mathewhe/aqua_rat huggingface dataset:
Question: A dog is tied to a tree by a long nylon cord. If the dog runs from the due North side of the tree to the due South side of the tree with the cord extended to its full length at all items, and the dog ran approximately 30 feet, what was the approximate length of the nylon cord W, in feet?
(A) 30
(B) 25
(C) 15
(D) 10
(E) 5
Rationale: Because the cord was extended to its full length at all items, the dog ran along a semi-circular path, from north to south.
The circumference of a full circle is 2*pi*r, but since we only care about the length of half the circle, the semi-circle path is pi*r.
W=pi*r = 30. Round pi = 3, then r = 10.
Chord is about 10 feet long.D
Answer: (D) 10
Question: There are two circles, one circle is inscribed and another circle is circumscribed over a square. What is the ratio of area of inner to outer circle?
(A) 1:2
(B) 2:3
(C) 2:1
(D) 1:4
(E) 1:3
Rationale: For simplicity consider side of the square as 1. Now radius of inner circle =1/2. Formula for diagonal of the square = side*sqrt(2) = 1*sqrt(2). Half the diagonal = (1/2)*sqrt(2) = 1/sqrt(2). We got radiuses of both circles. So calculate areas and find ratio. Inner circle area= pi*(1/2)^2 and Outer circle = pi*(1/sqrt(2))^2. Divide both, you will get ratio as 1:2
ANSWER:A
Answer: (A) 1:2
Question: In how many ways a hockey team of eleven can be elected from 16 players?
(A) 4368
(B) 4267
(C) 5368
(D) 4166
(E) None
Rationale: Solution
The required number of selections
= 3C1 × 4C1 × 2C1 (6C3 + 6C2 + 6C0) = 42 × 4!
Answer A
Answer: (A) 4368
Question: The average age of an adult class is 40 years. 2 new students with an avg age of 32 years join the class. Therefore decreasing the average by 4 year. Find what was the original strength of class?
(A) 10
(B) 12
(C) 16
(D) 2
(E) 22
Rationale: Let original strength = y
Then , 40y + 2 x 32 = ( y + 2) x 36
â‡’ 40y + 64 = 36y + 72
â‡’ 4y = 8
âˆ´ y = 2
D
Answer: (D) 2
Question: A cyclist rides a bicycle over a route which is 1/3 uphill, 1/3 level, and 1/3 downhill. If the cyclist covers the uphill part of the route at the rate of 8 km per hour and the level part at the rate of 12 km per hour, what rate in km per hour would the cyclist have to travel the downhill part of the route in order to average 12 km per hour for the entire route?
(A) 16
(B) 20
(C) 24
(D) 28
(E) 32
Rationale: Let V be the speed on the downhill section.
Let D be the distance of each of the three equal sections.
Total time T = T1+T2+T3 and 3D/T = 12 km/hour
3D / (D/8 + D/12 + D/V) = 12
1/4 = 1/8 + 1/12 + 1/V
1/V = 1/24 and so V = 24 km/h
The answer is C.
Answer: (C) 24
Question: The 30 members of a club decided to play a badminton singles tournament. Every time a member loses a game he is out of the tournament. There are no ties. What is the minimum number of matches that must be played to determine the winner ?
(A) 15
(B) 29
(C) 61
(D) 72
(E) None of these
Rationale: Explanation:
Clearly, every member except one (i.e. the winner) must lose one game to decide the winner. Thus, minimum number of matches to be played = 30 - 1 = 29.
Answer: B
Answer: (B) 29
Question: If $120 invested at a certain rate of simple interest amounts to $180 at the end of 3 years,How much will $150 amount to at the same rate of interest in 6 years?
(A) $190
(B) $180
(C) $200
(D) $240
(E) $300
Rationale: 120 amounts to 180 in 3 years.
i.e (principal + interest ) on 120 in 3 years = 180
120 + 120*(r/100)*(3) = 140 => r = 50/3
150 in 6 years = principal + interest
=300
Answer is E.
Answer: (E) $300
Question: A man purchased 15 pens, 12 books, 10 pencils and 5 erasers. The cost of each pen is Rs.36, each book is Rs.45, each pencil is Rs.8, and the cost of each eraser is Rs.40 less than the combined costs of pen and pencil. Find the total amount spent?
(A) Rs.1100
(B) Rs.1120
(C) Rs.1140
(D) Rs.1160
(E) None of these
Rationale: Cost of each eraser = (36 + 8 -40) = Rs.4
Required amount = 15 * 36 + 12 * 45 + 10 * 8 + 5 * 4
540 + 540 + 80 + 20 = Rs.1180
ANSWER:E
Answer: (E) None of these
Question: If M is the mean of x,y,z ; then what is the mean of x,z and y
(A) M
(B) 3M
(C) 10M
(D) M+10
(E) M-10
Rationale: order only changed
So new mean is M.
Answer (A)
Answer: (A) M
Question: A boy incurs 5% loss by selling a book for Rs. 1000. At what price should the book be sold to earn 5 % profit?
(A) 1105.26
(B) 1105.29
(C) 1105.22
(D) 11105.21
(E) 1103.26
Rationale: Explanation:
Let the new selling price be Rs. x
(100 – loss %) /1000 = (100 + gain %) / x
(100 – 5) / 1000 = (100 + 5) / x
x = (105 × 1000) / 95 = 105000 / 95
x = 1105.26.\
ANSWER: A
Answer: (A) 1105.26
Question: Uncle Bruce is baking chocolate chip cookies. He has 36 ounces of dough (with no chocolate) and 14 ounces of chocolate. How many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20% chocolate?
(A)  3
(B)  6
(C)  7.2
(D)  5
(E)  9
Rationale: Answer is D.
x/x+36=1/5
x=9
14-9=5
Answer: (D)  5
Question: Robert is travelling on his cycle andhas calculated to reach point A at 2 PM. if he travels at 10 kmph, he will reach there at 12Pm if he travels at 15 kmph. At what speed musthe travel to reach A at 1 PM?
(A) 40 km
(B) 45 km
(C) 60 km
(D) 65 km
(E) 70 km
Rationale: Let the distance travelled by x km.
Then, x - x = 2
10 15
3x - 2x = 60
x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60 hrs = 6 hrs.
10
So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.
Required speed = 60 kmph. = 12 kmph.
5
C
Answer: (C) 60 km
Question: If $30,000 interest is invested in x percent simple annual interest for 10 years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the n years?
(A) 5000 x
(B) 7000 x
(C) 6000 x
(D) 3000 x
(E) 8000 x
Rationale: 30000*x/100*10 = 3000 x
Answer : D
Answer: (D) 3000 x
Question: A driver took a trip consisting of three segments at three different speeds. The driver drove a distance of (3D) at a speed of (2V), then a distance of (4D) at a speed of (3V), then a distance of D at a speed of (6V). In terms of D and V, what was the total time of the trip?
(A) 3D/V
(B) 4D/V
(C) 5D/V
(D) 6D/V
(E) 7D/V
Rationale: The total time of the trip was:
3D/2V + 4D/3V + D/6V =
18D/12V + 16D/12V + 2D/12V =
36D/12V = 3D/V
The answer is A.
Answer: (A) 3D/V
Question: Qames can eat 25 marshmallows is 20 minutes. Dylan can eat 25 in one hour. In how much time will the two eat 150 marshmallows?
(A) 40 minutes.
(B) 1 hour and 30 minutes.
(C) 1 hour.
(D) 1 hour and 40 minutes.
(E) 2 hours and 15 minutes.
Rationale: Rate =Output/Time
Qames Rate=25/20=5/4
Dylan Rate=25/60=5/12
Combined rate = 5/4+5/12= 20/12
CombinedRate*CombinedTime= CombinedOutput
20/12*t=150
t=90 mins => 1 hr 30 min
Answer: (C) 1 hour.
Question: A person incurs loss for by selling a watch for Rs1140.at what price should the watch be sold to earn a 5% profit ?
(A) 1205
(B) 1260
(C) 1300
(D) 1340
(E) 1450
Rationale: let the new sp be Rsx.then
(100-loss%) : (1st sp)=(100+gain%) (2nd sp)
{(100-5)/1400}={(100+5)/x}=> x={(105*1140)/95} =1260.
ANSWER B
Answer: (B) 1260
Question: In a garden, there are 10 rows and 17 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is
(A) 20 m
(B) 22 m
(C) 34 m
(D) 26 m
(E) 28 m
Rationale: Explanation:
Each row contains 17 plants.
There are 15 gapes between the two corner trees (16 x 2) metres and 1 metre on each side is left.
Therefore Length = (32 + 2) m = 34 m.
Answer: C
Answer: (C) 34 m
Question: A car traveling with 5/75/7 of its actual speed covers 4242 km in 11 hr 4040 min 4848 sec. What is the actual speed of the car?
(A) 30 km/hr
(B) 35 km/hr
(C) 25 km/hr
(D) 40 km/hr
(E) 45 km/hr
Rationale: Explanation:
time =1=1 hr 4040 min 4848 sec
=1=1 hr +4060+4060 hr +483600+483600 hr
=1+23+175=12675hr=1+23+175=12675hr
distance =42=42 km
speed=distancetime=42(12675)speed=distancetime=42(12675) =42Ã—75126=25 km/hr=42Ã—75126=25 km/hr
â‡’57â‡’57 of the actual speed =25=25
â‡’â‡’ Actual speed =25Ã—75=35 km/hr
Answer is B
Answer: (B) 35 km/hr
Question: The average of 45 results is 10. The average of first 22 of them is 16 and that of last 22 is 20. Find the 23 result?
(A) 600
(B) 480
(C) 538
(D) 650
(E) 560
Rationale: 23th result = sum of 45results - sum of 44 results
10*45-16*22+20*22 = 450-352+440 = 538
Answer is C
Answer: (C) 538
Question: In a class, the average age of 30 boys is 13 years and the average of 20 girls is 12 years. what is the average age of the whole class?
(A) 12.5 Yrs
(B) 14.2 Yrs
(C) 12.3 Yrs
(D) 12.6 Yrs
(E) 12 Yrs
Rationale: Total age of 50 students
(30X 13+20 X 12) = 630
Average = 630/50 = 12.6 Years
ANSWER IS D
Answer: (D) 12.6 Yrs
Question: A car started running at a speed of 30 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 11 hours of the journey.
(A) 342 km
(B) 352 km
(C) 642 km
(D) 440 km
(E) 382 km
Rationale: The total distance covered by the car in the first 11 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 +48 + 50 = sum of 11 terms in AP whose first term is 30 and last term is 50 = 11/2 [30 + 50] = 440 km.
ANSWER:D
Answer: (D) 440 km
Question: F and E are midpoints of AB and AD respectively. If the side of square ABCD is 8, what is the area of triangle CEF?
(A) 8√2
(B) 9√3
(C) 18
(D) 16√2
(E) 24
Rationale: Area of Shaded figure = Area of Square - (Area of Triangle AEF + Area of Triangle FBC + Area of Triangle EDC )
= 8*8 - (1/2 * 4 * 4 + 1/2 * 4 * 8 + 1/2 * 4 * 8 )
= 24.
Answer E.
Answer: (E) 24
Question: The cash difference between the selling prices of an article at a profit of 4% and 8% is Rs 3. The ratio of two selling prices is
(A) 51:52
(B) 52:54
(C) 53:54
(D) 54:55
(E) None of these
Rationale: Explanation:
Let the Cost price of article is Rs. x
Required ratio = (104% of x) / (108% of x)
=104/108
=52/54 = 52:54.
Answer: B
Answer: (B) 52:54
Question: A walks around a circular field at the rate of one round per hour while B runs around it at the rate of eleven rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other after___ minutes?
(A) 6 min
(B) 12 min
(C) 10 min
(D) 15 min
(E) 16 min
Rationale: Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two.
Relative speed of A and B = 11 - 1 = 10 rounds per hour.
Time taken to complete one round at this speed = 1/10 hr = 6 min.
A
Answer: (A) 6 min
Question: A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent F of the distribution is less than m +d ?
(A) 16%
(B) 32%
(C) 48%
(D) 84%
(E) 92%
Rationale: D
The prompt says that 68% of the population lies between m-d and m+d.
Thus, 32% of the population is less than m-d or greater than m+d.
Since the population is symmetric, half of this 32% is less than m-d and half is greater than m+d.
Thus, F=(68+16)% or (100-16)% of the population is less than m+d.D
Answer: (D) 84%
Question: Which of the following inequalities is equivalent to −6 < x < 8?
(A) |x - 1| < 7
(B) |x + 2| < 6
(C) |x + 3| < 5
(D) |x - 2| < 6
(E) None of the above
Rationale: We know that |x| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0
Given is, -6 < x < 8, let's say by adding y to this inequality we will get into the above format
-6+y < x+y < 8+y
Now, to move this into the mod format, we need to have (-6+y) + (8+y) = 0 => y = -1
Thus, -7 < x-1 < 7 => |x-1| < 7.
Hence, answer is A
Answer: (A) |x - 1| < 7
Question: I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
(A) 298
(B) 280
(C) 279
(D) 267
(E) 297
Rationale: x*(85/100) = (480 - x)119/100
x = 280
Answer:B
Answer: (B) 280
Question: Of the 150 employees at company X, 60 are full-time, and 100 have worked at company X for at least a year. There are 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year?
(A) 20
(B) 30
(C) 50
(D) 80
(E) 100
Rationale: Full time employee who have NOT worked for at least one year = a
Full time employee who have worked for at least one year = b
NON Full time employee who have worked for at least one year = c
NON Full time employee who have NOT worked for at least one year = d
a+b+c+d = 150
a+b = 80
i.e. c+d = 70
b+c = 100
i.e. a+d = 50
d = 20
i.e. c = 70-20 = 50
i.e. b = 100-50 = 50
i.e. a = 80-50 = 30
b = 80
Answer: Option D
Answer: (D) 80
Question: Mr Katial buys a house for Rs 1,00,000 and rents it. He puts 12.5% of each month’s rent aside for upkeep and repairs, pays Rs 325 per year as taxes and realizes 5.5% annually on his investment . Find the monthly rent?
(A) Rs 634.76
(B) Rs 554.76
(C) Rs 654.76
(D) Rs 664.76
(E) none of these
Rationale: Let the monthly rent be Rs X.
We have,
5.5% of 100000 = 12 (X - 12.5% of X) - 325
5500/12 = X - (X/8) - 325/12
5500/12 + 325/12 = 7/8 x X
X = 5825/12 x 8/7
Rs 554.76 per month
ANSWER:B
Answer: (B) Rs 554.76
Question: On dividing a number by 357, we get 41 as remainder.On dividing the same number by 17, what will be the remainder ?
(A) 4
(B) 5
(C) 8
(D) 7
(E) 2
Rationale: Let x be the number and y be the quotient.Then,
x=357*y+41
=(17*21*y)+(17*2)+7
=17*(21y+2)+7.
Required number =7.
Answer is D
Answer: (D) 7
Question: If (1.001)^1259=3.52 and (1.001)^2062=7.85 then (1.001)^3321=?
(A) 27.632
(B) 29.632
(C) 17.632
(D) 39.632
(E) 7.632
Rationale: Values Given :
(1.001)^1259 = 3.52
(1.001)^2060 = 7.85
Therefore,
--> (1.001)^1259+2062 = (1.001)^1259 * (1.001)^2062
Substitute the values which is given. Then,
--> (1.001)^3321 = 3.52 * 7.85
--> (1.001)^3321 = 27.632
ANSWER:A
Answer: (A) 27.632
Question: s(n) is a n-digit number formed by attaching the first n perfect squares, in order, into one integer. For example, s(1) = 1, s(2) = 14, s(3) = 149, s(4) = 14916, s(5) = 1491625, etc. How many digits Y are in s(99)?
(A) Y=350
(B) Y=353
(C) Y=354
(D) Y=356
(E) Y=357
Rationale: Focus on the points where the number of digits in squares change:
1, 2, 3 - Single digit squares. First 2 digit number is 10.
4 , 5,...9 - Two digit squares. To get 9, the last number with two digit square, think that first 3 digit number is 100 which is 10^2. so 9^2 must be the last 2 digit square.
10, 11, 12, ... 31 - Three digit squares. To get 31, think of 1000 - the first 4 digit number. It is not a perfect square but 900 is 30^2. 32^2 = 2^10 = 1024, the first 4 digit square.
32 - 99 - Four digit squares. To get 99, think of 10,000 - the first 5 digit number which is 100^2.
So number of digits in s(99) = 3*1 + 6*2 + 22*3 + 68*4 = 3 + 12 + 66 + 272 = 353.B
Answer: (B) Y=353
Question: The digit at the ten’s place of a 2 digit no. is twice the digit at the unit’s place. If the sum of this no. and the no. formed by reversing the digits is 66. Find the no.
(A) 26
(B) 28
(C) 32
(D) 42
(E) 47
Rationale: Let the unit place digit = x
Ten’s place digit = 2x
Number formed = 10(2x ) + x = 20 x + x = 21x
Reversing the digit :
Unit digit = 2x
Ten’s digit = x
New number formed = 10 (x) + 2x = 10x + 2x = 12x
As the sum of the number is 66.
21x + 12 x = 66
33x = 66
X = 2
So unit digit = 2
Number = 21x = 21(2)
=42
D
Answer: (D) 42
Question: Find the base K of the number system, if (524)8 = (664)K ?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 5*8^2 + 2*8^1 + 4*8^0 = 6*K^2 + 6*K^1 + 4*K^0
320 + 16 + 4 = 6(K^2) + 6K + 4
340 = 6(K^2) + 6K + 4
6(K^2) + 6K + 4 - 340 = 0
6(K^2) + 6K - 336 = 0
dividing by 6;
(K^2) + K - 56 = 0
solving this quadratic equation we get, K=7 and K=-8
thus K=7
ANSWER:D
Answer: (D) 7
Question: A die is thrown twice and the sum of the numbers appearing is observed to be 6.
find the conditional probability that the number 4 has appeared at least once?
(A) 1/3
(B) 2/5
(C) 1/6
(D) 1/7
(E) 2/5
Rationale: Let E be the event that ‘number 4 appears at least once’ and F be
the event
that ‘the sum of the numbers appearing is 6’.
Then, E = {(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (1,4), (2,4), (3,4),
(5,4), (6,4)}
and F = {(1,5), (2,4), (3,3), (4,2), (5,1)}
We have P(E) = 11/36
and P (F) = 5/36
Also EnF = {(2,4), (4,2)}
Therefore P(EnF) = 2/36
the required probability
P(E|F) = P(EnF)/P(F) = (2/36)/(5/36) = 2/5.
B
Answer: (B) 2/5
Question: Ray writes a two digit number. He sees that the number exceeds 4 times the sum of its digits by 3. If the number is increased by 18, the result is the same as the number formed by reversing the digits. Find the sum of the digits of the number.
(A) 8
(B) 9
(C) 10
(D) 12
(E) 11
Rationale: Explanation:
Let the two digit number be xy.
4(x + y) +3 = 10x + y - - - (1)
10x + y + 18 = 10 y + x - - - (2)
Solving 1st equation,
4x + 4y + 3 = 10x + y
3y + 3 = 6x
6x – 3y = 3
Therefore, 2x – y = 1 - - - (3)
Solving 2nd equation,
xy + 18 = yx
⇒⇒ (10x + b) + 18 = 10y + x
⇒⇒ 18 = 9y – 9x
⇒⇒ 2 = y – x
we get y - x = 2 - - - (4)
adding 3 and 4, we get x = 3
By substituting in (4), we get y = 5
So the given number is 35. Sum of the digits = 8.
Correct option: A
Answer: (A) 8
Question: In a shop, 40% socks are white and rest are black. 60% socks are made of cotton and rest are made of wool. 25% white socks are made of cotton and 20 of the black socks are made of wool. How many black socks B are made of cotton?
(A) 100
(B) 80
(C) 60
(D) 50
(E) 25
Rationale: I'll prefer to solve this with plug n play method.
As we know, White Cotton socks are only 25% and Total Cotton socks is 60% - Hence Black Cotton socks B has to be [highlight]HIGH[/highlight]number. Thats why we've to pick high number... say 100 or 80.
100 fits perfectly after relevant calculations. Hence answer A.
Answer: (A) 100
Question: Indu gave Bindu Rs.3125 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
(A) s.10
(B) s.2
(C) s.5
(D) s.3
(E) s.4
Rationale: 3125 = D(100/4)2
D = 5
ANSWER:C
Answer: (C) s.5
Question: A Fruit store sells four varieties of Mangoes. A,B,C & D. IF A Costs 20% less than B, and C costs 25% less than A,and D costs 30% less than C what percent of B's cost is D?
(A) 40%
(B) 38%
(C) 44%
(D) 36%
(E) 42%
Rationale: Soln:-
B=100
A 20% less than B = 80
C 25% less than A = 60
D 30% less than C = 42
D is what percent of B = D/B * 100
= 42/100 * 100 = 42%
ANSWER:E
Answer: (E) 42%
Question: Machine A can process 6000 envelopes in 3 hours. Machines B and C working together but independently can process the same number of envelopes in 2.5 hours. If Machines A and C working together but independently process 3000 envelopes in 1 hour, then how many hours would it take Machine B to process 12000 envelopes.
(A) 2
(B) 3
(C) 4
(D) 6
(E) 60/7
Rationale: For 1 hour-
Machine A rate- 2000 envelopes
Machine B+C rate- 2400 envelopes
Since A + C = 3000 envelopes A's rate is 2000 envelopes as above, C has a rate of 1000 envelopes per hour.
Which makes machine B's rate as 1400 envelopes per hour.
Thus, it will take 8 hours to manufacture 12000 envelopes.
Answer:-E
Answer: (E) 60/7
Question: There is a 70% chance that Flora will visit Ghana this year, while there is a 70% chance that she will visit France this year. What is the probability that Flora will visit either Ghana or France this year, but NOT both?
(A) 34%
(B) 36%
(C) 38%
(D) 40%
(E) 42%
Rationale: P(Ghana but not France)=0.7*0.3=0.21
P(France but not Ghana)=0.7*0.3=0.21
P(Ghana or France but not both)=0.21+0.21=0.42
The answer is E.
Answer: (E) 42%
Question: P can do the work in 8 days and Q can do the same work in 12 days. If they work together for 4 days, what is the fraction of work that is left?
(A) 2/15
(B) 2/11
(C) 1/4
(D) 1/5
(E) 1/6
Rationale: 4/8 + 4/12 = 1/2 + 1/3 = 5/6 (completed work)
The work that is left is 1 - 5/6 = 1/6
The answer is E.
Answer: (E) 1/6
Question: If f(x) = 12 - x^2/2 and f(2k) = 7k, what is one possible value for k?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 7
Rationale: First of all, see thisGMAT blog postand check the related lesson linked below for some background on function notation.
We can plug anything in for x and get a result. You can find f(1), for example, by plugging in 1 where x is, and you would get 12 - 1/2 = 11.5. Or we could find f(2), which would be 12 - 4/2 = 10.
So the notation f(2k) means that we are going to plug a 2k in for x everywhere in the formula for f(x). That would be:
f(2k) = 12 - (2k)^2/2 = 12 - 2k^2.
Remember that we have to square both the 2 and the k, to get 4k2. Now, this expression, the output, we will set equal to 2k.
12 - 2k^2 = 2k --> k = -3 or k = 7.
All the answers are positive, so we choose k = 2.
Answer = E
Answer: (E) 7
Question: A and B can do a piece of work in 8 days. B and C can do it in 12 days and A and C in 16 days. Working together they will complete the work in how many days?
(A) 7.78 days
(B) 7.88 days
(C) 7.38 days
(D) 7.38 days
(E) 7.36 days
Rationale: A + B = 1/8
B + C = 1/12
C + A = 1/16
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2(A + B +C) = 1/8 + 1/12 + 1/16 = 13/48
A + B +C = 13/96
96/13 = 7.38 days
Answer: D
Answer: (D) 7.38 days
Question: A sock drawer contains four socks, each one a different solid color. The colors of the socks are green, blue, indigo, and violet. If the socks are laid next to each other, how many different arrangements of socks could be made?
(A) 2400
(B) 240
(C) 1,024
(D) 2,520
(E) 24
Rationale: I see no condition for arrangement.
So 4! ways - IMO option E is correct answer..
Answer: (E) 24
Question: Gold is 10 times as heavy as water and copper is 5 times as heavy as water. In what ratio should these be mixed to get an alloy 7 times as heavy as water?
(A) 3:2
(B) 1:2
(C) 3:1
(D) 5:2
(E) 2:3
Rationale: G = 10W
C = 5W
Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy
1gm gold + x gm copper = x+1 gm of alloy
10W+5Wx = x+1 * 7W
10+5x = 7(x+1)
x = 3/2
Ratio of gold with copper = 1:3/2 = 2:3
Answer is E
Answer: (E) 2:3
Question: Which of the following CANNOT be a product of two distinct positive integers p and q?
(A) p
(B) q
(C) 3q + 2p
(D) q - p
(E) qp
Rationale: In these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with
take p = 1 and q = 2 and work with the options
pq = 2
A) p take p =2, q = 1
B) q take p = 1 q = 2
C) 3q + 2p Seems tricky, lets see other options and then come back to it.
D) q - p take q = 1 and p = 2 --> q - p = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them?
E)qp Always true
You don't even have to worry what C is !
ans D
Answer: (D) q - p
Question: A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 1 a rupee. Find his net profit or loss percent?
(A) 330 %
(B) 390 %
(C) 200 %
(D) 250 %
(E) 300%
Rationale: The total number of mangoes bought by the shopkeeper be 12.
If he buys 4 a rupee, his CP = 1
He selling at 3 a rupee, his SP = 4
Profit = SP - CP = 4 - 1 = 3
Profit Percent = 3/1 * 100 = 300 %
Answer:E
Answer: (E) 300%
Question: John can complete a given task in 10 days. Jane will take only 20 days to complete the same task. John and Jane set out to complete the task by beginning to work together. However, Jane was indisposed 4 days before the work got over. In how many days did the work get over from the time John and Jane started to work on it together?
(A) 8
(B) 9
(C) 8.5
(D) 9.5
(E) 10.5
Rationale: In such questions, you need to start from the end. Last 4 days John works alone and completes 4 * (1/10) = 2/5 of the work.
So 3/5 of the work should have been completed by the two of them together before Jane left.
Their combined rate of work is 1/20 + 1/12 = 8/60
Time taken to complete 4/5 of the work = (3/5)/(8/60) = 9/2 days.
So total number of days taken to complete the work =9/2 + 4 = 8.5 days.
C
Answer: (C) 8.5