mathewhe/aqua_rat huggingface dataset:
Question: A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 90 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?
(A) 71.5
(B) 72
(C) 72.5
(D) 73
(E) 85.7
Rationale: Many approaches are possible, one of them:
Let the distance be 1 kilometer.
Time to cover this distance at 90 kilometers per hour is 1/90 hours = 3,600/90 seconds = 40 seconds;
Time to cover this distance at regular speed is 40+2=42 seconds = 42/3,600 hours = 7/600 hours;
So, we get that to cover 1 kilometer 1/(7/600) hours is needed --> regular speed 85.7 kilometers per hour (rate is a reciprocal of time or rate=distance/time).
Answer: E.
Answer: (E) 85.7
Question: If Rs.540/- are divided among A,B and C in such a way that A’s share is ½nd of B share and B’s share is 1/3rd of C’s share. The share of A is?
(A) Rs.40/-
(B) Rs.40/-
(C) Rs.60/-
(D) Rs.70/-
(E) Rs.90/-
Rationale: A:B:C = 1:2:6
Total parts = 9
A's share is = 1 parts
9 -----> Rs.540/-
1 -----> Rs.60/-
Answer: Option 'C'
Answer: (C) Rs.60/-
Question: Trains A and B start simultaneously from stations 200 miles apart, and travel the same route toward each other on adjacent parallel tracks. If Train A and Train B travel at a constant rate of 20 miles per hour and 20 miles per hour, respectively, how many miles will Train A have traveled when the trains pass each other, to the nearest mile?
(A)  100
(B)  133
(C)  150
(D)  167
(E)  188
Rationale: Since we know the distance (200) and the combined rate (40), we plug it into the formula:
Distance = Rate * Time
200 = 40 * Time
We can solve for the time they will meet cause we added the rate of Train A and Train B together.
So the time will be 200/40 from dividing 40 on both sides to isolate Time in the equation above.
Time will be 5 hours so now you can plug that in for Train A’s distance.
Distance = Rate * Time
Distance = 20 * 5
Distance = 100 according to answer choice A.
Answer: (A)  100
Question: Caleb spends $66.50 on 50 hamburgers for the marching band. If single burgers cost $1.00 each and double burgers cost $1.50 each, how many double burgers did he buy?
(A) 5
(B) 33
(C) 20
(D) 40
(E) 45
Rationale: Solution -
Lets say, Single hamburgersxand Double hamburgersy
Given that,
x+y=50 and 1x+1.5y=66.50. By solving the equations y=33. ANS B.
Answer: (B) 33
Question: If a train, travelling at a speed of 90 kmph, crosses a pole in 5 sec, then the length of train is?
(A) 281 m
(B) 112 m
(C) 117 m
(D) 125 m
(E) 123 m
Rationale: D
D = 90 * 5/18 * 5 = 125 m
Answer: (D) 125 m
Question: A certain ball team has an equal number of right- and left-handed players. On a certain day, two-thirds of the players were absent from practice. Of the players at practice that day, two-third were right handed. What is the ratio of the number of right-handed players who were not at practice that day to the number of left handed players who were not at practice?
(A) 1/3
(B) 2/3
(C) 5/7
(D) 7/5
(E) 3/2
Rationale: Say the total number of players is 18, 9 right-handed and 9 left-handed.
On a certain day, two-thirds of the players were absent from practice --> 12 absent and 6 present.
Of the players at practice that day, one-third were right-handed --> 6*2/3=4 were right-handed and 2 left-handed.
The number of right-handed players who were not at practice that day is 9-4=5.
The number of left-handed players who were not at practice that days is 9-2=7.
The ratio = 5/7.
Answer: C
Answer: (C) 5/7
Question: A certain gallery is hanging a series of 6 paintings. All the paintings will be exhibited in a row along a single wall. Exactly 2 of the paintings are on panel, the remainder are on canvas. In how many ways can the paintings be exhibited if the works on panel must be the second and sixth in the row?
OE
(A) 240
(B) 200
(C) 122
(D) 80
(E) 36
Rationale: We need to consider them separately because the question specifies:
1. Panel paintings have to be placed only at 2nd, 3nd and 6th place.
2. Implies that Canvas has to be placed 1,4,5th place.
So we have two separatebucketsto consider.
So panels can be ordered in 3!
Canvas can be ordered in 3!
since relative position of panels to canvas is fixed (Panels 2nd and 6th) the answer is 3! x 3! = 36
E
Answer: (E) 36
Question: In how many ways can five boys and three girls sit in a row such that all boys sit together?
(A) A)2888
(B) B)2885
(C) C)2880
(D) D)2876
(E) E)2224
Rationale: Treat all boys as one unit. Now there are four students and they can be arranged in 4! ways. Again five boys can be arranged among themselves in 5! ways.
Required number of arrangements = 4! * 5! = 24 * 120 = 2880.
Answer:C
Answer: (C) C)2880
Question: If n is a positive integer, what is the maximum possible number of prime numbers in the following sequences: n + 1, n + 2, n + 3, n + 4, n + 5, and n + 6?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: for n=1,
the numbers are 2,3,4,5,6,7
out if these 2,3,5,7 these 4 are prime numbers.
now for any value of n >1 all six consecutive numbers will be 3 odd and 3 even. so at max we will get 3 prime numbers(assuming all the odd numbers are prime)
so the ans is 4
ANSWER:C
Answer: (C) 4
Question: Rahul's housing colony have One tap, working alone at its maximum constant rate, can fill a certain tank in 230 seconds. A second tap, working alone at its maximum constant rate, can fill the same tank in 234 seconds. If both taps work together at their respective maximum constant rates, the time it will take to fill the tank is closest to
(A) 116 seconds
(B) 150 seconds
(C) 177 seconds
(D) 200 seconds
(E) 270 seconds
Rationale: Tap 1 : 230 secs
Tap 2 : 234 secs
Considering the average of these 2 taps : 232 secs.
So 1 tap can fill the tank in 232 secs, so 2 taps can fill the tank in 232/2 = 116 secs.
Closest answer is A.
Answer: (A) 116 seconds
Question: When the no.7y86038 is exactly divisible by 11, then the smallest whole no.in place of y?
(A) 3
(B) 4
(C) 6
(D) 7
(E) 9
Rationale: The given number =7y86038
Sum of the odd places =8+0+8+7=23
Sum of the even places = 3+6+y
(Sum of the odd places)- (Sum of even places) = Number (exactly divisible by 11)
23-(9+y) = divisible by 11
14 � y = divisible by 11.
Y must be 3, to make given number divisible by 11.
A
Answer: (A) 3
Question: In the Land of Oz only one or two-letter words are used. The local language has 66 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition?
(A) 65
(B) 66
(C) 67
(D) 131
(E) 132
Rationale: The seventh letter (Let it be @) can be used with other 65 in two type of arrangents
one when seventh letter is in 1st slot @_ (65 ways)
another, when seventh letter is in 2nd slot _@ (65 ways)
seventh letter (@) itself
Lost words = 1 + 65 + 65 = 131
ANSWER:D
Answer: (D) 131
Question: Seats for Mathematics, Physics and Biology in a school are in the ratio 5:7:8. There is a proposal to increase these seats by 40, 50 and 75 respectively. What will be the ratio of increased seats?
(A) 2:3:4
(B) 6:7:8
(C) 6:8:9
(D) None of these
(E) Cannot be determined
Rationale: Explanation :
Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.
And, the number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).
=>(140/100)×5x, (150/100)×7x, (175/100)×8x.
=>7x, 21x/2, 14x.
The required ratio :-
=>7x : 21x/2 : 14x.
=>14x : 21x : 28x.
=>2:3:4.
Answer : A
Answer: (A) 2:3:4
Question: A rectangular tank needs to be coated with insulation. The tank has dimensions of 3 feet, 6 feet, and 2 feet. Each square foot of insulation costs $20. How much will it cost to cover the surface of the tank with insulation?
(A) $980
(B) $1060
(C) $1220
(D) $1440
(E) $1650
Rationale: The total surface area is 2(2*3 + 3*6 + 2*6) = 72 square feet
The total cost is 72*$20 = $1440
The answer is D.
Answer: (D) $1440
Question: Baseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability Y that the World Series will consist of fewer than 7 games?
(A)  12.5%
(B)  25%
(C)  31.25%
(D)  68.75%
(E)  75%
Rationale: Your explanation is very close toManhattan GMAT's official answer - it's quite uncanny:
"There are many other ways this could happen. Using the permutation formula, there are 6!/(3!)(3!) = 20 ways for the two teams to split the first 6 games (3 wins for each).
There are then 2 possible outcomes to break the tie in Game 7. Thus, there are a total of 202 = 40 ways for the World Series to last the full 7 games.
The probability that any one of these 40 ways occurs can be calculated from the fact that the probability of a team winning a game equals the probability of a team losing a game = 1/2.
Given that 7 distinct events must happen in any 7 game series, and that each of these events has a probability of 1/2, the probability that any one particular 7 game series occurs is.
Since there are 40 possible different 7 game series, the probability that the World Series will last exactly 7 games is: (1/2)^7 = 1/128
40*1/128 = 40/128 = 31.25%
Thus the probability Y that the World Series will last less than 7 games is 100% - 31.25% = 68.75%.
The correct answer is D."
Answer: (D)  68.75%
Question: A and B complete a work in 6 days. A alone can do it in 10 days. If both together can do the work in how many days?
(A) 3.95 days
(B) 4.95 days
(C) 3.75 days
(D) 2.50 days
(E) 1.45 days
Rationale: 1/6 + 1/10 = 8/30 = 4/15
15/4 = 3.75 days
ANSWER:C
Answer: (C) 3.75 days
Question: Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made?
(A) Rs.16.90
(B) Rs.16.59
(C) Rs.16.60
(D) Rs.16.50
(E) Rs.18.50
Rationale: Let the quantities of A and B mixed be 3x kg and 7x kg.
Cost of 3x kg of A = 9(3x) = Rs. 27x
Cost of 7x kg of B = 15(7x) = Rs. 105x
Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x
Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66
Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 =Rs.16.50
Answer:D
Answer: (D) Rs.16.50
Question: The average price of three items of furniture is Rs. 10000. If their prices are in the ratio 3:5:7, the price of the cheapest item is?
(A) 2379
(B) 2600
(C) 9288
(D) 9000
(E) 28311
Rationale: Let their prices be 3x, 5x and 7x.
Then, 3x + 5x + 7x = (10000 * 3) or x = 866.6.
Cost of cheapest item = 3x = Rs. 2600.
Answer: B
Answer: (B) 2600
Question: R is the set of positive even integers less than 50, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?
(A) None
(B) Two
(C) Three
(D) Five
(E) Seven
Rationale: squares < 50 {1,4,9,16,25,36,49 }
S = {1,4,16,36}
R = {2,.....48}
Hence C.
Answer: (C) Three
Question: The H.C.F. of two numbers is 12 and their L.C.M. is 600. If one of the number is 20, find the other?
(A) 100
(B) 360
(C) 120
(D) 200
(E) 150
Rationale: Other number = 12*600/20= 360
Answer is B
Answer: (B) 360
Question: The length of a rectangle is one - fourth of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
(A) 350 sq.units
(B) 250 sq.units
(C) 300 sq.units
(D) 200 sq.units
(E) 100 sq.units
Rationale: Given that the area of the square = 6400 sq.units
=> Side of square = √6400= 80 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 1/4 * 80 = 20 units
Given that breadth = 10 units
Area of the rectangle = lb = 20 * 10 = 200 sq.units
Answer:D
Answer: (D) 200 sq.units
Question: It takes Joey the postman 1 hours to run a 4 mile long route every day. He delivers packages and then returns to the post office along the same path. If the average speed of the round trip is 5 mile/hour, what is the speed with which Joey returns?
(A) 6 2/3
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: let his speed for one half of the journey be 4 miles an hour
let the other half be x miles an hour
now,
avg speed =5 mile an hour
2*4*x/4+x=5
8x=5x+20=>3x=20=>x=6 2/3
A
Answer: (A) 6 2/3
Question: Find the ratio in which rice at Rs. 7.10 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg
(A) 2:0
(B) 3:4
(C) 2:1
(D) 2:2
(E) 2:8
Rationale: By the rule of alligation:
Cost of 1 kg rice of 1st kind Cost of 1 kg rice of 2nd kind
Required ratio = 60 : 80 = 3 : 4
Answer: B
Answer: (B) 3:4
Question: Find the number which is nearest to 3105 and is exactly divisible by 21
(A) 1208
(B) 3108
(C) 241
(D) 217
(E) 3147
Rationale: On dividing 3105 by 21, we get 18 as remainder.
Number to be added to 3105 = (21 - 18) - 3.
Hence, required number = 3105 + 3 = 3108.
ANSWER B 3108
Answer: (B) 3108
Question: The diameter of a cylindrical tin is 6cm and height is 5 cm. Find the volume of the cylinder?
(A) 28π cc
(B) 15π cc
(C) 4π cc
(D) 45π cc
(E) 27π cc
Rationale: Explanation:
r = 3 h = 5
π * 3 * 3 * 5 = 45 π cc
Answer: D
Answer: (D) 45π cc
Question: R campers fished for 2 hours. If m of the campers caught 2 fish apiece and the rest caught a combined total of n fish, how many fish did the R campers catch per hour?
(A) 2m + n(R-m)
(B) (2m + n(R-m))/3
(C) (2m + n(m-R))/3
(D) (2m + n)/2
(E) (2m + n)/R
Rationale: m of the campers caught 2 fish apiece in 2 hours --> total fish caught by m campers = 2m;
The rest caught a combined total of n fish.
Total fish caught in 2 hours = 2m+n --> per hour (2m+n)/2.
Answer: D.
Answer: (D) (2m + n)/2
Question: A no.when divided by 221 gives a remainder 43, what remainder will be obtainedby dividingthe same no.17?
(A) 3
(B) 6
(C) 9
(D) 11
(E) 14
Rationale: 221 + 43 = 264/17 = 9 (Remainder)
C
Answer: (C) 9
Question: A man walks at a speed of 3 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?
(A) 2 1/2
(B) 2 1/6
(C) 4 1/2
(D) 2 1/1
(E) 2 1/8
Rationale: Required time = (5 1/4)/3 + (5 1/4)/7 = 2 1/2 hours.
Answer: A
Answer: (A) 2 1/2
Question: 5 men and 12 boys finish a piece of work in 4 days, 7 men and 6 boys do it in 5 days. The ratio between the efficiencies of a man and boy is?
(A) 6:6
(B) 6:1
(C) 6:9
(D) 6:5
(E) 6:2
Rationale: 5M + 12B ----- 4 days
7M + 6B ------- 5 days
20M + 48B = 35M + 30B
18B = 15M => 5M = 6B
M: B = 6:5
Answer: D
Answer: (D) 6:5
Question: How many three letter words are formed using the letters of the word GAMER?
(A) 60
(B) 45
(C) 67
(D) 98
(E) 29
Rationale: The number of letters in the given word is four.
The number of three letter words that can be formed using these four letters is 5P3
= 5 * 4 *3 = 60.
Answer: A
Answer: (A) 60
Question: 2/5 of 3/7 of 23/11 of ? = 64 × 3
(A) 511
(B) 419
(C) 616
(D) 636
(E) 686
Rationale: Explanation:
2/5 &time; 3/7 &time; 20/11 &time; x = 192
X = 192 &time; 11 &time; 7 &time; 5/2 &time; 3 &time; 20 = 616
Answer: Option C
Answer: (C) 616
Question: Find the value of (2 − 1/3) (1 − 1/4)(1 − 1/5)……… (1 − 1/99)(1 − 1/100)
(A) 1/20
(B) 1/21
(C) 2/13
(D) 2/15
(E) None
Rationale: (2 − 1/3) (1 − 1/4)(1 − 1/5)..... (1 − 1/99)(1 − 1/100)
5/3 × 3/4 × 4/5 × ....... 98/99 × 99/100 = 5/100 = 1/20
A)
Answer: (A) 1/20
Question: The average of first 10 natural numbers is?
(A) 5.6
(B) 5.5
(C) 5.9
(D) 5.4
(E) 5.1
Rationale: Sum of 10 natural no. = 110/2 = 55
Average = 55/10 = 5.5
Answer:B
Answer: (B) 5.5
Question: A and B participate in a 5000 m bicycle race which is being run on a circular track of 500 m. If the speed of A and B are 20 m/s and 10 m/s respectively, what is the distance covered by A when he passes B for the seventh time ?
(A) 2500
(B) 2800
(C) 4000
(D) 4500
(E) situation not possible
Rationale: Track length = 500 m
Speed of A and B are 20m/s and 10 m/s respectively
Time taken by them to meet = length/ relative speed = 500/(20-10) 50 sec.
Time taken to meet for the 7th time = 7 *50 =350 sec ……..(1)
Total duration of race = total legth of race/ speed
= 500/20 = 250 sec ……..(2)
From (1) and (2) we can find out that 7th time meeting is not possible.
ANSWER:E
Answer: (E) situation not possible
Question: A board 10ft. 9 inches long is divided into 3 equal parts . What is the length of each part?
(A) 3ft. 7 inches
(B) 6ft. 7 inches
(C) 4ft. 7 inches
(D) 2ft. 7 inches
(E) 1ft. 7 inches
Rationale: Length of board=10ft. 9 inches=(10*12+9)inches=129 inches.
Therefore, Length of each part = (129/3) inches = 43 inches = 3ft. 7 inches
Answer is A.
Answer: (A) 3ft. 7 inches
Question: I. Class A has a higher enrollment than Class B.
II. Class C has a lower enrollment than Class B.
III.Class A has a lower enrollment than Class C.
If the first two statements are true, the third statement is
(A) true
(B) false
(C) uncertain
(D) none
(E) two
Rationale: Explanation:
From the first two statements, we know that of the three classes, Class A has the highest enrollment, so the third statement must be false.
Answer: B) false
Answer: (B) false
Question: Amy's grade was 90th percentile of the 80 grades for her class. Of the 100 grades from another class, 19 were higher than Amy's, and the rest were lower. If no other grade was the same as Amy's grade, then Amy's grade was what percentile of the grades of the two classes of two classes combined?
(A) 72nd
(B) 80th
(C) 81st
(D) 85th
(E) 92nd
Rationale: Being in 90% percentile out of 80 grades means Amy was 73rd (from the least grade) in the class (as long as nobody had Amy's grades), she outscored 72.
In another class her grade would rank her 82 (from the least grade out of 101, 100+Amy), 81 had the grades lower than Amy.
So in combined classes she outscored 72+81=153. There are 180 students 153/180=0.85
Answer: D (85%)
Answer: (D) 85th
Question: Two persons C & D started traveling from A and B which are 300 km apart, towards B and A respectively at 1.00 p.m. C travels at a constant speed of 30 kmph whereas D doubles his speed every hour. If D reaches A in 4 5/8 hours, at what time did C and D meet each other ?
(A) 4:30 p.m.
(B) 4:40 p.m.
(C) 5:00 p.m.
(D) 5:10 p.m.
(E) 5:20 p.m.
Rationale: Let speed of D in first hour = x
D’s speed = x+ 2x+ 4x+ 8x+ 16x*(5/8) = 25x
Given 25x=300 :. X = 12
At the end of four hours C traveled 120 (30 *4) kmph and D traveled 12 + 24+ 48 +96 = 180kmph
:. They meet each other after 4 hours ie at 5:00 p.m.
ANSWER:C
Answer: (C) 5:00 p.m.
Question: A radio station has to choose one day of the seven in a week to broadcast a certain program, and that set will repeat each week. The program can be broadcast equally on any of the seven weekdays —- weekdays vs. weekends don’t matter at all —- nor does it matter whether the days the program airs are adjacent or not. Absolutely any three of the seven weekdays can be chosen. How many different three-day combinations of the seven weekdays can be constructed?
(A) 7
(B) 15
(C) 21
(D) 35
(E) 56
Rationale: Behind the story, we are really being asked to evaluate 7C1. We could use the factorial formula, but above we conveniently happen to have Pascal’s Triangle written out to the seventh row. We see that 7C1, the third entry of the seventh row, is 7. Answer = A.
Answer: (A) 7
Question: At what rate percent on simple interest will a sum of money double itself in 60 years?
(A) 3 1/3%
(B) 3 1/9%
(C) 1 2/3%
(D) 3 2/3%
(E) 3 6/3%
Rationale: P = (P*60*R)/100
R = 1 2/3%
Answer: C
Answer: (C) 1 2/3%
Question: When positive integer Q is divided by 6 the remainder is 3. Which of the following CANNOT be an even integer?
(A) a. k + 1
(B) b. k -11
(C) c. 4k + 2
(D) d. (k-3)/3 +2
(E) e. Q/3
Rationale: When positive integer Q is divided by 6 the remainder is 3
So, Q could equal 3, 9, 15, 21, etc
let's TEST Q =3
a.3+ 1 = 4 (EVEN)
b.3-11 = -8 (EVEN)
c. 4(3) + 2 = 14 (EVEN)
d. (3-3)/3 +2 = 2 (EVEN)
At this point, we can already see the answer must be E.
Let's check E forfun
e.3/3 = 1 (ODD)
Great!
Answer: E
Answer: (E) e. Q/3
Question: Find the compound ratio of (2:3), (3:4) and (1:4) is
(A) 1:2
(B) 2:3
(C) 1:8
(D) 4:5
(E) 3:2
Rationale: Required ratio = 2/3 * 3/4 * 1/4 = 1/8 = 1:8
Answer is C
Answer: (C) 1:8
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is
(A) 153550 m^2
(B) 153600 m^2
(C) 153700 m^2
(D) 153800 m^2
(E) 153900 m^2
Rationale: Explanation:
Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m^2.
Option B
Answer: (B) 153600 m^2
Question: Let S be the set {1, 2, 3, . . . , n} consisting of the first n positive integers.
What is the maximum value of n for which every 100-element subset of
S contains two integers which differ by 25 ?
(A) 171
(B) 172
(C) 173
(D) 174
(E) 175
Rationale: Let n be as large as possible so that every 100-element subset of S contains two integers
differing by 25. Observe that the set
A = {1, 2, . . . , 25} [ {51, 52, . . . , 75} [ {101, 102, . . . , 125} [ {151, 152, . . . , 175}
has 100 elements no two of which differ by 25. So n 174. We show now that S = {1, 2, . . . , 174}
has the property that every 100-element subset of S contains two integers differing by 25. For
0 j 24, let Tj be the subset of S consisting of the integers from S that have a remainder of j
when we divide by 25. The sets Tj have no common elements. If S0 is a subset of S consisting of
exactly 100 elements, then there are exactly 74 elements of S not in S0. These must lie in the 25
sets Tj . One of the sets Tj contains at most 2 of these 74 elements of S not in S0 (by the pigeon-hole
principle). Fix such a j. Since Tj contains at least 6 elements, the intersection Tj \S0 contains two
consecutive elements of Tj , that is two elements of Tj that differ by 25. Thus, S has the property
that every 100-element subset of S contains two integers differing by 25
correct answer D
Answer: (D) 174
Question: A jar of 144 marbles is divided equally among a group of marble-players today. If 2 people joined the group in the future, each person would receive 1 marble less. How many people are there in the group today?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: 144 = 16*9 = 18*8
There are 16 people in the group today.
The answer is C.
Answer: (C) 16
Question: A set of football matches is to be organized in a “round-robin” fashion, i.e., every participating team plays a match against every other team once and only once. If 21 matches are totally played, how many teams participated?
(A) 6 teams
(B) 7 teams
(C) 5 teams
(D) 4 teams
(E) 2 teams
Rationale: For a match you need 2 teams.suppose there are totally ‘n ‘teams.Now you have to choose 2 teams out of ‘n’ teams.so answer =no of such choices=no. of possible combinations. So we’ve ans = nC2(ncombination2)=21;solve to get n=7.
Sol: n(n-1)/2=21. so n=7.if u don’t understand c the graph below each team plays no. of matches=no of teams ahead of it. One bar ” represents one team. ————7 6 5 4 3 2 1 0 ———–21last team is written as 0 matches because this team has already played with all other teams-hence sum of matches =6+5+4+3+2+1=21 which is correct only if no of teams =7
answer is :7 teams
Answer B
Answer: (B) 7 teams
Question: Marketing executives for a certain chewing gum company projected a 20 percent increase in revenue this year over that of last year, but revenue this year actually decreased by 25%. What percent of the projected revenue was the actual revenue ?
(A) 53%
(B) 58%
(C) 62.5%
(D) 64%
(E) 75%
Rationale: Last year revenue = 100 (assume);
This year revenue = 75;
Projected revenue = 120.
Actual/Projected*100=75/120*100 = 62.5%.
Answer: C
Answer: (C) 62.5%