mathewhe/aqua_rat huggingface dataset:
Question: A train travels from station A to station B. If it travels at a speed of 100 miles per hour, it ends up reaching the station 30 minutes late. If it travels at 120 miles per hour, it reaches the station 30 minutes early. What is the amount of time that the train is scheduled to take for the journey and what is the distance between the stations?
(A) 	2 hours, 225 miles
(B) 	5.5 hours, 600 miles
(C) 	4 hours, 450 miles
(D) 	5 hours, 550 miles
(E) 	6 hours, 650 miles
Rationale: Let t be the usual time and x be the distance between AB. So we need to find t and Distance x. The question gives us 2 combinations of speedtime, but the distance remains the same for both condition.
Equation 1 - x= 100 (t+.5) (converted 30 mins into hr) added .5 hrs because it is late or took more time than usual.
Equation 2 - x= 120 (t-.5) subtracted .25 hrs because it is early or took less time than usual.
Now equating 12 we get 100(t+.5)=120(t-.5)
=> 10t +5 = 12t - 6
=> 2t=11 => t= 5.5 hrs.
Hence x= 100(5.5+.5) =>100 X 6 => 600 miles.
Hence correct answer B
Answer: (B) 	5.5 hours, 600 miles
Question: Sandy can do a job in 12 days and Molly can do the same job in 24 days. If they work together, in how many days will they complete the job?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Sandy can do 1/12 of the job each day.
Molly can do 1/24 of the job each day.
The combined rate is 1/12 + 1/24 = 1/8 of the job each day.
The job will take 8 days.
The answer is C.
Answer: (C) 8
Question: How many positive integers R less than 20 are either a multiple of 2, an odd multiple of 9, or the sum of a positive multiple of 2 and a positive multiple of 9 ?
(A) 19
(B) 18
(C) 17
(D) 16
(E) 15
Rationale: We're asked to deal with the positive integers LESS than 20. There are only 19 numbers in that group (1 to 19, inclusive). We're asked to find all of the numbers that fit one (or more) of the given descriptions. Looking at the answer choices, we have every value form 15 to 19, inclusive, so most (if not all) of the numbers from 1 to 19 fit one (or more) of the descriptions. How long would it take you to find the ones that DON'T fit.....?
The first several should be pretty easy to find - the prompt wants us to focus on multiples of 2 and 9 (and sums of those multiples). So what ODD numbers are less than 9?
1, 3, 5, 7
None of these values fit the given descriptions. That's 4 out of 19 that we know for sure do NOT fit. 19 - 4 = 15 = E
Answer: (E) 15
Question: Mark bought a set of 6 flower pots of different sizes at a total cost of $7.80. Each pot cost 0.25 more than the next one below it in size. What was the cost, in dollars, of the largest pot?
(A) $1.75
(B) $1.93
(C) $2.00
(D) $2.15
(E) $2.30
Rationale: This question can be solved with a handful of different Algebra approaches (as has been shown in the various posts). Since the question asks for the price of the largest pot, and the answers are prices, we can TEST THE ANSWERS.
We're told that there are 6 pots and that each pot costs 25 cents MORE than the next. The total price of the pots is $8.25. We're asked for the price of the largest (most expensive) pot.
Since the total price is $7.80(a 25-cent increment) and the the difference in sequential prices of the pots is 25 cents, the largest pot PROBABLY has a price that is a 25-cent increment. From the answer choices, I would then TEST Answer C first (since answers B and D are NOT in 25-cent increments).
IF....
The largest pot = $1.75
The other 5 pots are....
1.75
1.50
1.25
1.00
0.75
Total = $7.80
So this MUST be the answer.
B
Answer: (B) $1.93
Question: A box contains 11 apples, 10 of which are red. An apple is drawn from the box and its color is noted before it is eaten. This is done a total of n times, and the probability that a red apple is drawn each time is less than 0.5. What is the smallest possible value of n?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: P(choosing a red apple 6 times in a row) = 10/11*9/10*8/9*7/8*6/7*5/6 = 5/11 < 0.5
The answer is D.
Answer: (D) 6
Question: 1 ltr of water is added with 3 ltr of a solution containing 33%of alcohol in the water. The %of alcohol in the new mixture is?
(A) 22%
(B) 23%
(C) 24.5%
(D) 24.75%
(E) 30%
Rationale: We have a 3 litre solution containing 33% of alcohol in the water.
=> Quantity of alcohol in the solution
=3Ã—33/ 100
Now 1 litre of water is added to the solution.
=> Total quantity of the new solution = 3 + 1 = 4
Percentage of alcohol in the new solution
=3Ã—33/100
4
Ã—
100
=3Ã—331004Ã—100
=3Ã—8.25/100
=24.75%
D
Answer: (D) 24.75%
Question: Find out the ratio of milk to that of water ,if a mixture is formed after mixing milk and water of 3 different vessels containning the mixture of milk to that of water in the proportion 3:2, 7:3, 9:2 respectively.
(A) 233:97
(B) 235:98
(C) 236:97
(D) 265:98
(E) 234:97
Rationale: 3+2=5,7+3=10,9+2=11
now,
3/5+7/10+9/11 : 2/5+3/10+2/11
=>233/110 : 97/110
=> 233 : 97
ANSWER:A
Answer: (A) 233:97
Question: Which of the following is a parallelogram?
(A) 110,70,110,70(angle in deg)
(B) 120,30,130,20(angle in deg)
(C) 90,90,95,95(angle in deg)
(D) a & c
(E) none
Rationale: sum of adjacent angles is 180 degrees.
ANSWER:A
Answer: (A) 110,70,110,70(angle in deg)
Question: If n divided by 7 has a remainder of 2, what is the remainder when 4 times n is divided by 7?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 8
Rationale: As per question => N=7P+2 for some integer p
hence 4N => 28Q + 8 => remainder => 6 for some integer Q
Alternatively => N=2 > 3N=> 8 => 8 divided by 7 will leave a remainder 1
hence A
Answer: (A) 1
Question: A certain car dealership sells economy cars, luxury cars, and sport utility vehicles. The ratio of economy to luxury cars is 3:2. The ratio of economy cars to sport utility vehicles is 4:1. What is the ratio of luxury cars to sport utility vehicles?
(A) 9:8
(B) 8:3
(C) 3:2
(D) 2:3
(E) 1:2
Rationale: The ratio of economy to luxury cars is 3:2 --> E:L = 3:2 = 12:8.
The ratio of economy cars to sport utility vehicles is 4:1 --> E:S = 4:1 = 12:3.
Thus, L:S = 8:3.
Answer: B.
Answer: (B) 8:3
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 38, the dividend is:
(A) 3648
(B) 3642
(C) 3636
(D) 3644
(E) 3864
Rationale: Divisor = (5 * 38) = 190
= 10 * Quotient = Divisor
=> Quotient = 190/10 = 19
Dividend = (Divisor * Quotient) + Remainder
Dividend = (190 * 19) + 38 = 3648.
A
Answer: (A) 3648
Question: What is the simplified result of following the steps below in order?
(1)	add 5y to 2q
(2)	multiply the sum by 3
(3)	subtract q + y from the product
(A) 5q + 14y
(B) 5x + 16y
(C) 5x + 5y
(D) 6x + 4y
(E) 3x + 12y
Rationale: 3(5Y+2Q) -Q-Y= 14Y+5Q
'A' is the answer
Answer: (A) 5q + 14y
Question: In how many ways can 5 apples (identical) be distributed among 3 children? (Some children may get no apples.)
(A) 14
(B) 18
(C) 21
(D) 24
(E) 27
Rationale: Generalised form for n = number of identical objects, and r = number of children is n+r-1Cr-1.
n=5 r= 3
7C2 =21
Answer : C
Answer: (C) 21
Question: Find the average of all prime numbers between 30 and 50?
(A) 18.9
(B) 19.8
(C) 39.8
(D) 29.8
(E) 20.8
Rationale: there are five prime numbers between 30 and 50.
They are 31,37,41,43 and 47.
Therefore the required average=(31+37+41+43+47)/5 199/5  39.8
ANSWER C 39.8
Answer: (C) 39.8
Question: Which of the following is the product of two integers whose sum is 18?
(A)  -42
(B)  -28
(C)  12
(D)  26
(E)  32
Rationale: I solved this Question like this,
Let the two integers are x,y
x+y=18 (Given)
xy=? (Needed)
instead of solving this algebraically, Test the Answer choices
E. 32
Do the factorization : (1,32)----> There sum is not 18--eliminate
(2,16)---->There sum is 18 Bingo!!!!
So, my answer is E...
As the answer is in E, it took me very less time to answer the question. but i think this method is be simple and efficient.
Answer: (E)  32
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
(A) 33
(B) 277
(C) 40
(D) 88
(E) 11
Rationale: The total CP = Rs. 16000 + Rs. 6250 = Rs. 22250 and SP = Rs. 31150
Profit(%) = (31150 - 22250)/22250 * 100 = 40%
Answer: C
Answer: (C) 40
Question: Shipment --- No. of Defective Chips/shipment --- Total Chips in shipment
S1 ---------------------- 3 ------------------------------------------ 8,000
S2 ---------------------- 5 ------------------- ---------------------- 12,000
S3 ---------------------- 6 ------------------------------------------ 18,000
S4 ---------------------- 4 ------------------------------------------ 16,000
A computer chip manufacturer expects the ratio of the number of defective chips to the total number of chips in all future shipments to equal the corresponding ratio for shipments S1, S2, S3, and S4 combined, as shown in the table above. What’s the expected number of defective chips in a shipment of 60,000 chips?
(A) 14
(B) 22
(C) 20
(D) 24
(E) 25
Rationale: for a total of 51000 chips (adding S1,S2,S3,S4) total number of defective chips is 17 ((adding defective chips of S1,S2,S3,S4) so ratio is 18/54000 or 1 every 3000 chips.
Keeping this ratio constant for 60000 chips number of defective chips will be (1/3000) * 60000 = 20
C
Answer: (C) 20
Question: I. All the offices on the 9th floor have wall-to-wall carpeting.
II. No wall-to-wall carpeting is pink.
III.None of the offices on the 9th floor has pink wall-to-wall carpeting.
If the first two statements are true, the third statement is
(A) true
(B) false
(C) uncertain
(D) none
(E) 223
Rationale: Explanation:
If no wall-to-wall carpeting is pink and all the offices have wall-to-wall carpeting, none of the offices has pink wall-to-wall carpeting.
Answer: A) true
Answer: (A) true
Question: If d and y are positive integer and d/y is an even integer, which of the following can be an odd integer?
(A) x
(B) xy
(C) x−y
(D) x+2y
(E) d/3
Rationale: C d-Y
Let says d =12 Y=3 iT BECOMES d-Y =9 This is odd True
d = 12 Y = 6 THEN d-Y = 2, Which is even hence this is False.
so both Yes and NO situations are exists for this Option. C can't be the correct answer same logic goes for E. I believe this question is incomplete b'coz of Irrelevant Options.
Answer: (E) d/3
Question: The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is?
(A) Rs.4007
(B) Rs.4000
(C) Rs.4028
(D) Rs.4050
(E) Rs.4032
Rationale: Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (5050 * 2) = 10100 --- (i)
Q + R = (6250 * 2) = 12500 --- (ii)
P + R = (5200 * 2) = 10400 --- (iii)
Adding (i), (ii) and (iii), we get:
2(P + Q + R) = 33000 = P + Q + R = 16500 --- (iv)
Subtracting (ii) from (iv), we get, P = 4000.
P's monthly income = Rs. 4000.
Answer:B
Answer: (B) Rs.4000
Question: If r is even and t is odd, which of the following is odd r or t?
(A) rt
(B) 6rt
(C) 6(r^2)t
(D) 6r + 5t
(E) 5r + 6t
Rationale: Just checking options (In case you have difficulty then choose values of r=2 and t=1)
r = even
t= Odd
A. rt = Even*Odd = EvenINCORRECT
B. 5rt = Odd*Even*Odd = EvenINCORRECT
C. 6(r^2)t = 6*(Even^2)*Odd = EvenINCORRECT
E. 5r + 6t = 5*Even + 6*Odd = Even+Even = EvenINCORRECT
D. 6r + 5t = 6*Even + 5*Odd = Even+Odd = OddCORRECT
Answer: option E
Answer: (E) 5r + 6t
Question: If a car went the first third of the distance at 80 kmh, the second third at 24 kmh, and the last third at 54kmh, what was the average speed of the car for the entire trip?
(A) 36 kmh
(B) 40 kmh
(C) 41 kmh
(D) 44 kmh
(E) 50 kmh
Rationale: Assume D/3 = 2160 (this number is convenient because it is divisible by 80, 24 and 54)
So:
2160 = 80*T1 = 27 hrs
2160 = 24*T2 = 90 hrs
2160 = 54*T3 = 40 hrs
T = T1 + T2 + T3 = 157 hrs
D = RT
(240*3) = R*157
R = 41.27
ANSWER: C
Answer: (C) 41 kmh
Question: If p and n are positive integers, with p > n, what is the average of n consecutive multiples of p (starting with p), less the average of p consecutive multiples of n (starting with n)?
(A) (p + n)/2
(B) (p – n)/2
(C) p + n
(D) p – n
(E) p^2 – n^2
Rationale: Let, n = 2
and p = 3
i.e. Average of 2 (n) consecutive multiples of 3 (p) starting from 3 (p) = (3+6)/2 = 9/2
and Average of 3 (p) consecutive multiples of 2 (n) starting from 2 (n) = (2+4+6)/3 = 12/3 = 4
The average of n consecutive multiples of p (starting with p), less the average of p consecutive multiples of n (starting with n) = (9/2)-4 = (1/2)
A. (p + n)/2 = (3+2)/2 = 7/2 INCORRECT
B. (p – n)/2 = (3-2)/2 = 1/2 CORRECT
C. p + n = (3+2) = 7 INCORRECT
D. p – n = (3-2) = 1 INCORRECT
E. p^2 – n^2 = 3^2 - 2^2 = 5 INCORRECT
Answer: option B
Answer: (B) (p – n)/2
Question: Kim bought a total of $2.95 worth of postage stamps in four denominations. If she bought an equal number of 5-cent and 25-cent stamps and twice as many 10-cent stamps as 5-cent stamps, what is the least number of 1-cent stamps she could have bought?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 45
Rationale: Let:
# of 5 and 25 cents stamps = n
# of 10 cent stamps = 2n
# of 1 cent stamps = m
Therefore:
5n + 25n + 10(2n) + m = 295 cents
50n + m = 295
Forleastnumber of 1 cents stamps, maximize 50n. Hence,
50*5 + m = 295
m = 45 i.e. 45 stamps 1 cents each
Answer: E
Answer: (E) 45
Question: Sripad has scored average of 65 marks in three objects. In no subjects has he secured less than 58 marks. He has secured more marks in Maths than other two subjects. What could be his maximum score in Maths ?
(A) 79
(B) 47
(C) 29
(D) 27
(E) 19
Rationale: Explanation:
Assuming Sripad has scored the least marks in subject other than science,
Then the marks he could secure in other two are 58 each.
Since the average mark of all the 3 subject is 65.
i.e (58+58+x)/3 = 65
116 + x = 195
x = 79 marks.
Therefore, the maximum marks he can score in maths is 79.
Answer: A
Answer: (A) 79
Question: Awordis defined as a sequence of four dots arranged in a row. Each dot is colored either red or blue. How many distinct words can be formed?
(A) 16
(B) 15
(C) 6
(D) 18
(E) 9
Rationale: Each dot can be either yellow or blue, so 2 options for each dot: 2*2*2*2 = 16.
Answer: A.
Answer: (A) 16
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
(A) 5.76
(B) 5.78
(C) 5.76
(D) 5.75
(E) 5.71
Rationale: M = 6
S = 1.2
DS = 7.2
US = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
D = 2.88 * 2 = 5.76
Answer: C
Answer: (C) 5.76
Question: A man purchases 2 watches for $ 520. He sells one at 15% profit and the other at a loss of 10%. He neither gains nor loses on the whole. Thus, the cost price of two watches are :
(A) $ 208 and $ 312
(B) $210 and $ 350
(C) $224 and $336
(D) $560 and $560
(E) $224 and $ 350
Rationale: x + y = 520 --- (1)
1.15x + 0.9y = 520 --- (2)
(2) - (1) --> 0.15x - 0.1y = 0
15x = 10y
x/y = 2/3 = (2*104)/(3*104) = 208/312
Answer: A
Answer: (A) $ 208 and $ 312
Question: If p and q are positive integers each greater than 1, and 17(p+1)=21(q+1), what is the least possible value of p+q?
(A) 36
(B) 42
(C) 44
(D) 46
(E) none
Rationale: 17(p+1)=21(q+1) --> (p+1)/(q+1) = 21/17 --> the least positive value of p+1 is 21, so the least value of p is 20 and the least positive value of q+1 is 17, so the least value of q is 16 --> the least value of p+q is 20+16=36.
Answer: A.
Answer: (A) 36
Question: The roof of an apartment building is rectangular and its length is 3 times longer than its width. If the area of the roof is 675 feet squared, what is the difference between the length and the width of the roof?
(A) 38.
(B) 30.
(C) 42.
(D) 44.
(E) 46.
Rationale: Let the width= x
x*3x=675
x^2= 225
x= 15
Length= 3*15= 45
difference= 45-15= 30
B is the answer
Answer: (B) 30.
Question: If a, b, and c are integers and a*b^2/c is a positive even integer, which of the following must be true?
I. c is even
II. ab > 2
III. ab is even
(A) I only
(B) III only
(C) I and II
(D) I and III
(E) I, II, and III
Rationale: Two ways this can happen: 1- Even/ Even= Even or 2- Even/Odd= Even
So Ab MUST be even, with either A or B being even, Ab does not have to be positive, as B could be negative and once it is raised to 2 it becomes positive again, and of course, C could be Odd or Even as described above.
III only.letter B
Answer: (B) III only
Question: X and Y are integers, X is even and negative, Y is odd and positive. Which of the following could be false?
1. (X + Y) is an odd number.
2. Y^(X + Y) is an integer.
3. X^Y is a positive number.
(A) 2 only
(B) 3 only
(C) 1 and 3 only
(D) 2 and 3 only
(E) 1, 2 and 3
Rationale: Using the properties for even and odd numbers along with positive and negatives,
1. (X + Y) is an odd number : even + odd is always a odd number, so eliminate 1
2. Y^(X + Y) is an integer. : an odd and positive number could be raised to power of either positive or negative, so not conclusive, eliminate 2
3. X^Y is a positive number. : a negative number raised to power of odd number is always negative.
Answer : B
Answer: (B) 3 only
Question: A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
(A) 3
(B) 4
(C) 5
(D) 7
(E) 9
Rationale: Area of the park = (60 x 40) m2 = 2400 m2.
Area of the lawn = 2109 m2.
Area of the crossroads = (2400 - 2109) m2 = 291 m2.
Let the width of the road be x metres. Then,
60x + 40x - x2 = 291
x2 - 100x + 291 = 0
(x - 97)(x - 3) = 0
x = 3
A)
Answer: (A) 3
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 57?
(A) 3944
(B) 920
(C) 7290
(D) 3876
(E) 3729
Rationale: Explanation:
Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 57 = Rs. 3876.
Answer: Option D
Answer: (D) 3876
Question: A can do a piece of work in 10 days and B can do it in 15 days and C can do it 20 days. They started the work together and A leaves after 2 days and B leaves after 4 days from the beginning. How long will work lost?
(A) 10 2/9
(B) 10 2/6
(C) 10 2/3
(D) 10 2/2
(E) 10 2/1
Rationale: 2/10 + 4/15 + x/20 = 1
x = 32/3 = 10 2/3
Answer:C
Answer: (C) 10 2/3
Question: 16! is equal to which of the following?
(A) 20,922,789,888,321
(B) 20,922,789,888,000
(C) 20,922,789,888,525
(D) 20,922,789,888,416
(E) 20,922,789,888,928
Rationale: After 4!, the units digit of every factorial is 0.
5!=120
6!=720
etc...
The answer is B.
Answer: (B) 20,922,789,888,000
Question: If a 3-member subcommittee is to be formed from a certain 7-member committee, how many different such subcommittee are possible?
(A) 6
(B) 18
(C) 35
(D) 108
(E) 216
Rationale: 1st member can be selected in 7 ways
2nd can be selected in 6 ways
3rd can be selected in 5 ways
So total ways : 210
But to avoid the similar scenarios 210/3!=35
ANS:C
Answer: (C) 35
Question: For integers x, y, and z, if (3^x) (4^y) (5^z) = 209,715,200,000 and x + y + z = 18, what is the value of xy/z?
(A) 0
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: The number 209,715,200,000 is not divisible by 3. (We can verify this by adding the digits of the number to see that the sum is not a multiple of 3.)
Thus x = 0 and xy/z = 0.
The answer is A.
Answer: (A) 0
Question: Which of the following expressions CANNOT have a negative value
(A) |a + b| – |a – b|
(B) |a + b| – |a|
(C) |2a + b| + |a + b|
(D) a^2 - b^2 – 2|ab|
(E) |a^3 + b^3| – a – b
Rationale: Whenever you are required to find if the equation is a perfect square or not, try to bring everything in the form of a perfect square as they are always positive.
Of the given options, only option D can be written in from of a perfect square.
|2a + b| + |a + b|
This will always be positive.
Correct Option: C
Answer: (C) |2a + b| + |a + b|
Question: The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is:
(A) 3500
(B) 4000
(C) 4050
(D) 5000
(E) None
Rationale: EXPLANATION
Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (5050 x 2) = 10100 …. (i)
Q + R = (6250 x 2) = 12500 …. (ii)
P + R = (5200 x 2) = 10400 …. (iii)
Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33000 or P + Q + R = 16500 …. (iv)
Subtracting (ii) from (iv), we get P = 4000.
P’s monthly income = Rs. 4000.
Answer B
Answer: (B) 4000
Question: P can do a work in 24 days. Q can do the samework in 9 days & R can do the same work in 12 days. Q & R start the work and leave after 3 days. P finishes the remaining work in how many days.
(A) 8
(B) 10
(C) 14
(D) 16
(E) 19
Rationale: Work done by P in 1 day = 1/24
Work done by Q in 1 day = 1/9
Work done by R in 1 day = 1/12
Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36
Work done by Q and R in 3 days = 3×7/36 = 7/12
Remaining work = 1 – 7/12 = 5/12
Number of days in which P can finish the remaining work = (5/12) / (1/24) = 10
B
Answer: (B) 10
Question: Two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
(A) 18 sec
(B) 70 sec
(C) 21 sec
(D) 20 sec
(E) 19 sec
Rationale: Relative speed = (42 + 30) * 5/18 = 4 * 5
= 20 mps.
Distance covered in passing each other
= 120 + 280 = 400 m.
The time required = d/s
= 400/20
= 20 sec.
Answer: D
Answer: (D) 20 sec
Question: 4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 10 mat-weavers in 10 days?
(A) 25
(B) 19
(C) 39
(D) 61
(E) 16
Rationale: Let the required number of bottles be x.
More weavers, More mats (Direct Proportion)
More days, More mats (Direct Proportion)
Wavers	4	:	10 :: 4 : x
Days	4:10
4 * 4 * x = 10 * 10 * 4
x =	(10 * 10 * 4)/(4 x 4)
x = 25.
Answer is A.
Answer: (A) 25
Question: A grocer wants to arrange 13 fruits in a line among which 3 are mangoes, 4 are apples, 2 are oranges, 1 pineapple and remaining are guavas. In how many different ways can he do so, if fruits of one kind are identical?
(A) 13!/{(2!)(3!^2)(4!)}
(B) 13!/{(2!)(3!^2)}
(C) 13!/{(2!)(4!)}
(D) 13!
(E) 13!/(3!^2)
Rationale: The total number of ways in which a total N items, out of which p are identical of one type, q are identical of another type and rest are different, can be arranged in a line is N!/{p!q!}
Here we have 13 fruits out of which there are 3 alike mangoes, 4 alike apples, 2 alike oranges, 3 alike guavas and 1 pineapple.
Hence the number of ways in which he can arrange these in a line are 13!/(3!4!2!3!) = 13!/{(2!)(3!^2)(4!)}
Ans A
Answer: (A) 13!/{(2!)(3!^2)(4!)}
Question: In how many ways 6 persons can be formed from 8 men and 7 women?
(A) 5005
(B) 6452
(C) 4516
(D) 2313
(E) 3564
Rationale: Total number of persons = 15
Required number of ways = 15C6 = 5005
Answer is A
Answer: (A) 5005
Question: If x = 4 and y = −2, what is the value of (x − 2y)^y?
(A) −100
(B) 0.015
(C) 0.25
(D) 4
(E) 8
Rationale: Quickly we can spot that answer is neither integer nor negative. Eliminate A, DE
by inversing and squaring 0.015
Answer: B
Answer: (B) 0.015
Question: At a certain college there are twice as many Economics majors as history majors and three times as many Economics majors as mathematics majors. What is the ratio of the number of history majors to the number of mathematics majors?
(A) 6 to 1
(B) 6 to 4
(C) 2 to 3
(D) 1 to 5
(E) 1 to 6
Rationale: This is how I translated the question:
At a certain college there are twice as many economics majors as history majors
E = 2H
and three times as many economics majors as mathematics majors.
E = 3M
What is the ratio of the number of history majors to the number of mathematics majors?
What is H:M?
Just set E equal to each other to get the ratio in terms of H and M.
2H = 3M
H/M = 3/2
The answer is 6:4
Answer : B
Answer: (B) 6 to 4
Question: Simplify: 6005-6000+10
(A) 4505
(B) 4509
(C) 5405
(D) 4508
(E) None of them
Rationale: 6005-6000+10
=6005-(6000/10)
=6005-600
=5405.
Answer is C
Answer: (C) 5405