X and 1/Y will always be less than 2 as long as both X and Y are not both equal to one at the same time.
Another way of putting it is:
X*Y>1.B
Answer: (B)  xy>1
Question: Find the odd man out. 24,36,52,72,96
(A) 72
(B) 52
(C) 36
(D) 24
(E) 34
Rationale: Explanation :
All except 52 are multiples of 6. Answer : Option B
Answer: (B) 52
Question: 20. A certain church bell rings the bell twice at half past the hour and four
times at the hour plus an additional number of rings equal to what ever
time it is. How many rings will the clock make from 6:20 in the morning
to 08:10 in the morning?
(A) 27
(B) 36.
(C) 42.
(D) 46.
(E) 50.
Rationale: @ 6:30 - 2
@ 7 - 4+7 =11
@ 7:30 - 2
@ 8 - 12
totals to A=27
Answer: (A) 27
Question: Ben left a job paying $75,000 per year to accept a sales job paying $45,000 per year plus 15 percent commission. If each of his sales is for $750, what is the least number of sales he must make per year if he is not to lose money because of the change?
(A) 40
(B) 200
(C) 266
(D) 267
(E) 600
Rationale: In order not to lose money because of the change Ben's total commission must beat least$75,000-$45,000=$30,000, so total sales must beat least$30,000/0.15=$200,000. Which means that he must makeat least$200,000/750=800/3=266.6 sales, so 267 sales.
Answer: D.
Answer: (D) 267
Question: When the integer p is divided by 12, the remainder is 3. Which of the following, when divided by 12, will have a remainder of 6 ?
I. 2p
II. 6p
III. 4p + 6
(A)  I only
(B)  II only
(C)  III only
(D)  I and II only
(E)  I, II, and III
Rationale: is it E.
p = 12*a + 3
2p = 12*2*a + 6
6p = 12*6*a + 18 ( 18 = 12+6)
4p + 6 = 12*4*a + 18 (18 = 12 + 6)
Answer: (E)  I, II, and III
Question: A merchant sells an item at a 10% discount, but still makes a gross profit of 20 percent of the cost. What percent of the cost would the gross profit on the item have been if it had been sold without the discount?
(A) 30%
(B) 40%
(C) 50%
(D) 60%
(E) 75%
Rationale: original SP = X
Cost =C
current selling price = .9x ( 10% discount)
.9x = 1.2C (20% profit)
x= 1.2/.9 *C
x= 4/3 C
Original selling price is 1.3C which is 30% profit
Answer A
Answer: (A) 30%
Question: There are 13 stamps from which two stamps will be selected. We have five stamps which are the same as five of the stamps which could be selected. What is the probability that the two stamps selected will be different from the stamps that we have?
(A) 17/52
(B) 14/39
(C) 12/31
(D) 9/23
(E) 7/17
Rationale: P(first stamp is different) = 8/13
P(second stamp is different) = 7/12
P(both stamps are different) = 8/13*7/12 = 14/39
The answer is B.
Answer: (B) 14/39
Question: If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area ?
(A) 108 sq.cm
(B) 112 sq.cm
(C) 116 sq.cm
(D) 120 sq.cm
(E) NONE OF THESE
Rationale: Explanation:
The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle =1/2 x base x height => 1/2 x 24 x 10 = 120 sq.cm
ANSWER IS D
Answer: (D) 120 sq.cm
Question: A dozen eggs and 10 pounds of apples are currently at the same price. If the price of a dozen eggs rises by 10 percent and the price of apples rises by 2 %. How much more will it cost to buy a dozen eggs and 10 pounds of apples.
(A) 2%
(B) 6%
(C) 10%
(D) 12%
(E) 12.2%
Rationale: Say currently both a dozen eggs and 10 pounds of apples cost $50 (they are at the same price). So, to buy a dozen eggs and 10 pounds of apples we need $100.
After the increase, the price of a dozen eggs will be $55 and the price of 10 pounds of apples will be $51. So after the increase, to buy a dozen eggs and 10 pounds of apples we'll need $106.
Increase = 6%.
Answer: B
Answer: (B) 6%
Question: A perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer. How many positive integers n are there such that n is less than 50,000 and at the same time n is a perfect square and a perfect cube?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: If n is a perfect square and a perfect cube, then n = a^6 for some integer a.
The numbers are 1^6=1, 2^6=64, 3^6= 729, 4^6=4096, 5^6=15,625, 6^=46,656.
The answer is D.
Answer: (D) 6
Question: (4+√3+√5)^2-(√3+√5)^2=?
(A) 1+2√3+2√5
(B) 16+8√3+8√5
(C) 1-√3+√5
(D) 1+√3-√5
(E) √3+√5
Rationale: (4+√3+√5)^2-(√3+√5)^2
(4+√3)^2 + 5 +2 (4+√3) (√5) - ( 3 +5 + 2√3√5)
16+ 3+ 8√3 +5 +8 √5 + 2 √15 - 3-5 -2√15
16+8√3+8√5
B is the answer
Answer: (B) 16+8√3+8√5
Question: If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is:
(A) 53.33
(B) 54.68
(C) 55
(D) 56
(E) None of these
Rationale: Explanation:
Required average = (55 × 50 + 60 × 55 + 45 × 60/55 + 60 + 45)
= (2750 + 3300 + 2700/160)
= 8750/160
= 54.68
Answer: B
Answer: (B) 54.68
Question: A sock drawer contains two socks, each one a different solid color. The colors of the socks are Indigo, and violet. If the socks are laid next to each other, how many different arrangements of socks could be made?
(A) 24
(B) 240
(C) 1,024
(D) 2,520
(E) 2
Rationale: I see no condition for arrangement.
So 2! ways - IMO option E is correct answer..
Answer: (E) 2
Question: A car was initially traveling at an average speed of 36 miles per hour. During each of ten successive 5-minute intervals, the car decreased its average speed by 2 miles per hour. How many miles did the car travel in the fourth 5-minute interval?
(A) 1.32
(B) 5.32
(C) 4.56
(D) 2.33
(E) 1.44
Rationale: The question does not specifically mentioned whether 36miles/h is the speed in first interval or before that... So I got confused.
If former is the case, then average speed of the car in 4th interval will be 28. This gives 28 * (5/60) = m = 2.33 miles
correct option is D
Answer: (D) 2.33
Question: The average of 7 consecutive numbers is 20. The largest of these numbers is
(A) 20
(B) 22
(C) 23
(D) 24
(E) 25
Rationale: Let the first number be x, Then the last number is ( x+6)
Average = (x+(x+1)+(x+2)+(x+3)+(x+3)+(x+4)+(x+5)+(x+6))/7 = 20
7x + 21 = 20*7 = 140, 7x =119, x = 17
The largest number =x+6 =17+6 = 23
ANSWER:C
Answer: (C) 23
Question: A combustion reaction forms carbon dioxide. A carbon dioxide molecule contains one carbon and two oxygen atoms. If, over a period of 15 minutes, a combustion reaction creates 15,000 molecules of carbon dioxide then approximately how many more atoms of oxygen than carbon are created on average per minute?
(A) 1,000
(B) 500
(C) 250
(D) 50
(E) 0
Rationale: Solution:
15,000 carbon dioxide molecules are created over a period of 15 minutes. Therefore 15,000/15 = 1,000 carbon dioxide molecules are created on average per minute
Each carbon dioxide molecule contains one carbon atom and two oxygen atoms. So 1,000 carbon dioxide molecules contain 1 × 1,000 = 1,000 carbon atoms and 2 × 1,000 = 2,000 oxygen atoms. The difference is 2,000 – 1,000 = 1,000.
The correct answer is A.
Answer: (A) 1,000
Question: Two dice are tossed. The probability that the total score is a prime number is:
(A) 1/6
(B) 5/12
(C) 1/2
(D) 7/9
(E) 9/4
Rationale: Clearly, n(S) = (6 x 6) = 36.
Let E = Event that the sum is a prime number.
Then E	= { (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3),
(5, 2), (5, 6), (6, 1), (6, 5) }
n(E) = 15.
P(E) =	n(E)/n(S)
=	15/36	=	5/12
Answer: (E) 9/4
Question: Twenty four men can do a work in 14 days. How many men are required to complete the work in 10 days?
(A) 33.6
(B) 10.12
(C) 50
(D) 14.2
(E) 60
Rationale: A
33.6
We have M1 D1 = M2 D2
So, 24 * 14 = M2 * 10 => M2 = 33.6.
Answer is A
Answer: (A) 33.6
Question: In five football games thus far this season, Barry has run for 98, 107, 85, 89, and 91 yards. At a minimum, how many yards Q will he need to gain this Sunday if he wants to keep his season average above 100 yards?
(A) 101
(B) 116
(C) 130
(D) Q=131
(E) Q=141
Rationale: Sorry Q=141 the answer is D.
Answer: (D) Q=131
Question: Boy sells a book for Rs. 540 he gets a loss of 10 %, To gain 10%, what should be the SP?
(A) 430
(B) 450
(C) 550
(D) 590
(E) 660
Rationale: Cost price = 540/90 x 100 = 600
To gain 10% = 600 x 10/100 = 60
SP = CP + gain = 600 + 60 = 660
Answer :E
Answer: (E) 660
Question: Three unbiased coins are tossed. What is the probability of getting 1 heads and 1 Tail?
(A) 3/4
(B) 1/4
(C) 3/8
(D) 7/8
(E) 1/8
Rationale: Let, H --> Head , T --> Tail
Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
Let E = event of getting 3 heads
Then E = {THT, HTH }
P(E) = n(E)/n(S) =2/8 = 1/4
Answer is B
Answer: (B) 1/4
Question: Starting with the initial speed of 30 km/hr, the speed is increased by 4 km/hour every two hours. How many hours will it take to cover a distance of 288 km?
(A) 4
(B) 6
(C) 12
(D) 8
(E) None of these
Rationale: Hour Speed (km/h) Distance travelled (in km)
=2x30=60
=2x34=68
=2x38=76
=2x42=84
=2+2+2+2=8
=60+68+76+84=288
Hence, the required time = 8 hours
Answer D
Answer: (D) 8
Question: There are between 140 and 150 cards in a collection of cards. If they are counted out 3 at a time, there are 2 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection?
(A) 141
(B) 143
(C) 145
(D) 147
(E) 149
Rationale: The numbers with the form 4n+1 are 141, 145, and 149.
Only 149 has the form 3k+2.
The answer is E.
Answer: (E) 149
Question: A is twice as good a workman as B and together they finish a piece in 18 days. In how many days will A alone finish the work?
(A) 15 days
(B) 3 days
(C) 12 days
(D) 27 days
(E) 18 days
Rationale: Sol. (A’s 1 day’s work):)(B’s 1 days work) = 2 : 1.
(A + B)'s 1 day's work = 1/18
Divide 1/18 in the ratio 2 : 1
A’s 1 day's work =(1/18*2/3)=1/27
Hence, A alone can finish the work in 27 days.
Ans: D
Answer: (D) 27 days
Question: List R contains five numbers that have an average value of 50. If the median of the numbers in the list is equal to the mean and the largest number is equal to 20 more than two times the smallest number, what is the smallest possible value in the list?
(A) 18
(B) 22
(C) 26
(D) 30
(E) 34
Rationale: The middle number is 50.
Let the smallest number be x. Then the largest number is 2x+20.
To make x as small as possible, let's make the remaining numbers as large as possible.
So the second largest = the largest = 2x+20.
The second smallest should be equal to the median.
The numbers are x, 50, 50, 2x+20, 2x+20.
x + 50 + 50 + 2x + 20 + 2x + 20 = 5*50 = 250
5x = 110
x = 22
The answer is B.
Answer: (B) 22
Question: Set Q consists of all even integers between 2 and 100, inclusive. Set X is derived by reducing each term in set Q by 50, set Y is derived by multiplying each term in set Q by 1.5, and set Z is derived by dividing each term in set Q by -4. Which of the following represents the ranking of the three sets in descending order of standard deviation?
(A)  X, Y, Z
(B)  X, Z, Y
(C)  Y, Z, X
(D)  Y, X, Z
(E)  Z, Y, X
Rationale: Set Q - {2, 4, ..., 100};
Set X - {-48, -46, ..., 50};
Set Y - {3, 6, ..., 150};
Set Z - {-2/4, -4/4, ..., -100/4} = {-1/2, -1, -3/2, ..., -25}.
If we add or subtract a constant to each term in a set the SD will not change, so sets Q and X will have the same SD.
If we increase or decrease each term in a set by the same percent (multiply by a constant) the SD will increase or decrease by the same percent, so set Y will have 1.5 times greater SD than set Q and set Z will have 4 times less SD than set Q (note SD can not be negative so SD of Z wil be SD of Q divided by 4 not by -4).
So, the ranking of SD's in descending order is: Y, Q=X, Z.
Answer: D.
Answer: (D)  Y, X, Z
Question: A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 5 years ago?
(A) 8
(B) 10
(C) 9
(D) 14
(E) 16
Rationale: Let's say
Age of Richard is "R"
Age of David is "D"
Age of Scott is "S"
Now
Richard is 6 years older than David,
i.e. R = D +6
David is 8 years older than Scott
i.e. D = S +8
If in 8 years, Richard will be twice as old as Scott
i.e. R+8 = 2x(S+8)
i.e. R+8 = 2S + 16
i.e. R = 2S+8
But R = D+6 = (S+8)+6 = S+14
therefore, 2S + 8 = S +14
i.e. S = 6
i.e. R = 20
i.e. D = 14
Now,
how old was David 5 years ago?
i.e. D-5 = 14-5 = 9 years
ANSWER:C
Answer: (C) 9
Question: A and B started a business by investing Rs.4000/- and Rs.5000/- respectively. Find the A’s share out of a total profit of Rs.1800:
(A) Rs.600/-
(B) Rs.660/-
(C) Rs.800/-
(D) Rs.820/-
(E) Rs.840/-
Rationale: A = Rs.4000/-
B = Rs.5000/-
A share 4 parts & B share 5 parts
Total 9 parts -----> Rs.1800/-
----> 1 part -------> Rs.200/-
A share = 4 parts -----> Rs.800/-
C
Answer: (C) Rs.800/-
Question: There are 6 people and 3 chairs. In how many different ways people can occupy the chairs?
(A) 330
(B) 340
(C) 350
(D) 360
(E) 370
Rationale: number of ways = 6*5*4*3 = 360
Answer is D
Answer: (D) 360
Question: How many 3 digit integers can be chosen such that none of the digits appear more than twice and none of the digits equal zero ?
(A) 729
(B) 720
(C) 648
(D) 640
(E) 57
Rationale: number of ways without restriction = 9*9*9 = 729
number of ways that break restriction = 9*1*9 = 9
so the answer is 729-9 = 720
ANS:B
Answer: (B) 720
Question: Before 4 years, dog A’s age was 4 times of dog B’s age and after 4 years, dog A’s age will be 3 times of dog B’s age. What is the difference of dog A’s age and dog B’s now?
(A) 36
(B) 42
(C) 52
(D) 60
(E) 64
Rationale: A - 4 = 4(B - 4) --> A - 4B = -12.............1
A + 4 = 3(B + 4) --> A - 3B = 8.............2
(2) - (1) --> B = 20 --> A = 3(24) = 72
A - B = 72 - 20= 52
Answer: C
Answer: (C) 52
Question: A certain number X when divided by 223 leaves a remainder of 93. Which of the following can be subtracted from X to make X divisible by 85?
(A) 17
(B) 27
(C) 37
(D) 47
(E) 71
Rationale: Least possible value of the number is 233 + 93 = 326
Further it is given the number must be divisible by 85 .
326/85 = Gives remainder as 71
So, 71 must be subtracted from the number , answer is (E)
Answer: (E) 71
Question: If x + y = 9 and x – y = 3, then x^2 - y^2 =
(A) -4
(B) 4
(C) 10
(D) 27
(E) 40
Rationale: The fastest approach has already been shown. Here's one more option.
Given:
x + y = 9
x – y = 3
Add the two equations to get: 2x = 12, which means x = 6
If x = 6, we can plug that value into either equation, to conclude that y = 3
If x = 6 and y = 3, then x² - y² = 6² - 3² = 27
Answer: D
Answer: (D) 27