mathewhe/aqua_rat huggingface dataset:
Question: How many differentsix letter words can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R?
(A) 59
(B) 11!/(2!*2!*2!)
(C) 55
(D) 23
(E) 11!/(3!*2!*2!*2!)
Rationale: E- -R
We are left with the following 11 letters: {M, D, I, T, R, EE, AA, NN} out of which 8 are distinct: {M, D, I, T, R, E, A, N}.
We should consider two cases:
1. If the two middle letters are the same, we'd have 3 words: EEER, EAAR and ENNR.
2. If the two middle letters are distinct, then we are basically choosing 2 letters out of 8 when the order of the selection matters, so it's 8P2 = 56.
Total = 56 + 3 = 59.
Answer: C.
Answer: (C) 55
Question: A factory has a fixed cost of $42,000 a month, and a cost of $2.5 for every item produced. If the selling price of a single item is $5, what is the number of items must be sold monthly for the factory to cover its cost exactly?
(A) 9,000
(B) 14,000
(C) 16,800
(D) 22,500
(E) 27,000
Rationale: selling price - Cost price = 2.5 so per unit profit =2.5
cost to recover =42000
no of items required = 42000/2.5 = 16800
Answer: C
Answer: (C) 16,800
Question: A company conducted a survey about its two brands, A and B. x percent of respondents liked product A, (x – 20) percent liked product B, 23 percent liked both products, and 23 percent liked neither product. What is the minimum number D of people surveyed by the company?
(A) 46
(B) 80
(C) D.90
(D) D.100
(E) 200
Rationale: 100 = x + x - 20 + 23 - 23
x = 60,
So, Product A = 60%, Product B = 40%, Both = 23%, Neither = 23%
23% of the total no. of people should be an integer. So, A,BC are out.
60% of D and 40% of D are both integers. So, D satisfies all conditions.
So, answer is D.
Answer: (D) D.100
Question: The greatest number that divides 180, 565 and 705 leaving remainder 5, 5 and 5 respectively is:
(A) 31
(B) 33
(C) 35
(D) 38
(E) 39
Rationale: explanation:
180-5=175 , 565-5=560 and 705-5= 700
Highest number that divides 175, 560 and 700 is HCF of numbers.
HCF of 175, 560 and 700= 35
Answer:C
Answer: (C) 35
Question: What is the difference between the compound interests on $5000 for 1 years at 4% per annum compounded yearly and half-yearly?
(A) 2.04
(B) 3.06
(C) 4.8
(D) 8.3
(E) 9.3
Rationale: CI = 5000*(1/4/100)*(1+1/2*4/100)
=(5000*26/25*51/50)
=5304
=5306.04
difference = $(5306.04 - 5304) = $2.04
ANSWER A
Answer: (A) 2.04
Question: Two equal glasses are respectively
1 3
and
1 4 full of milk. They are then filled up with water and the contents are mixed in a tumbler. Find the ratio of milk and water in the tumbler
(A) 22
(B) 88
(C) 27
(D) 19
(E) 11
Rationale: Answer:A
Answer: (A) 22
Question: A wooden box of dimensions 8m×7m×6m is to carrry rectangular boxes of dimensions 8cm×7cm×6cm . The maximum number of boxes that can be carried in 1 wooden box is :
(A) 1200000
(B) 1000000
(C) 9800000
(D) 7500000
(E) none
Rationale: Explanation:
Number of boxes = Volume of wooden box in cm3/Volume of 1 small ball = 800×700×600/8×7×6=1000000
Correct Option: B
Answer: (B) 1000000
Question: A, B and C can do a work in 90, 15 and 45 days respectively. If they work together, in how many days will they complete the work?
(A) 10
(B) 66
(C) 77
(D) 88
(E) 11
Rationale: One days's work of A, B and C = 1/90 + 1/15 + 1/45
= (1 + 6 + 2)/90 = 1/10
A, B and C together can do the work in 10 days.
Answer:A
Answer: (A) 10
Question: The divisor is 19, the quotient is 6 and the remainder is 1.
What is the dividend?
(A) 115
(B) 114
(C) 113
(D) 110
(E) 105
Rationale: D = d * Q + R
D = 19 * 6 + 1
D = 114 + 1
D = 115
Answer: A
Answer: (A) 115
Question: A cistern 6 m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the west surface is :
(A) 49 m2
(B) 50 m2
(C) 53.5 m2
(D) 55 m2
(E) None of these
Rationale: Solution
Area of the west surface = [2(lb + bh + lh) - lb] = 2 (bh + lh) + lb
= [2(4 × 1.25 + 6 × 1.25) + 6 × 4]m2 = 49m2.
Answer A
Answer: (A) 49 m2
Question: Difficulty:
There are five sales agents in a certain real estate office. One month Andy sold seven times as many properties as Ellen, Bob sold 3 more than Ellen, Cary sold seven times as many as Bob, and Dora sold as many as Bob and Ellen together. Who sold the most properties that month?
(A) Andy
(B) Bob
(C) Cary
(D) Dora
(E) Ellen
Rationale: a= 7e
b =3 +e
c = 7b = 21+ 7e (highest of all)
d = b + e = 3+ e +e = 3 + 2e
Ans. C
Answer: (C) Cary
Question: If the quantity (p − 5) is 5 times the quantity (q + 5), then what is the relationship between p and q?
(A) p = 5q + 30
(B) p = 5q − 30
(C) 5p = q + 20
(D) p = 5q
(E) p = 5q − 20
Rationale: p-5=5(q+5)
p-5=5q+25
p=5q+30
option A
Answer: (A) p = 5q + 30
Question: A freight elevator can carry a maximum load of 1000 pounds. Sean, who weighs 200 pounds, is in the elevator with two packages weighing 150 pounds and 280 pounds. If he needs to fit three more packages in the elevator that weigh as much as possible without exceeding the elevator limit, what is the difference between their average and the average of the two packages already in the elevator?
(A) 25
(B) 85
(C) 190
(D) 215
(E) 210
Rationale: The average of existing 2 package is150 + 280/2 = 430/2 = 215
Remaining allowed weight = 1000 - 200 - 430 = 1230.
allowed per package = 1230 / 3 = 410
So difference in average of existing and allowable = 410-215 = 195
Hence A
Answer: (A) 25
Question: On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.60 per glass on the first day, what was the price per F glass on the second day?
(A)  $015
(B)  $0.20
(C)  $0.30
(D)  $0.40
(E)  $0.45
Rationale: On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade;
On the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade;
So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3.
We are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day.
Say the price of the glass of the orangeade on the second day was $x then 2*0.6=3*x --> x=$0.4.
Answer: D.
Answer: (D)  $0.40
Question: In 2010, a basketball team won 30 percent of its 20 basketball games. In 2011, the team won 28 percent of its 25 basketball games. What was the percent increase from 2010 to 2011 in the number of basketball games the team won?
(A) 5%
(B) 14 2/7%
(C) 16 2/3%
(D) 23 1/3%
(E) 60%
Rationale: 30% of 20 = 6 and 28% of 25 = 7, so percent increase =7−6/6=16.6
Answer C
Answer: (C) 16 2/3%
Question: Farm Tax is levied on the 25% of the cultivated Land. The tax department collected total $ 3840 through the farm Tax from the village of Mr. william. Mr. william paid only $ 480 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is :
(A) 15%
(B) 25%
(C) 50%
(D) 0.2083%
(E) none
Rationale: This will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village. That leads to (480/3840)x100 =12.5%in percentage terms.
But the question asks ratio between his total land to total cultivated land. Hence the answer is 12.5%x (100/25) = 50%
The correct answer is (C).
Answer: (C) 50%
Question: A watch passes through three hands and each gains 25%. If the 3rd sells it for Rs250, what did the 1st pay for it?
(A) 120
(B) 125
(C) 128
(D) 130
(E) 154
Rationale: First Purchased = 250 Wes= 128
C
Answer: (C) 128
Question: If a1 = 1 and an+1= 2an + 5, n = 1, 2 .. , then a100 is equal to ?
(A) 5*2^99-6
(B) 5*2^99+6
(C) 6*2^99+5
(D) 6*2^99-5
(E) 6*2^99-6
Rationale: a(n+1)= 2a(n) + 5
Even+Odd=Odd
Therefore all the values are Odd. A, B and E out.
a(2)=2+5=7
Now lets take a2 and try solving it with the equations in C and D. Note they are similar and only differ by the sign before 5. So we have to only decide if our equation takes + or - 5.
Now, the equation in C and D looks like this 6*2^99 + (or -) 5.
In other words, a100=6*2^(n-1) + (or -) 5.
Now a2=7=6*2^1 +(or-) 5
7=12+(or-)5
Therefore the sign has to be -
Answer: D
Answer: (D) 6*2^99-5
Question: 550−(104÷20.8)=?
(A) 545
(B) 525
(C) 535
(D) 625
(E) 105
Rationale: Explanation:
=550−(104/208X10)
=550−5=545
Option A
Answer: (A) 545
Question: Jackson has $313,195 dollars in his investment accounts. What is the least amount of money (in whole number of dollars) that he must remove from his account if he wants to split this money evenly among nine new investors?
(A) $1
(B) $2
(C) $3
(D) $4
(E) $5
Rationale: In order to divide the sum in 9 parts, the amount must also be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 313,195 = 22 and 18 is divisible by 9.
Hence we need to subtract 4 to this number for it to be divisible by 9
Correct Option: D
Answer: (D) $4
Question: How many odd four-digit integers greater than 9000 are there such that all their digits are different?
(A) 84
(B) 104
(C) 168
(D) 224
(E) 280
Rationale: Case 1: Numbers starting with 9 followed by an EVEN number
The hundreds digit can take 5 numbers (0,2,4 ,6 , 8) so 5 ways
The unit digit can take 4 numbers (1,3,5,7) to be ODD so 4 ways.
The tens digit can take remaining 7 numbers left after using 3 numbers so 7 ways.
Total = 5*4*7=140
Case 2: Numbers starting with 9 followed by an ODD number
The hundreds digit can take 4 numbers (1,3,5,7) so 4 ways
The unit digit can take remaining 3 ODD numbers left after using 2 ODD numbers so 3 ways.
The tens digit can take remaining 7 numbers left after using 3 numbers so 7 ways.
Total = 4*3*7 = 84
Hence 140+84=224, correct answer is D
Answer: (D) 224
Question: Speed of a boat in standing water is 11kmph and speed of the stream is 2.5kmph. A man can rows to a place at a distance of 105km and comes back to the starting point. The total time taken by him is?
(A) 21.12hours
(B) 20.12hours
(C) 19.12hours
(D) 18.12hours
(E) 17.12hours
Rationale: Speed upstream = 8.5kmph
Speed downstream = 13.5kmph
Total time taken = 105/8.5 + 105/13.5 = 20.12 hours
Answer is B
Answer: (B) 20.12hours
Question: If Jimmy drinks 8 ounces of water each time for 8 times a day. How much gallons of water he would have to prepare ahead to drink for 5 days? (1 ounce = 0.0078125 gallon)
(A) 1
(B) 1.5
(C) 2
(D) 2.5
(E) 3
Rationale: 8 ounces* 8 times/day = 64 ounces of water = 64 * 0.0078125 = 0.5 gallon. 5 days need 0.5 * 5 = 2.5 gallons. Correct Option: 2.5 Answer: D
Answer: (D) 2.5
Question: If q = 45! + 1, which of the following cannot be a prime factor of q?
I. 11
II. 29
III. 41
(A) I​ only
(B) III only
(C) II and III
(D) I and II
(E) I​, II, and III
Rationale: The numbers 11, 29, and 41 are all factors of 45!
Therefore they can not be factors of 45! + 1.
The answer is E.
Answer: (E) I​, II, and III
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green?
(A) 23/35
(B) 23/37
(C) 23/29
(D) 23/30
(E) 23/36
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: 5 cards have to be put into their 5 respective envelopes. If the letters are inserted randomly into the envelopes, what is the probability that all the cards go into their respective envelopes?
(A) 1/30
(B) 1/60
(C) 1/240
(D) 1/120
(E) 3/5
Rationale: A-B-C-D-E (envelopes)
a-b-c-d-e (letters)
5 letters (a, b, c, d, and e) can be assigned to 5 envelopes (arranged) in 5! ways, out of which only one will be correct, thus the probability is 1/5! = 1/120.
Answer: D.
Answer: (D) 1/120
Question: In how many ways can 15 people be seated around two round tables with seating capacities of 7 and 8 people?
(A) 15! /8!
(B) 7! *8!
(C) 15C7 *6! *7!
(D) 2 * 15C7 *6! *7!
(E) 15C8 *8!
Rationale: Solution:
'n' objects can be arranged around a circle in (n−1)! ways.
If arranging these 'n' objects clockwise or counter clockwise means one and the same, then the number arrangements will be half that number.
i.e., number of arrangements =(n−1)! /2.
You can choose the 7 people to sit in the first table in 15C7 ways.
After selecting 7 people for the table that can seat 7 people, they can be seated in:
(7−1)! =6!
The remaining 8 people can be made to sit around the second circular table in: (8−1)! =7! Ways.
Hence, total number of ways: 15C7 *6! *7!.
Answer: Option C
Answer: (C) 15C7 *6! *7!
Question: Solve using synthetic division or long division(x2 + 13x + 40) ÷ (x + 8)
(A) x + 9
(B) x + 0
(C) x + 5
(D) x + 2
(E) x + 1
Rationale: e solved the division in both the ways;
(x2 + 13x + 40) ÷ (x + 8) by using synthetic division
Synthetic Division
Save
Quotient = x + 5
Remainder = 0
Answer: C
Answer: (C) x + 5
Question: A car traveled 420 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 6 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city?
(A) 14
(B) 16
(C) 21
(D) 24
(E) 27
Rationale: Let the speed in highway be h mpg and in city be c mpg.
h = c+6
h miles are covered in 1 gallon
420 miles will be covered in 420/h.
Similarly c miles are covered in 1 gallon
336 miles will be covered in 336/c.
Both should be same (as car's fuel capacity does not change with speed)
=> 336/c = 420/h
=> 336/c = 420/(c+6)
=> 336c+336*6=420c
=>c=336*6/84=24
Answer D.
Answer: (D) 24
Question: The y intercept of a line L is 6. If the slope of L is negative, which of the following could be the x intercept of L.
I. -1
II. 0
III. 6
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III
Rationale: C) III only
The y-intercept is 6. Therefore we have y=mx+6
It is given that the slope is negative. Therefore the line must go from top left to bottom right.
i.e: the x-intercept has to be positive. That itself rules out III.
If you choose to go with the options directly, here's an approach.
y=mx+6. For the x-intercept, y=0.
i.e. mx+6=0.
We know that the slope m is negative. Therefore, if x=-1 or x=0, the equation mx+6 =0 would never be satisfied.
If x=6, we have 6m+6=0. A value of m=-1 would satisfy this equation. 9answer C)
Answer: (C) III only
Question: A football coach must choose 5 freshers from a team of 12players. How many different ways can the coach choose the freshers?
(A) 650
(B) 670
(C) 729
(D) 740
(E) 760
Rationale: Choose 5 starters from a team of 12 players. Order is not important.
\inline {\color{Black} 12C_{5}}= 729
C
Answer: (C) 729
Question: A trader purchased two colour televisions for a total of Rs. 35000. He sold one colour television at 30% profit and the other 40% profit. Find the difference in the cost prices of the two televisions if he made an overall profit of 32%?
(A) 21000
(B) 21007
(C) 21004
(D) 21009
(E) 21001
Rationale: Let the cost prices of the colour television sold at 30% profit and 40% profit be Rs. x and Rs. (35000 - x) respectively.
Total selling price of televisions = x + 30/100 x + (35000 - x) + 40/100 (35000 - x)
=> 130/100 x + 140/100 (35000 - x) = 35000 + 32/100 (35000)
x = 28000
35000 - x = 7000
Difference in the cost prices of televisions = Rs. 21000
Answer:A
Answer: (A) 21000
Question: If s and t are positive integers such that s/t = 56.12, which of the following could be the remainder when s is divided by t ?
(A) 2
(B) 4
(C) 8
(D) 20
(E) 90
Rationale: The remainder is 0.12 or 12/100. You can go one step further and say that X/Y=12/100, where X and Y are whole numbers. Plug in all the answer choices for X and see which one makes Y a whole number.
One thing that jumps out at me is that A, B, C, and D are all even. E on the other hand is odd. Why? Maybe I'll start plugging in here first.
90/Y=12/100
12Y=9000
Y=750
Answer: E.
Answer: (E) 90
Question: Bradley owns b video game cartridges. If Bradley’s total is one-seventh the total owned by Andrew and four times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?
(A) 27b / 4
(B) 29b / 4
(C) 31b / 4
(D) 33b / 4
(E) 35b / 4
Rationale: b = Bradley’s total
7b = Andrew’s total
b/4 = Charlie’s total
The total number of cartridges is:
b + 7b+ b/4 = (4b + 28b + b) / 4 = 33b / 4
The answer is D.
Answer: (D) 33b / 4
Question: Tom purchased 8kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 45 per kg. How much amount did he pay to the shopkeeper?
(A) A)1040
(B) B)1045
(C) C)965
(D) D)1060
(E) E)1075
Rationale: Cost of 8 kg apples= 70 × 8 = 560.
Cost of 9 kg of mangoes = 45 × 9 = 405.
Total cost he has to pay = 560 + 405 = 965.
C)
Answer: (C) C)965
Question: Which one of the following numbers is exactly divisible by 11?
(A) 415618
(B) 415620
(C) 415621
(D) 415623
(E) 415624
Rationale: (4 + 5 + 2) - (1 + 6 + 3) = 1, not divisible by 11.
(2 + 6 + 4) - (4 + 5 + 2) = 1, not divisible by 11.
(4 + 6 + 1) - (2 + 5 + 3) = 1, not divisible by 11.
(4 + 6 + 1) - (2 + 5 + 4) = 0, So, 415624 is divisible by 11.
E)
Answer: (E) 415624
Question: A single letter is selected at random from the word 'PROBABILITY'. The probability that it is a vowel is..??
(A) 2/11
(B) 3/11
(C) 4/11
(D) 0
(E) 1
Rationale: total vowels = 4, total number of letters = 11
so probability = 4/11
ANSWER:C
Answer: (C) 4/11
Question: The average number of shirts with Salman, Ambani and Dalmiya is 60, if all of them reached a shopping mall in Delhi and purchased 4 shirts each of them then average number of shirt each of them now has
(A) 66
(B) 63
(C) 62
(D) 64
(E) 61
Rationale: Required average
= Old average + New average
= 60 + 4 = 64
answer :D
Answer: (D) 64
Question: Ifaequals the sum of the even integers from 2 to 20, inclusive, andbequals the sum of the odd integers from 1 to 19, inclusive, what is the value of a * b ?
(A) 10000
(B) 11000
(C) 19000
(D) 20000
(E) 21000
Rationale: Yes! there is really a faster way to solve it.
Sum of consecutive odd or even integers = (no. of odd or even ints) * (first int + last int) / 2
Here A = sum of even ints from 2 to 20, inclusive
number of even ints = 10,
first int + last int = 2+20 = 22
A = 10*22 / 2 = 110
B = sum of odd ints from 1 to 19, inclusive
number of odd ints = 10,
first int + last int = 1+19 = 20
A = 10*20 / 2 = 100
A*B = 110 * 100 = 11000
Ans : B
Answer: (B) 11000
Question: If two numbers are in the ratio 2:5. If 10 is added to both of the numbers then the ratio becomes 3:7 then find the smallest number?
(A) 40
(B) 80
(C) 60
(D) 20
(E) 100
Rationale: Given ratio - 2:5
2x + 10 : 5x + 10 = 3 : 7
7[2x + 10] = 3[5x + 10]
14x + 70 = 15x + 30
15x - 14x = 70 - 30
x = 40
Then smallest number is = 2
2x = 80
ANS - B
Answer: (B) 80
Question: An Olympic diver received the following scores: 5, 6, 3, 2. The standard deviation of her scores is in which of the following ranges?
(A) 5.01 to 5.99
(B) 3.01 to 3.99
(C) 4.01 to 4.99
(D) 2.01 to 2.99
(E) 1.01 to 1.99
Rationale: 5+6+3+2/4=4
∣5-4∣^2 =1^2 = 1
∣6-4∣^2 =2^2 = 4
∣3-4∣^2 =1^2 = 1
∣2-4∣^2 =2^2 = 4
sqrt 10/4 =1.58
Answer : E
Answer: (E) 1.01 to 1.99
Question: Claire has 3 books. She averages the amount of pages of each book to have 305 pages. If her mom buys her a new book which has 400 pages, what will the new average be?
(A) 342.5
(B) 328.75
(C) 330.87
(D) 342.75
(E) 335
Rationale: (sum of the pages of the 3 books)/3 = 305
sum of the pages of the 3 books = 915
new sum = 915+400 = 1315
new average = 1315/4 = 328.75
ans: B
Answer: (B) 328.75
Question: When the oil from a circular cylinder leaked, the formula for the speed of the leak is V = kh^2, where h was the height of the remaining oil and k was constant. If the height of the cylinder is 4, the speed of the leak is Vâ€™, When the height of the oil remaining is 16, what was the speed of the leak, in terms of Vâ€™?
(A) 2Vâ€™
(B) 4Vâ€™
(C) Vâ€™/2
(D) Vâ€™/4
(E) 16Vâ€™
Rationale: When h=4 v=V'
So V' = k.16
Hence k = V'/16
Now when h=16
v=(V'/16).16^2
v=V'.16
v=16V'
Ans : E
Answer: (E) 16Vâ€™
Question: Visitors to show were charged Rs.15 each on the first day. Rs.7.50 on the second day, Rs.2.50 on the third day and total attendance on the three days were in ratio 2:5:13 respectively. The average charge per person for the whole show is?
(A) 6
(B) 9
(C) 5
(D) 3
(E) 4
Rationale: 2: 5: 13
2x 5x 13x
15 7.5 2.5
30x + 37.5x + 32.5x = 100x/20x
Average = 5
Answer: C
Answer: (C) 5
Question: Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one green marble. Suppose we are going to put them into three cups: a black cup, a white cup, and a purple cup. The only restriction is that the two red marbles can’t be in the same cup. We could put as many as five (all except one of the reds) in any cup. We could leave one cup empty, or put some in each of the three cups. All combinations are allowed that don’t involve the two red marbles in the same cup. How many combinations are possible?
(A) 90
(B) 180
(C) 360
(D) 540
(E) 720
Rationale: 3 Blue Marble:
Different distribution : (1) All 3 in the same cup (2) Split 2-1 in two cups (3) Split 1-1-1
Case (1) 3 possibilities
Case (2) 6 possibilities ,
Case (3) 1 possibility
tot. 10 possibilities.
One Green Marble :
3 possibilities (one for each cup at the time)
First Red marble:
3 possibilities (one for each cup at the time)
Second Red marble:
2 possibilities ( because can't go in the same cup with the other Red marble)
TOTAL:
10*3*3*2 = 180 , answer, B .
Answer: (B) 180
Question: If c is an integer greater than 6, which of the following must be divisible by 3?
(A) c (c+4) (c-2)
(B) c (c+2) (c-1)
(C) c (c+3) (c-5)
(D) c (c+1) (c-4)
(E) c (c+5) (c-6)
Rationale: anything in the form of (c-1) (c) (c+1) is divisible by 3. in other word, a product of any 3 consecutive intevers is divisible by 3.
c (c+1) (c-4) = c (c+1) ((c-1)-3) is equivalant to (c-1) (c) (c+1)
c (c+2) (c-1) is equivalant to (c+1) missing.
c (c+3) (c-5) is equivalant to (c-1) missing and c repeating.
c (c+4) (c-2) is equivalant to odd/even consqcutive integers
c (c+5) (c-6) is equivalant to (c+1) missing and c repeating.
Answer : D
Answer: (D) c (c+1) (c-4)
Question: The Kiljaro Highway is marked with Milestones denoting the distance to the town of Kiljaro. Tommy left kiljaro and drove the highway, passing the 40 km milestone at 8:30. Some time afterwards, Tommy got a phone call asking him to return home, and he made a U-turn at the 160 km milestone. At 09:A0 Tommy passed the milestone marking 70 km to Kiljaro. The variable A represents the tens digit of the minutes in 09:A0. Assuming Tommy maintained the same constant speed during the entire drive, how many kilometers did Tommy travel in one minute?
(A) 210/(30+10A)
(B) 210/(30+60A)
(C) 210/35A
(D) 210/(30+10A)
(E) 220/40A
Rationale: Since we are dealing with the variables in the answer choices,the best possible method according to me would be substitution.
Substitute A with 3.meaning tommy would have travelled a distance of ((160-40) + (160-70)) in 60 minutes.
210 Kms in 60 minutes ==> 3.5km/hr.
Substitute A with 3 in the answer options.
Option A
Answer: (A) 210/(30+10A)
Question: A, B and C started a business A's investment is 2 times of B's investment is 5 times of C's investment. Find the profit of B in the total profit of Rs. 1600.
(A) Rs. 25600
(B) Rs. 8500
(C) Rs. 7200
(D) Rs. 500
(E) None of these
Rationale: Explanation:
A = 2B and B = 5C
=> A : B = 2:1 and B : C = 5 : 1
=> A : B : C = 10 : 5 : 1
Ratio of capitals of A, B and C = 10 : 5 : 1
B's share = Rs.[(5/16) × 1600] = Rs. 500
Answer: Option D
Answer: (D) Rs. 500