mathewhe/aqua_rat huggingface dataset:
Question: David obtained 74, 65, 82, 67 and 90 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
(A) A)87
(B) B)99
(C) C)68
(D) D)82
(E) E)76
Rationale: Average = (74 + 65 + 82 + 67 + 90)/5
= 380/5
= 76.
Answer:E
Answer: (E) E)76
Question: In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 4000, the number of valid votes that the other candidate got, was:
(A) 3500
(B) 1200
(C) 1650
(D) 3700
(E) 1800
Rationale: Number of valid votes = 80% of 4000 = 3200.
Valid votes polled by other candidate = 45% of 4000
=(45/100)X4000 =1800
ANSWER = E
Answer: (E) 1800
Question: The total car population in a Mumbai is 2,94,00 out of which 1,50,00 are made by Honda. Out of every 100 Honda cars, 98 are red in color, but only 53% of the total car population is red. Find the % of non-Honda cars that are red
(A) 5.24%
(B) 5.35%
(C) 6.125%
(D) 7.45%
(E) 8%
Rationale: Total Car.29.10 i.e., Honda +non Honda = 29400 Given: Whim. tractor .150W
Now,5346 of 2..00 = Honda +Red Non-Honda 29400 .:4 =15582 Thus...El Mall... 1.0 Now Honda 15582 flow, Non-. Honda =15582 - 15.582-14700=8B2 96 non-Honda =1=1.100 = 6.125%
C
Answer: (C) 6.125%
Question: Look at this series: V, VIII, __, XIV, XVII, XX, ... What number should fill the blank?
(A) IX
(B) XXIII
(C) XV
(D) XI
(E) None
Rationale: Explanation: This is a simple addition series; each number is 3 more than the previous number.
Answer: D
Answer: (D) XI
Question: A train passes a station platform in 39 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 276 m
(B) 279 m
(C) 240 m
(D) 207 m
(E) 285 m
Rationale: Speed = [54 * 5/18] m/sec
= 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 39 = 15
x + 300 = 585
x =285m.
Answer: E
Answer: (E) 285 m
Question: An intern wants to label folders with numbers using digit stickers only. If the intern uses 999 stickers, how many folders have been numbered? (The numbers of the folders are consecutive and the number of the first folder is 1).
(A) 287
(B) 369
(C) 370
(D) 371
(E) 430
Rationale: For the first 9 folders we need 9 stickers.
For the next 90 we need 2 stickers each or 180 stickers.
For the next 900 folders we need 3 stickers each.
The first 99 folders correspond to 189 stickers.
Subtract 189 from the total number of stickers (999).
This leaves 810 stickers for folders that use 3 stickers each. So, divide 810 by 3 to get 270 folders.
Add 99 folders to 270 folders to get the total number of folders, 369.
Answer: B
Answer: (B) 369
Question: A train 440 meters long is running with a speed of 65 kmph. The time taken by it to cross a tunnel 180 meters long is?
(A) 40.338 sec
(B) 41.338 sec
(C) 42.338 sec
(D) 40 sec
(E) 34.338 sec
Rationale: D = 440 + 180 =620
S = 65 * 5/18 = 18.05556 mps
T = 620/18.05556 =34.33846
E
Answer: (E) 34.338 sec
Question: If x is an integer, then x(x - 1)(x - y) must be evenly divisible by three when y is any of the following values EXCEPT
(A) -4
(B) -2
(C) -1
(D) 2
(E) 5
Rationale: here's another approach
x(x - 1)(x - y)
all three are consecutive, so the product MUST be a multiple of 3
we don't know the value of y just yet ... so let's extend the series ... the extension itself reveals the answers
..(x-5)..(x-2)(x-1)x(x+1)..(x+4)..
we can see the possible values of y too from the series
y = 2 OR 2+3n [25]
y = -1 OR -1+3n [-1-4]
B i.e. -2 does not fit in any value of y
so B it is
Answer: (B) -2
Question: A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 2,000 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?
(A) 1.25%
(B) 3.75%
(C) 6.25%
(D) 6.67%
(E) 11.7%
Rationale: The amount of sodium chloride is 0.05*10,000 = 500 gallons
500/8000 = 1/16 = 6.25%
The answer is C.
Answer: (C) 6.25%
Question: If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players?
(A) 1342
(B) 1543
(C) 1578
(D) 1654
(E) 1365
Rationale: A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players.
=. Required number of ways = 14C10 = 14C4
= 14!/4!x19! = 1365
E
Answer: (E) 1365
Question: Solution X is 10 percent alcohol by volume, and solution Y is 30 percent alcohol by volume. How many milliliters of solution Y must be added to 200 milliliters of solution X to create a solution that is 25 percent alcohol by volume?
(A) 250/3
(B) 500/3
(C) 400
(D) 480
(E) 600
Rationale: we know that X is 10% , Y is 30% and W.Avg = 25% . what does this mean with respect to W.Avg technique ?
W.Avg is 1 portion away from Y and 3 portion away from X so for every 1 portion of X we will have to add 3 portions of Y.
If X = 200 then Y = 600
ANSWER:E
Answer: (E) 600
Question: 6) A marketing firm determined that , of 300 households surveyed, 80 used neither Brand A nor Brand B soap.60 used only Brand A soap and for every household that used both brands of soap, 3 used only brand B soap.how many of the 200 household surveyed used both brands of soap?
(A) a) 15
(B) b) 20
(C) c) 30
(D) d) 40
(E) e) 45
Rationale: 220 = At least one of Soap A or B
Both brands = x
Brand B = 3x
=> 60 + x + 3x = 220
=> 4x = 160
=> x = 40
Answer - D
Answer: (D) d) 40
Question: There are 6 red shoes, 4 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe
(A) 1/9
(B) 2/9
(C) 3/5
(D) 4/9
(E) 2/3
Rationale: total 10 from take one.
10c1=10
red 6 from one
6c1=6
6/10= 3/5
ANSWER:C
Answer: (C) 3/5
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is?
(A) 76
(B) 28
(C) 27
(D) 80
(E) 25
Rationale: 1/2 * d (10 + 6) = 640
d = 80
Answer: D
Answer: (D) 80
Question: If the a radio is sold for Rs 490 and sold for Rs 465.50.find loss%.
(A) 4%
(B) 5%
(C) 6%
(D) 3%
(E) 5.5%
Rationale: sol. cp=rs490,sp= 465.50.
loss=rs(490-465.50)=rs 24.50.
loss%=[(24.50/490)*100]%=5%
Answer is B.
Answer: (B) 5%
Question: Find the value of 72519 x 9999 = m?
(A) 455465473
(B) 654676854
(C) 667676753
(D) 725117481
(E) 764534522
Rationale: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Answer: (D) 725117481
Question: A cube with its sides numbered 1 through 6 is rolled twice, first landing on a and then landing on b. If any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6, what is the probability Q that a + b is prime?
(A)  0
(B)  1/12
(C)  5/12
(D)  7/18
(E)  4/9
Rationale: Total # of outcomes is 6*6=36;
Favorable outcomes:
a-b --> prime
1-1 --> 2;
1-2 --> 3;
2-1 --> 3;
1-4 --> 5;
4-1 --> 5;
2-3 --> 5;
3-2 --> 5;
1-6 --> 7;
6-1 --> 7;
2-5 --> 7;
5-2 --> 7;
3-4 --> 7;
4-3 --> 7;
6-5 --> 11;
5-6 --> 11.
Total of 15 favorable outcomes
Q=15/36.
Answer: C.
Answer: (C)  5/12
Question: A car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 180 kilometers?
(A) 3.5 gallons
(B) 2.7 gallons
(C) 5.7 gallons
(D) 4.5 gallons
(E) 7.5 gallons
Rationale: Each 40 kilometers, 1 gallon is needed. We need to know how many 40 kilometers are there in 180 kilometers?
180 ÷ 40 = 4.5 × 1 gallon = 4.5 gallons
correct answer is D) 4.5 gallons
Answer: (D) 4.5 gallons
Question: The number of boys in a class is (7/2) times the number of girls. Which one of the following numbers cannot represent the total number of children in the class ?
(A) A)48
(B) B)54
(C) C)42
(D) D)40
(E) E)38
Rationale: Explanation:
Let number of girls = x and number of boys = 3.5x.
Then, 3.5x + x = 4.5x = total number of students.
Thus, to find exact value of x, the total number of students must be divisible by 4.5
Answer: B
Answer: (B) B)54
Question: What is the rate percent when the simple interest on Rs.1500 amount to Rs.250 in 5 Years?
(A) 3.33%
(B) 6%
(C) 2%
(D) 95%
(E) 1%
Rationale: Interest for 5yrs = 250
Interest for 1yr = 50
Interest rate = 50/1500 x 100 = 3.33%
Answer : A
Answer: (A) 3.33%
Question: If 40% of a number is 16, then the number is
(A) number is 60
(B) number is 70
(C) number is 90
(D) number is 40
(E) None of these
Rationale: Solution:
Let "a" be the number we seek. We get
40% × a = 16
2 × 40% × a = 2 × 16 = 32
80% × a = 32
10% × a = 32 : 8 = 4
100% × a = 4 × 10 = 40
a = 40
Answer D
Answer: (D) number is 40
Question: In how many ways can the letters of the word CAVES be arranged in a row so that the vowels appear in alphabetic order?
(A) 60
(B) 30
(C) 120
(D) 240
(E) 180
Rationale: Two letters can be arranged in 2! ways.
only one combination EIU is required.
5 letters can be arranged in 5! ways.
thus 5!/ 2! * 1 = 60.
A
Answer: (A) 60
Question: According to the directions on a packet of smoothie mix, 1 3-ounce packet of smoothie mix is to be combined with 15 ounces of water to make a smoothie. How many 3-ounce packets of smoothie mix are required to prepare 150 12-ounce smoothies?
(A)  120
(B)  150
(C)  180
(D)  240
(E)  600
Rationale: This question wasn't particularly grueling, but I think it's the first where I had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the GMAT. It actually came to me by accident. Basically, if we thought that the 3 packets of powder were included in the 12 ounces of water, that would mean we would need 150 packets of smoothie mix (along with 12(150) ounces of water for a total of 150 packets. However, we know, after a more careful reading of the stimulus, that the 3 ounces are NOT included in the 12 ounces. As such, the answer has to be LESS than 150 packets, since 150 would be too much powder considering you already have 150(12) ounces of water and need less packets than water to make a smoothie. As such, the only answer less than 150 is 120, A. Does this make sense? Or am I way off base?
C
Answer: (C)  180
Question: A palindrome is a number that reads the same forward and backward, such as 616. How many even, 4-digit numbers are palindromes?
(A) 40
(B) 45
(C) 50
(D) 90
(E) 2500
Rationale: First recognize you only need to consider the first two digits (because the second two are just the first two flipped)
There are 90 possibilities for the first two digits of a 4 digit number, 10-99 inclusive. Everything starting with a 2,4,6,8 will be odd, which is 4/9ths of the combinations.
4/9*90 = 40
ANSWER:A
Answer: (A) 40
Question: David was born 8 years after his father's marriage. His mother is 4 years younger than his father but 30 years older than David who is 8 years old. At what age did the father get married ?
(A) 24 years
(B) 26 years
(C) 23 years
(D) 20 years
(E) 18 years
Rationale: Explanation:
David's present age = 8 years.
His mother's present age = (30 + 8) years = 38 years.
His father's present age = (38 + 4) years = 42 years.
His father's age at the time of David's birth = (42 - 8) years = 34 years.
Therefore David's father's age at the time of marriage = (34 - 8) years = 26 years.
Answer: B
Answer: (B) 26 years
Question: I sold a book at a profit of 10%. Had I sold it for $150 more, 15% would have been gained. Find the cost price?
(A) $2000
(B) $2500
(C) $3000
(D) $3120
(E) $1540
Rationale: 115% of cost - 110% of cost = $150
5% of cost = $150
cost = 150*100/5 = $3000
Answer is C
Answer: (C) $3000
Question: A marble shop contains 6 blue marbles, 6 red marbles, and 6 green marbles. If 4 marbles are purchased at random from the shop, what is the probability that the 4 marbles will be the same color?
(A) 1/68
(B) 60/68
(C) 13/68
(D) 13/48
(E) 1/48
Rationale: It doesn't matter which type of card you choose, so:
Probability of choosing 1st card: 1
Probability of choosing 2nd card of the same type: 5/17
Probability of choosing 3rd card of the same type: 4/16
Probability of choosing 4th marble of the same type: 3/15
Multiply and you get 1/68
Answer A.
Answer: (A) 1/68
Question: Faiza has 8 purses, she gives 3 purse as gift. Now how many purse she have in that?
(A) 2
(B) 5
(C) 11
(D) 9
(E) 4
Rationale: 8-3=5. Answer is B
Answer: (B) 5
Question: In a certain diving competition, 5 judges score each dive on a scale from 1 to 10. The point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty. If a dive with a degree of difficulty of 3.2 received scores of 7.5, 7.8, 9.0, 6.0, and 8.5, what was the point value of the dive?
(A) 68.8
(B) 73.6
(C) 75.2
(D) 76.16
(E) 81.6
Rationale: Degree of difficulty of dive = 3.2
Scores are 6.0 , 7.5 , 8.0 , 8.5 and 9.0
We can drop 6.0 and 9.0
Sum of the remaining scores = (7.5+7.8+8.5)= 23.8
Point of value of the dive = 23.8*3.2 =76.16
Answer D
Answer: (D) 76.16
Question: A team of eight entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score?
(A) 23/35
(B) 23/32
(C) 23/329
(D) 23/29
(E) 23/291
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green
= (⁶C₁ * ⁹C₁)/¹⁵C₂ + ⁶C₂/¹⁵C₂
= (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7
= 46/70 = 23/35
Answer: A
Answer: (A) 23/35
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.5 sec
(B) 1.3 sec
(C) 7.6 sec
(D) 10 sec
(E) 3.6 sec
Rationale: Answer: Option A
Speed = 144 * 5/18 = 40 m/sec
Time taken = 100/40 = 2.5 sec.
Answer: (A) 2.5 sec
Question: Convert 250 inches into centimeter?
(A) 635cm
(B) 620cm
(C) 650cm
(D) 610cm
(E) 654cm
Rationale: 1 inch = 2.54cm
250 inches = 250*2.54 = 635cm
Answer is A
Answer: (A) 635cm
Question: Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $9 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 25 percent, what is the discount rate on Pony jeans?
(A) 9%
(B) 10%
(C) 11%
(D) 12%
(E) 25%
Rationale: x discount on Pony jeans, (0.25-x) discount on Fox jeans.
Set the equation: 3*15(0.25-x)+2*18x=9 --> x=0.25=25%
Answer: E.
Answer: (E) 25%
Question: If 12 people contributed a total of $20.00 toward a gift and each of them contributed at least $1.00, then the maximum possible amount any one person could have contributed is
(A)  $1.00
(B)  $1.25
(C)  $5.00
(D)  $9.00
(E)  $20.00
Rationale: D for me
11 people with 1$ each -> maximum = 9
Answer: (D)  $9.00
Question: The ratio of sodium chloride to ammonium in 100 kg of mixed ammonium normally used by three chemists is 7: 25. The amount of sodium chloride to be added to 100 kg of mixed ammonium to make the ratio 9 :25 is
(A) 5 kg
(B) 6.625 kg
(C) 6.25 kg
(D) 6.35 kg
(E) 6.55 kg
Rationale: sodium chloride in 100 kg = 7/32 x 100 = 21.875 kg
ammonium in 100 kg = 25/32 x 100 = 78.125 kg
Now 78.125 is 25 parts out of (25 + 9) = 34 parts.
Hence 9 parts = 9/25 x 78.125 = 28.125
Amount to be added = 28.125 - 21.87 5= 6.25 Kg
ANSWER:C
Answer: (C) 6.25 kg
Question: A merchant gets a 5% discount on each meter of fabric he buys after the first 2,000 meters and a 7% discount on every meter after the next 1,500 meters. The price, before discount, of one meter of fabric is $2, what is the total amount of money the merchant spends on 4,500 meters of fabric?
(A) $8,617
(B) $8,710
(C) $8,810
(D) $8,835
(E) $8,915
Rationale: for first 2000 metres he does not get any discount
amount = 2*2000 = $4000
for next 1500 metres he gets 5% discount
amount = 2*1500 - (1/20)*3000 = $2850
for the nest 1000 metres he gets 7% discount
amount = 2*1000 - 7*20 = $1860
total amount = $4000 + $2850 + $1860 = $8710
ANSWER:B
Answer: (B) $8,710
Question: A cycle is bought for Rs.900 and sold for Rs.990, find the gain percent?
(A) 39%
(B) 20%
(C) 23%
(D) 74%
(E) 10%
Rationale: 900 ---- 90
100 ---- ? =>
10%
Answer:E
Answer: (E) 10%
Question: There are equal numbers of male and female horses in a ranch.The number of brown horses is 30% more than the number of female brown horses.What percentage of female horses are brown if the total number of male horse is ten times more than the number of brown male horses.
(A) 30
(B) 33.3
(C) 55.1
(D) 32.1
(E) 20
Rationale: Since we are dealing in percentage let us pick 100 as the number of brown female horses.
That means that the total number of brown horses is= 130 (30% more),
therefore the number of brown male horses is 30.
The total number of male horses is 10x the number of brown male= 30*10=300 male horses.
female horses are 50% of the horses, and because there are 300 male horses, then there must also be 300 female horses.
Therefore percentage of female horses that are brown= 100/300*100=33.3
Correct option is B
Answer: (B) 33.3
Question: Which one of the following is a composite number?
(A) 31
(B) 61
(C) 85
(D) 73
(E) 2
Rationale: 85 is divisible by 5,17. So, it is a composite number.
C
Answer: (C) 85
Question: Suppose that f(x) is a function such that for every real number x,i)f(x)+f(1-x) = 12 and (ii) f(1+x) = 3+f(x). Then f(x)+f(-x)
must equal
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: Since (ii) holds for every real number x, it will remain valid if we replace x with
-x. Therefore, f(1-x) = 3+f(-x). Now, from (i), 12 = f(x)+f(1-x) = f(x)+3+f(-x)
so that f(x) + f(-x) = 12-3 = 9. (Observe that f(x) = 3x + 4 satisfies the conditions
in the problem.)
correct answer B
Answer: (B) 9
Question: A and B can do a work in 15days, B and C in 30days, C and A in 45days. If A,B and C work together , they will complete the work in?
(A) 10days
(B) 16days
(C) 20days
(D) 25days
(E) 22days
Rationale: A+B 1day work = 1/15
B+C 1day work = 1/30
C+A 1day work = 1/45
Adding we get 2(A+B+C) = 1/15 + 1/30 + 1/45 = 11/90
A+B+C 1 day work = 11/180
A,B,C can finish the work in 180/11 days = 16days approximately
Answer is B
Answer: (B) 16days
Question: In 1996, the property tax of a community is increased by 6% over the 1995 tax.
An additional surcharge of $200 is also added for a special project.
If the Petersons' 1996 tax totals $2108, find their property tax for the year 1995
(A) 1600
(B) 1800
(C) 1900
(D) 2000
(E) 2500
Rationale: Tax for the year 1996= 2108
Surcharge add : 200
ie 2000-200= 1800
1800*6%=108+2000=2108
so the answer is B
Answer: (B) 1800
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
(A) 13 km/hr
(B) 50 km/hr
(C) 17 km/hr
(D) 18 km/hr
(E) 12 km/hr
Rationale: Speed of the train relative to man = (125/10) m/sec
= (25/2) m/sec. [(25/2) * (18/5)] km/hr
= 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed
= (x - 5) km/hr. x - 5 = 45 ==> x
= 50 km/hr.
Answer:B
Answer: (B) 50 km/hr
Question: If the cost price of 40 articles is equal to the selling price of 25 articles, what is the % profit or loss made by the merchant?
(A) 25% loss
(B) 25% profit
(C) 20% loss
(D) 60% profit
(E) 75% profit
Rationale: Let the cost price of 1 article be $1.
Therefore, cost price of 40 articles = 40 * 1 = $40
The selling price of 25 articles = cost price of 40 articles = $40.
Now, we know the selling price of 25 articles. Let us find the cost price of 25 articles.
Cost price of 25 articles = 25 * 1 = $25.
Therefore, profit made on sale of 25 articles = Selling price of 25 articles - cost price of 25 articles
= 40 - 25 = $15.
As the profit is in the positive, the merchant has made a profit of $15.
Therefore, % loss = loss/cp * 100
% loss = 15/25 * 100 = 60%profit.
D
Answer: (D) 60% profit
Question: 27 is a perfect cube. When x is added to the prime factor of 27, the result is a prime number. What is x?
(A) 1
(B) 3
(C) 5
(D) 8
(E) 11
Rationale: 27 is 3*3*3
then
A 3+1 = 4
B 3+3 = 6
C 3+5 = 8
D 3+8 = 11
E 3+11= 14
here D is the only addition that gives a prime number.
Answer: (D) 8
Question: If 12 men do a work in 80 days, in how many days will 20 men do it?
(A) 18 days
(B) 38 days
(C) 42 days
(D) 48 days
(E) 44 days
Rationale: 12 * 80 = 20 * x
x = 48 days
ANSWER:D
Answer: (D) 48 days
Question: A life insurance company insured 25,000 young boys, 14,000 young girls and 16,000 young adults. The probability of death within 10 years of a young boy, young girl and a young adult are 0.02, 0.03 and 0.15 respectively. One insured person dies. What is the probability that the dead person is a young boy?
(A) 36/165
(B) 25/166
(C) 26/165
(D) 32/165
(E) 33/165
Rationale: The number of young boys that will die = 0.02 x 25,000 = 500
The number of young girls that will die = 0.03 x 14,000 = 420
The number of young adults that will die = 0.15 x 16,000 = 2400
The required probability = The number of young boys who will die / The total number of people who will die.
= 500 / (500 + 420 + 2400) = 25/166
ANSWER:B
Answer: (B) 25/166
Question: Integer x is equal to the product of all even numbers from 2 to 60, inclusive. If y is the smallest prime number that is also a factor of x-1, then which of the following expressions must be true?
(A) 0<y<4
(B) 4<y<10
(C) 10<y<20
(D) 20<y<30
(E) y>30
Rationale: x = the product of all even numbers from 2 to n, where n is any even integer value from 2 to 60 including.
If x = 2, x - 1 = 2! -1
If x = 2x4, x - 1 = 2! (2^2) - 1
If x = 2x4x6, x - 1 = 3! (2^3) - 1
If x = 2x4x6x8, x - 1 = 4! (2^4) - 1
.
.
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If x = 2x4x6x.......x60, x - 1 = 30! (2^30) - 1
Lets find y, a smallest prime factor of (x-1):
If y were 2, [(30!) (2^30) -(1)] would be divisible by 2 however thats not the case.
If y were 3, [(30!) (2^30) -(1)] would be divisible by 3 however thats not the case.
If y were 5, [(30!) (2^30) -(1)] would be divisible by 5 however thats not the case.
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If y were 29, [(30!) (2^30) -(1)] would be divisible by 29 however thats not the case.
If none of the primes under 31 is a factor of (x-1), (x-1) must have a prime factore above 30.
ANSWER:E
Answer: (E) y>30
Question: If a function f is defined by f(x)= -1/x for all non zero numbers x. If f(a) = -1/2 and f(ab) = 1/8 then b= ?
(A) -1/4
(B) 1/4
(C) 4
(D) -4
(E) 12
Rationale: f(a) = -1/2 = -1/a, and thus a = 2
f(ab) = 1/8, and thus ab = -8
2b = -8
b = -4
The answer is D.
Answer: (D) -4
Question: The equal amounts of money are deposited in two banks each at 15% per annum for 3.5 years and 5 years respectively. If the difference between their interests is Rs.144, find the each sum?
(A) Rs.648
(B) Rs.640
(C) Rs.629
(D) Rs.620
(E) Rs.622
Rationale: (P*5*15)/100 - (P*3.5*15)/100 = 144
75P/100 – 52.5P/100 = 144
22.5P = 144 * 100
=> P = Rs.640
Answer: B
Answer: (B) Rs.640
Question: What is the place value of 9 in the numeral 2934?
(A) 600
(B) 900
(C) 700
(D) 760
(E) 768
Rationale: Option 'B'
9 * 100 = 900
Answer: (B) 900
Question: A certain football team played seven games and scored an average of 5 goals per game. If, in the team’s first five games, it scored 5, 4, 2, 5, and 4 goals, what was the average (arithmetic mean) number of goals scored over the last two games?
(A) 5
(B) 1
(C) 2
(D) 7.5
(E) Cannot be determined from the information given.
Rationale: Avg goals for total of 7 games = 5
So A+B+C+D+E+F+G/7=5
and A+B+C+D+E+F+G = 35
Given A+B+C+D+E = 20
So F+G = 15
So average (arithmetic mean) number of goals scored over the last two games is 15/2 = 7.5
Correct answer is D) 7.5
Answer: (D) 7.5
Question: The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?
(A) 18 9/11%
(B) 18 2/11%
(C) 18 2/81%
(D) 19 2/11%
(E) 38 2/11%
Rationale: 13 CP = 11 SP
11 --- 2 CP
100 --- ? =>18 2/11%
Answer: B
Answer: (B) 18 2/11%