mathewhe/aqua_rat huggingface dataset:
Question: The mean of set P does not exceed mean of any subset of set P. Which of the following must be true about set P?
I. Set P contains only one element
II. All elements in set P are equal
III. The median of set P equals the mean of set P
(A) of the three qualities is necessary
(B) II only
(C) III only
(D) II and III only
(E) I, II, and III
Rationale: The only necessary condition seems to be II.
If all nos are equal.... them mean of any subset is the same.
I is obviously ruled out ( e.g. P = {1,1,1} )
But III, what about 3?
It is not necessary in itself, rather, is automatically implied by II.
All sets that satsify II satisfy III=D
Answer: (D) II and III only
Question: If the sides of a cube are in the ratio 9:7. What is the ratio of their diagonals?
(A) 4:3
(B) 16:9
(C) 9:7
(D) 3:4
(E) 3:8
Rationale: Explanation:
Diagonal of a Cube=a√3 where a is side
a1:a2 = 9:7
d1:d2 = 9:7 where√3 cancelled both side
ANSWER:C
Answer: (C) 9:7
Question: If you roll a fair-sided die twice, what is the probability of getting a (2 ,2)?
(A) 1/4!
(B) 1/3!
(C) 1/2!
(D) 1/36
(E) 1/24
Rationale: total no. in two dice (1,1) ,(2,2) .....(6,)
Total number of events= 6*6
Total events of getting same pair(2, 2) = 6
Probability= 6/6*6= 1/6=1/3!
B
Answer: (B) 1/3!
Question: What is the difference between the largest number and the least number written with the digits 7, 3, 1, 4?
(A) 6084
(B) 6184
(C) 5084
(D) 6048
(E) 6049
Rationale: 1347
7431
------------
6084
ANSWER:A
Answer: (A) 6084
Question: The game of blackjack is played with a deck consisting of 13 cards (one of each of the numbers 2-10, one jack, one queen, one king, and one of ace) in each of four suits: clubs, diamonds, hearts, and spades.
In a game of blackjack, if your first card is a spade, what are the odds that it is a 9?
(A) 1/13
(B) 1/26
(C) 5/13
(D) 1/4
(E) 1/52
Rationale: The question should ask about the probability not the odds.
There are 13 spades, the probability that the spade we already have is 9 is therefore 1/13.
Answer: A.
Answer: (A) 1/13
Question: Each shelf of a bookcase contains 20 books. If the librarian took out 42 books and rearranged the remaining books so that all shelves but the last one contained 16 books and the last shelf contained 22 books, how many shelves does the bookcase have?
(A) A)4
(B) B)12
(C) C)6
(D) D)8
(E) E)9
Rationale: Denoting x the number of the shelves,
we can build an equation: 20x=16(x−1)+22+42
Solving the equation, we get x=12
Answer: B
Answer: (B) B)12
Question: A sum fetched a total simple interest of $4061.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?
(A) $8829
(B) $2840
(C) $6578
(D) $7782
(E) $8926
Rationale: E
8926
Principal
= $100 x 4016.25/9 x 5
= $406125/45
= $8926.
Answer: (E) $8926
Question: A fair 2 sided coin is flipped 3 times. What is the probability that tails will be the result at least twice, but not more than 3 times?
(A) 5/8
(B) 3/4
(C) 3/8
(D) 7/4
(E) 5/6
Rationale: at least twice, but not more than 3 timesmeans exactly 2 times, 3 times
The probability of getting exactly k results out of n flips is nCk/2^n
3C2/2^3=3/8
Option: C
Answer: (C) 3/8
Question: A library has an average of 510 visitors on Sundays and 240 on other day. The average number of visitors in a month of 30 days starting with sunday is
(A) 280
(B) 285
(C) 290
(D) 295
(E) 275
Rationale: Explanation:
As the month begin with sunday, so there will be five sundays in the month. So result will be:
=(510×5+240×25 / 30)=(8550 / 30)=285
Option B
Answer: (B) 285
Question: Jim and Renee will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Renee have an equal chance of choosing any one of the hand signs, what is the probability that Jim will win or draw?
(A) 5/6
(B) 2/3
(C) 1/2
(D) 5/12
(E) 1/3
Rationale: There are 3*3=9 combinations (cases) possible. In 3 cases there will be a tie (rock-rock, scissors/scissors, paper/paper). Now, out of 6 cases left Jim and Renee have equal chances of winning, so in 3 cases Jim will win and in other 3 Renee will win. So the probability Jim winning the game is (favorable outcomes)+Drawing the game / (total # of outcomes) = 6/9 = 2/3.
Or: no matter what sign Renee will select Jim can select 1 sign to win, 1 sign to get tie and 1 sign to loose, so the probability Jim winning the game or drawing is 2/3.
Answer: B
Answer: (B) 2/3
Question: If 2 cards are selected (with replacement) at random from the deck of 52 cards then what is the probability that one of the selected cards will be a heart and the other will be a club?
A deck of cards has a total of 52 cards, consisting of 4 suits: spades (black), hearts(red), diamonds (red), and clubs (black). In each suit, there are 13 cards including 1 king, 1 queen, and 1 jack.
(A) 1/8
(B) 1/16
(C) 1/32
(D) 1/64
(E) 1/128
Rationale: P(1 heart and 1 club) = 2(1/4*1/4) = 1/8
The answer is A.
Answer: (A) 1/8
Question: A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?
(A) 3.6 sec
(B) 18 sec
(C) 36 sec
(D) 72 sec
(E) 84 sec
Rationale: Speed of train relative to jogger = (45 - 9) km/hr = 36 km/hr.
= 36 x	5/18	m/sec
= 10 m/sec.
Distance to be covered = (240 + 120) m = 360 m. Answer: Option C
Time taken = 360/10	sec	= 36 sec.
Answer: (C) 36 sec
Question: A policeman noticed a criminal from a distance of 180 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 = (180 - 50) m = 130 m.
Answer : C
Answer: (C) 130 m
Question: What percent of 500 is 125?
(A) 0.25%
(B) 4%
(C) 25%
(D) 40%
(E) 250%
Rationale: 500*x /100 = 125
x = 125/5
x = 25
Ans: C
Answer: (C) 25%
Question: Tough and Tricky questions: Word Problems.
Micheal , Saren and Donald decided to club together to buy a present. Each of them gave equal amount of money. Luckily Saren negotiated a 20% discount for the present so that each of them paid 4 dollars less. How much did they pay for a present?
(A) 20
(B) 36
(C) 48
(D) 60
(E) 72
Rationale: Answer C.
We know that Saren negotiated a discount of 20%, so each of them paid $4 less. Since there are three people, the 20% of the original price amounts to $12. 5 times 12$ is 60$, so the original price, before Saren negotiated the discount, had been $60. They paid $12 less than the base price, so they spent $48.
Answer: (C) 48
Question: The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 80% profit?
(A) 1152
(B) 230
(C) 960
(D) 780
(E) 400
Rationale: C.P. = Rs. x.
Then, 832 - x = x - 448
2x = 1280 => x = 640
Required S.P. = 180% of Rs. 640 = 180/100 * 640 = Rs. 1152.
A
Answer: (A) 1152
Question: How many meters are there in 550 centimeters?
(A) 550 meters
(B) 5.5 meters
(C) 100 meters
(D) 2.5 meters
(E) 1 meter
Rationale: Solution:
1 meter = 100 centimeters
Just divide 550 by 100
550 Ã· 100 = 5.5, so there are 5.5 meters in 550 centimeters
Option B
Answer: (B) 5.5 meters
Question: The length of a rectangle is 5 more than the width. What are the dimensions of the rectangle if the perimeter is 34?
(A) 11
(B) 12
(C) 13
(D) 14
(E) None
Rationale: Pretend width = 1, then length = 6 ( 1 + 5)
2 × 1 + 2 × 7 = 2 + 14 = 16. Notice that 16 is far from a perimeter of 34
Try much bigger number.
How about if we...
Pretend width = 4, then length = 9 ( 4 + 5)
2 × 4 + 2 × 9 = 6 + 18 = 24. We are getting closer to a perimeter of 34
Pretend width = 5, then length = 10 ( 5 + 5)
2 × 5 + 2 × 10 = 10 + 30 = 30.
Pretend width = 7, then length = 12 ( 7 + 5)
2 × 7 + 2 × 12 = 14 + 24 = 38. This is higher than a perimeter of 34. So width should be higher than 5 and smaller than 7. May be a width of 6 will work.
Pretend width = 6, then length = 11 ( 6 + 5)
2 × 6 + 2 × 11 = 12 + 22 = 34.
Use of algebra:
Let width = x
Let length = x + 5
P = 2 × L + 2 × W
34 = 2 × ( x + 5) + 2 × x
34 = 2x + 10 + 2x
34 = 4x + 10
34 - 10 = 4x + 10 - 10
24 = 4x
24/4 = 4x/4
6 = x
Therefore, width = 6 and length = x + 5 = 6 + 5 = 11
Answer A
Answer: (A) 11
Question: Average families of 4 pay $3000 for their health insurance deductibles annually. There will be a 2/3 increase in the deductibles for next year. How much more will the average family pay in deductibles next year?
(A)  $1000
(B)  $2000
(C)  $3000
(D)  $4000
(E)  $5000
Rationale: A certain percentage of questions in the Quant section of the GMAT are just 'math questions' - you'll use a formula, do some calculations and you'll have the answer. This is one of those types of questions. You still have to write everything down and stay organized, but the work involved is relatively straight-forward.
Here, we're told that the current annual deductible is $3000 and that the deductible is to be increased by 2/3. We're asked how MUCH MORE will the deductible cost a family next year.
Original Deductible = $3000
Increase in Deductible = 2/3
The answer is calculated by the equation:
$3000 × 2/3 = $2000.
B
Answer: (B)  $2000
Question: Scott's average (arithmetic mean) golf score on his first four rounds was 78.What score does he need on his fifth round to drop his average score by 2 points?
(A) 68
(B) 72
(C) 78
(D) 88
(E) 312
Rationale: Average score for first 4 rounds = 78
Average score after 5 rounds = 76
Score Scott needs on his 5th round to drop average score by 2 points = 78 - (2*5) = 68
Answer A
Alternatively , sum of scores of first 4 rounds = 78*4 = 312
Sum of scores after 5 rounds = 76*5 = 380
Score Scott needs on his 5th round to drop average score by 2 points = 380 - 312 = 68
Answer A
Answer: (A) 68
Question: Two vertical poles 2 meter and 8 meter high stand apart on a horizontal plane. find the height in meters of the point of intersection of the lines joining the top of each pole to the bottom of the other pole.
(A) 1.8
(B) 1.9
(C) 1.6
(D) 1.7
(E) 56
Rationale: Let A be the point of the top of the 2m pole.
Let B be the point of the foot of the 2m pole.
Let C be the point of the top of the 8m pole.
Let D be the point of the foot of the 8m pole.
Let E be the point of intersection of the line segments AD and BC.
From E drop a perpendicular to the ground.
Let F be the point on the ground where perpendicular from E meets the ground.
Let X be the distance from E to F.
Let P be the distance from B to F.
Let Q be the distance from F to D.
Triangles BEF and BCD are similar so we get Equation 1:
X/P = 8/(P+Q)
Triangles DEF and DAB are similar so we get:
X/Q = 2/(P+Q)
Multiplying both sides by 4 we get Equation 2:
(4X)/Q = 8/(P+Q)
Combining Equations 1 and 2 we get:
X/P = (4X)/Q
Simplifying this we get:
1/P = 4/Q
And then we get:
Q = 4P
Substituting Q=4P into Equation 1 we get:
X/P = 8/(P+4P)
Simplifying this we get:
X/P = 8/(5P)
X = (8P)/(5P)
X = 8/5
X = 1.6
Therefore, the desired height is 1.6 meters.
ANSWER:C
Answer: (C) 1.6
Question: Find the odd man out
25, 49, 81, 121, 144, 169
(A) 49
(B) 121
(C) 144
(D) 169
(E) 25
Rationale: 144 is square of 12 which is even number where as all others are squares of odd numbers.
ANSWER:C
Answer: (C) 144
Question: You have a battery that is charged during the day by a solar panel. At night, 3 Iphones use that battery and deplete the charge after 4.8 hours. Your family shows up and they have brought 9 of their own Iphones. How many hours before the charge on the battery is depleted now?
(A) 5.3
(B) 1.2
(C) 1.8
(D) 2.2
(E) 1.5
Rationale: First set up a ratio with all the relevant values and also the unknown variable:
3*4.8 = 12*x
Now solve by multiplying 3 by 4.8 and then dividing that product by 12:
3*4.8 = 14.4
14.4/12 = x
x = 1.2
The value of x equals the number of hours the battery charge will last if 12 Iphones are connected to it.
Answer: B
Answer: (B) 1.2
Question: A part of certain sum of money is invested at 16% per annum and the rest at 20% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?
(A) 4:6
(B) 4:9
(C) 4:3
(D) 4:1
(E) 5:4
Rationale: 20:16
= 5:4
Answer: E
Answer: (E) 5:4
Question: If 16^y = 4^16, what is y?
(A) 2
(B) 4
(C) 8
(D) 12
(E) 16
Rationale: 16^y = 4^2y = 4^16
2y=16
y = 8
The answer is C.
Answer: (C) 8
Question: Two trains of equal are running on parallel lines in the same direction at 48 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
(A) 60 m
(B) 72 m
(C) 80 m
(D) 82 m
(E) 84 m
Rationale: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 48 - 36 = 12 km/hr.
= 12 * 5/18 = 10/3 m/sec.
2x/36 = 10/3=> x = 60.
ANSWER:A
Answer: (A) 60 m
Question: To produce an annual income of Rs. 1200 from a 12 % stock at 90,the amount of stock needed is :
(A) Rs. 10,000
(B) Rs. 10,800
(C) Rs. 14,400
(D) Rs. 16,000
(E) None of these
Rationale: Solution
For an income of Rs. 12, stock needed = Rs. 100.
For an income of Rs. 1200, stock needed = Rs. 100/12x1200 = 10000
Answer A
Answer: (A) Rs. 10,000
Question: On a windy day, out of every 3 sand dunes formed, only 1 remains. Out of 5 blown-out
sand-dunes, 1 has treasure and only 2 out of 3 sand dunes formed have lucky coupons. Find
the probability that the blown-out sand dune will contain both the things.
(A) 2/25
(B) 4/75
(C) 7/75
(D) 3/5
(E) 4/45
Rationale: Probability of sand dune blown out = 2/3
Probability that it has treasure = 1/5
Probability that it has lucky coupon = 2/3
total probability = 2/3 * 1/5 * 2/3 = 4/45
ANSWER:E
Answer: (E) 4/45
Question: The average age of a family of 6 members is 34 years.If the age of the youngest member is 7 years,what was the average age of the family at the birth of the youngest member?
(A) 15
(B) 18
(C) 21
(D) 12
(E) 27
Rationale: Present age of total members = 6 X 34 = 204
7 yrs back their ages were = 6 x 7 = 42
Ages at the birth of youngest member = 204 - 42 = 162
Therefore, avg age at the birth of youngest member = 162/6 = 27.
ANSWER:E
Answer: (E) 27
Question: The banker's discount on Rs.1450 due a certain time hence is Rs.145. Find the true discount and the banker's gain.
(A) 13
(B) 15
(C) 18
(D) 21
(E) None
Rationale: Solution
Sum	=B.D x T.D/ B.D - T.D
= B.D x T.D/ B.G
T.D / B. G	=Sum / B.D
= 1450 / 145
= 10 / 1
If B.D is Rs. 11,T.D= Rs.10.
If B.D is Rs.145,
T.D	= Rs.(10 / 11 x 145)
= Rs.132.
And, B.G	= Rs(165 - 132)
= Rs.13.
Answer A
Answer: (A) 13
Question: A certain theater has 100 balcony seats. For every $2 increase in the price of a balcony seat above $10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is $10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is $1,460 ?
(A) $12
(B) $14
(C) $18.6
(D) $17
(E) $18
Rationale: I solved it as follows:
10+2(x) = 100 -5(x)
x= 12
Equation should be (10+$2*x)(100-5x)=1,460, where x is the # of times we increased the price by $2. (10+$2*x)(100-5x)=1,460 --> (5+x)(20-x)=146 --> x=4.3 or x=10.7 --> price=10+$2*4.3=$18.6 or price=10+$2*10.7=$31.4.
Answer: C.
Answer: (C) $18.6
Question: A person took some amount with some interest for 2 years, but increase the interest for 1%, he paid Rs.130/- extra, then how much amount he took?
(A) s.5500/-
(B) s.6500/-
(C) s.4000/-
(D) s.7000/-
(E) s.8000/-
Rationale: Explanation:
2 years = Rs.130/-
year = 130/2
Rate of Interest = 1%
100/1% × 130/2 = Rs.6500/-
P = Rs.6500/-
Answer: Option B
Answer: (B) s.6500/-
Question: If two times of the daughter’s age in years is included to the mother’s age, the total is 70 and if two times of the mother’s age is included to the daughter’s age, the total is 95. So the Mother’s age is,
(A) 30
(B) 40
(C) 50
(D) 60
(E) 39
Rationale: B
40
Let daughter’s age = A and mother’s age = B
Given:
2A+B = 70 and,
A+2B = 95
Solving B, we will get B = 40.
Answer: (B) 40
Question: A boutique sold 500 dress shirts at $25 each, 600 belts at $10 each, 700 pants at $50 each and 1000 shoes at $200. What % of the stores revenue came from dress shirts and pants?
(A) 19.5%
(B) 17.5%
(C) 16.5%
(D) 13.5%
(E) 18.5%
Rationale: Correct Answer: E
The company's total revenue from dress shirts=500*$25=$12500
The company's total revenue from belts=600*$15=$9000
The company's total revenue from pants=700*$50=$35000
The company's total revenue from shoes=1000*$200=$200000
The combined total of all sales=$256500
The combined total of dress shirts and pants=$12500+$35000=$47500
Therefore % of dress shirts and pants sales=47500/256500*100= 18.5%
Answer: (E) 18.5%
Question: How long does a train 110 meters long running at the speed of 72 km/hour take to cross a bridge 132
meters in length ?
(A) 15 seconds
(B) 12.1 seconds
(C) 10 seconds
(D) 8.1 seconds
(E) None of these
Rationale: Explanation:
Speed = 72 km/hour = 72*(5/18) m/sec
= 20 m/sec
Total distance to be covered = 110+132 = 142 meters
Time = Distance/Speed
= 242/20 = 12.1 seconds
Answer: B
Answer: (B) 12.1 seconds
Question: 25% of a number is more than 20% of 650 by 190. Find the number?
(A) 288
(B) 278
(C) 800
(D) 267
(E) 1280
Rationale: (25/100) * X â€“ (20/100) * 650 = 190
1/4 X = 320
X = 1280
Answer:E
Answer: (E) 1280
Question: How many different section of 4 books can be made from 10 different books if two particular books are never selected?
(A) 90
(B) 50
(C) 60
(D) 80
(E) 70
Rationale: This means four books are seclected out of the remaining 8 books. Required number of ways = 8C4= 8!/4!x4!=70. Ans: E.
Answer: (E) 70
Question: A man whose bowling average is 12.4, takes 5 wickets for 26 runs and there by decreases his average by 0.4. The number of wickets taken by him before his last match is?
(A) 82
(B) 83
(C) 84
(D) 85
(E) 86
Rationale: 12.4x+26/(5+x)=12
12.4x+26=60+12x
x=34/0.4=85
ANSWER:D
Answer: (D) 85
Question: If the cost price of 30 articles is equal to the selling price of 45 articles, what is the % profit or loss made by the merchant?
(A) 33.33% loss
(B) 25% profit
(C) 20% loss
(D) 20% profit
(E) 5% profit
Rationale: Let the cost price of 1 article be $1.
Therefore, cost price of 30 articles = 30 * 1 = $30
The selling price of 45 articles = cost price of 30 articles = $30.
Now, we know the selling price of 45 articles. Let us find the cost price of 45 articles.
Cost price of 45 articles = 45 * 1 = $45.
Therefore, profit made on sale of 45 articles = Selling price of 45 articles - cost price of 45 articles
= 30 - 45 = -$15.
As the profit is in the negative, the merchant has made a loss of $15.
Therefore, % loss = loss/cp * 100
% loss = -15/45 * 100 = 33.33% loss.
A
Answer: (A) 33.33% loss
Question: The 4 sticks in a complete bag of Pick-Up Sticks are all straight-line segments of negligible width, but each has a different length: 1 inch, 2 inches, 3 inches, and 4 inches, respectively. If Tommy picks a stick at random from each of 3 different complete bags of Pick-Up Sticks, what is the probability D that Tommy CANNOT form a triangle from the 3 sticks?
(A) 11/32
(B) 13/32
(C) 15/32
(D) 17/32
(E) 19/32
Rationale: In order to form a triangle, the sum of two sides must be greater than the third side.
So we can choose the combination of numbers which will NOT result in a triangle.
Favorable outcomes:
1,1,4 (4>1+1): 3 ways of arriving at this (1,1,4), (1,4,1), (4,1,1) or
1,2,4 (4>1+2): 6 ways of arriving at this (1,2,4), (1,4,2), (2,1,4), (2,4,1), (4,1,2), (4,2,1) which is same as 3!
1,3,4 (4=1+3): 6 ways of arriving at this
2,2,4 (4=2+2): 3 ways of arriving at this
1,1,3 (3>1+1): 3 ways of arriving at this
1,2,3 (3=1+2): 6 ways of arriving at this
1,1,2 (2+1+1): 3 ways of arriving at this
Overall favourable outcomes: 30
Total outcomes: 4*4*4 = 64 (4 ways of choosing a stick from each of the 3 bags)
Probability D that a triangle is not formed = 30/64 = 15/32
C is the correct option here.
Answer: (C) 15/32
Question: A confectioner decides to sell all of his pastry due to the coming holiday. His pastry goods are equally divided among a group of 30 regular customers. If only 49 customers come to the bakery, each one will receive 6 less pastry goods. How much pastry does the confectioner needs to sell?
(A) 450.
(B) 412.
(C) 432.
(D) 502.
(E) 522.
Rationale: Pastry is divided in 30 customers equally. So,total number of pastry must be a multiple of 30
Only option A satisfies the condition, and hence is the answer
Answer: (A) 450.
Question: What is the total cost of 2 sandwiches at $2.44 each and 4 sodas at $0.87 each?
(A) $3.36
(B) $6.85
(C) $8.36
(D) $10.08
(E) $11.85
Rationale: Answer = C
2 * 2.44 + 4 * 0.87
= 2 (2.50 - 0.06) + 4 (1.00 - 0.13)
= 5 + 4 - 0.12 - 0.52
= 9 - 0.64
= 8.36
Answer: (C) $8.36
Question: A class average mark in an exam is 70. The average of students who scored below 60 is 50. The average of students who scored 60 or more is 75. If the total number of students in this class is 20, how many students scored below 60?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: Let n the number of students who scored below 60 and N the number of students who scored 60 or more. Xi the grades below 60 and Yi the grades 60 or above.
[sum(Xi) + sum(Yi)] / 20 = 70 : class average
sum(Xi) / n = 50 : average for less that 60
sum(Yi) / N = 75 : average for 60 or more
50n + 75N = 1400 : combine the above equations
n + N = 20 : total number of students
n = 4 and N = 16 : solve the above system
correct answer D
Answer: (D) 20
Question: A student committee on academic integrity has 132 ways to select a president and vice president from a group of candidates. The same person cannot be both president and vice president. How many candidates are there?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 12
Rationale: xC1 * (x-1)C1= 132
x^2 - x - 132 =0
(X-12) (X+11) = 0
X= 12 , - 11
- 11 can't possible.
Hence 12 should be the answer
E
Answer: (E) 12
Question: The average of ten numbers is 8. If each number is multiplied by 12, then what is the average of the new set of numbers?
(A) 8
(B) 12
(C) 20
(D) 96
(E) 120
Rationale: The sum of the ten numbers is 8*10 = 80
If each number is multiplied by 12, the new sum is 12*(80).
The average is then 12*8 = 96
The answer is D.
Answer: (D) 96
Question: 18 business executives and 7 chairmen meet at a conference. If each business executive shakes the hand of every other business executive and every chairman once, and each chairman shakes the hand of each of the business executives but not the other chairmen, how many handshakes would take place?
(A) 144
(B) 131
(C) 279
(D) 90
(E) 45
Rationale: there are 18 business exec and in each handshake 2 business execs are involved.
hence 18C2=153
Also, each of 18 exec will shake hand with every 7 other chairmen for total of 126 handshake.
total=153+126=279
ANS: C
Answer: (C) 279
Question: A and B can finish a work 30 days if they work together. They worked together for 20 days and then B left. A finished the remaining work in another 20 days. In how many days A alone can finish the work?
(A) 30
(B) 60
(C) 40
(D) 20
(E) 50
Rationale: Amount of work done by A and B in 1 day = 1/30
Amount of work done by A and B in 20 days = 20 × (1/30) = 20/30 = 2/3
Remaining work – 1 – 2/3 = 1/3
A completes 1/3 work in 20 days
Amount of work A can do in 1 day = (1/3)/20 = 1/60
=> A can complete the work in 60 days
Answer is B.
Answer: (B) 60
Question: Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
(A) 648
(B) 1800
(C) 2700
(D) 10800
(E) None
Rationale: Let the number of required bottles be x
machine 6 : 10
Time 1: 4
= :: 270 : x
Therefore 6 x 1 x X = 10 x 4 x 270
=> x= (10 x 4 x 270) /(6)
=> x = 1800
Answer: Option B
Answer: (B) 1800
Question: The average of six number is x and the average of three of these is y. if the average of the remaining three is z, then :
(A) x = y+z
(B) 2x = y+z
(C) x = 2y+2z
(D) None of these
(E) Cannot be determined
Rationale: Solution
Clearly, we have X=(3y+3z/6) or 2x= y + z. Answer B
Answer: (B) 2x = y+z