mathewhe/aqua_rat huggingface dataset:
Question: In a garden, trees are planted in rows. In each row there are as many trees as the number of rows in the garden. Each tree bears as many fruits as the number of trees in each row, and each fruit has as many seeds as the number of trees in each row. If the total number of seeds from the trees in that garden is n, then :
(A) n is a perfect square
(B) n is an odd number
(C) n is an even number
(D) n is a perfect cube.
(E) none
Rationale: If there were 4 rows of trees, each row would have 4 trees, each tree would have 4 fruits, and each fruits would have 4 seeds. The total seeds are 4*4*4*4=256. 256 is a square of 16.
Answer: A
Answer: (A) n is a perfect square
Question: A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
(A) 7 sec
(B) 6 sec
(C) 4 sec
(D) 2 sec
(E) 9 sec
Rationale: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 110 * 3/55 = 6 sec.
Answer: B
Answer: (B) 6 sec
Question: A, B, C, D, E, F, G, and H are all integers, listed in order of increasing size. When these numbers are arranged on a number line, the distance between any two consecutive numbers is constant. If G and H are equal to 5^12 and 5^15, respectively, what is the value of A?
(A) -24(5^12)
(B) -25(5^12)
(C) -24(5^6)
(D) 23(5^12)
(E) 24(5^12)
Rationale: Ans : B
Assume that the numbers appear as shown below on the number line
A-----B-----C-----D-----E-----F-----G-----H
(5^12) (5^13)
As the values for G and H are given , we can calculate the difference between any two terms of the series .
Common Difference ,d = (5^13) - (5^12)
= (5^12) *[ 5-1 ]
= (5^12)*(4)
Also F + d = G as the terms are in equidistant and in increasing order.
So F + (5^12)*(4) = (5^12).
That is , F = (5^12) - (5^12)*(4)
= (5^12)[ 1-4]
= (5^12) (-3)
Similarly , E = F - d
= (5^12)[-3-4]
= (5^12)*(-7)
You can see a -4 getting added to the non-exponent part of the values . That is , according to the pattern , D SHOULD BE (5^12)*(-7-4)= (5^12)*(-11)
Following this pattern , A = (5^12)*(-25)
B
Answer: (B) -25(5^12)
Question: How many positive factors do 160 and 96 have in common?
(A) 6
(B) 12
(C) 16
(D) 18
(E) 24
Rationale: The number of common factors will be same as number of factors of the Highest Common Factor(HCF)
HCF of 160 and 96 is 32
Number of factors of 32 = 6
Answer :A
Answer: (A) 6
Question: An engineer undertakes a project to build a road 10 km long in 15 days and employs 30 men for the purpose. After 5 days, he finds only 2 km of the road has been completed. Find the (approximate) number of extra men he must employ to finish the work in time.
(A) 15
(B) 20
(C) 25
(D) 28
(E) 30
Rationale: 30 workers working already
Let x be the total men required to finish the task in next 10 days
2 km done hence remaining is 8 km
Also, work has to be completed in next 10 days (15 - 10 = 5)
We know that, proportion of men to distance is direct proportion
and, proportion of men to days is inverse proportion
Hence, X = (30 * 8 * 5) / (2 *10)
thus, X = 60
Thus, more men needed to finish the task = 60-30=30
Answer : E
Answer: (E) 30
Question: 13 ltr of water is added with 11 ltr of a solution containing 16%of alcohol in the water. The %of alcohol in the new mixture is?
(A) 7.33%
(B) 9%
(C) 9.67%
(D) 11%
(E) 11.5%
Rationale: We have an 11 litre solution containing 16% of alcohol in the water.
=> Quantity of alcohol in the solution
=11Ã—16/ 100
Now 13 litre of water is added to the solution.
=> Total quantity of the new solution = 11 + 13 = 24
Percentage of alcohol in the new solution
=11Ã—16/100
24
Ã—
100
=11Ã—1610024Ã—100
=11Ã—0.67/100
=7.33%
A
Answer: (A) 7.33%
Question: In how many ways T can the crew of a ten oared boat be arranged ,when of the ten persons available, 2 of whom can row only on the bow side and 3 of whom can row only on the stroke side?
(A) 1. 10!/(2! * 3!)
(B) 2. 10!/(8! * 7!)
(C) 3. 5!/(3! * 2!)
(D) 4. (5!)^3/(3! * 2!)
(E) 5. 5!/(8! * 7!)
Rationale: Ans is D.
Going by the assumtion that both the Bow side and Stroke side will have 5 person each.
Five(3+2) of them had allready been selected(according to their preference), so from the remaining 5 we have to select 2 for the stroke side or 3 for the bow side.
and the 5 crew of each side can be arranged in 5! ways.T
Hence answer is 5C3 * 5! * 5!= (5!)^3/ 3!2!.D
Answer: (D) 4. (5!)^3/(3! * 2!)
Question: The number of new words that can be formed by rearranging the letters of the word 'IS' is?
(A) 6
(B) 7
(C) 4
(D) 1
(E) 3
Rationale: Number of words which can be formed
= 2! - 1 = 2 - 1
= 1.
Answer:D
Answer: (D) 1
Question: A shopkeeper has 280 kg of apples. He sells 40% of these at 30% profit and remaining 60% at 30% profit. Find his % profit on total.
(A) 24%
(B) 25%
(C) 26%
(D) 28%
(E) 30%
Rationale: If the total quantity was 100
Then 40X 30% + 60 X30%= 30
This profit will remain same for any total quantity unless the % of products remains the same. Hence 'E' is the answer
Answer: (E) 30%
Question: The captain of a cricket team of 11 members is 25 years old and the wicket keeper is 5 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
(A) 20
(B) 21
(C) 23
(D) 25
(E) 26
Rationale: Let the average age of the whole team be x years.
11x - (25 + 30) = 9 (x - 1)
11x - 9x = 46
2x = 46
x = 23.
The average age of the team is 23 years.
The answer is C.
Answer: (C) 23
Question: When a producer allows 36% commission on retail price of his product, he earns a profit of 8.8%. what would be his profit % if the commision is reduced by 24%?
(A) 49.6%
(B) 49%
(C) 50%
(D) 48.6%
(E) 48%
Rationale: Let the retail price =Rs 100.then, commission=Rs 36
S.P=Rs(100-36)=Rs 64
But, profit=8.8%
C.P=Rs(100/108.8*64)=Rs 1000/17
New commission =Rs12. New S.P=Rs(100-12)Rs 88
Gain=Rs(88-1000/17)=Rs 496/17
Gain%=(496/17*17/1000*100)%=49.6%
Answer is A.
Answer: (A) 49.6%
Question: A certain company charges $20 per package to ship packages weighing less than 5 pounds each. For a package weighing 5 pounds or more, the company charges an initial fee of $20 plus $5 per pound. If the company charged $65 to ship a certain package, which of the following was the weight of the package, in pounds?
(A) 13
(B) 15
(C) 17
(D) 19
(E) 21
Rationale: Let the weight of the package be X. Then the cost is 5*X + 20= 85 ---> 5X=65 ---> X=13
Answer : A
Answer: (A) 13
Question: If –6 and 3 are the solutions to the equation x^2 + bx + c = 0, where b and c are constants, what is the value of b + c?
(A) –18
(B) –15
(C) –3
(D) 3
(E) 8
Rationale: –6 and 3 are the solutions to the equation x^2 + bx + c = 0
= x^2 + bx + c = (x+6)(x-3) -> x^2+3x-18
we get b=3 and c=-18 ->b+c=3+(-18)=-15
ANSWER:B
Answer: (B) –15
Question: In an election contested by two parties, Party A secured 14% of the total votes more than Party B. If party B got 140,000 votes, by how many votes did it lose the election?
(A) 14,000
(B) 36,279
(C) 164,000
(D) 242,000
(E) 303,000
Rationale: A + B = 100 ---- (1)
A - B = 14 ---- (2)
Solving (1) and (2) A = 57% and B = 43%
43% of Total = 140000
Total = 316279
A = 176279
Difference = 176279 - 140000 = 36279
Answer: B
Answer: (B) 36,279
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 46, the dividend is:
(A) 5330
(B) 5336
(C) 5343
(D) 5345
(E) 5350
Rationale: Divisor = (5 * 46) = 230
= 10 * Quotient = Divisor
=> Quotient = 230/10 = 23
Dividend = (Divisor * Quotient) + Remainder
Dividend = (230 * 23) + 46 = 5336.
B
Answer: (B) 5336
Question: A furniture dealer purchased a desk for $150 and then set the selling price equal to the purchase price plus a markup that was 50% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk?
(A) 60%
(B) 70%
(C) 100%
(D) 90%
(E) 80%
Rationale: Anyway, in this question, there is no discount but the mark up is given as 50% of the selling price. So it is not 50% of $150 but instead, 50% of Selling price which is obtained by adding mark up to $150.
So if selling price is S,
150 + 50% of S = S
S = 300
Profit = 150 which is calculated on cost price in % terms. So 150/150 * 100 = 100% is profit.
C
Answer: (C) 100%
Question: Tommy's seafood restaurant gets a delivery of fresh seafood every day, 7 days per week, and her delivery company charges her dollars per delivery plus cents per item delivered. If lst week Sarah's seafood restaurant had an average of x items per day delivered, then which of the following is the total cost, in dollars, of last week's deliveries ?
(A) 7cdx/100
(B) d + 7cx/100
(C) 7d + xc/100
(D) 7d + 7xc/100
(E) 7cdx
Rationale: Answer is D. direct question.
Answer: (D) 7d + 7xc/100
Question: There is a 30% chance that Tigers will not win at all during the whole season. There is a 30% chance that Portugeese will not play at all in the whole season. What is the greatest possible probability that the Tigers will win and Portugeese will play during the season?
(A)  55%
(B)  60%
(C)  70%
(D)  72%
(E)  80%
Rationale: There is a 30% chance that Tigers will not win at all during the whole season
We can infer that there is 70% chance Tigers will win .
Similarly There is a 30% chance that Portugeese will not play at all in the whole season
We can also infer that there is 70% chance that Portugeese will play.
Answer C
Answer: (C)  70%
Question: Which of the following is closest to (3!-2!)/(3!+2!)?
(A) 0.01
(B) 0.1
(C) 0.2
(D) 0.5
(E) 10
Rationale: (3!-2!)/(3!+2!)
2! (3-1)/2! (3+1)
2/4 = 0.5
D is the answer
Answer: (D) 0.5
Question: A, Band C enter into a partnership by investing in the ratio of 3 : 2: 4. After 1 year, B invests another Rs. 2,70,000 and C, at the end of 2 years, also invests Rs.2,70,000. At the end of three years, profits are shared in the ratio of 3 : 4 : 5. Find initial investment of each.
(A) 360000;180000;270000
(B) 270000;180000;360000
(C) 180000;360000;270000
(D) 270000;360000;270000
(E) None of them
Rationale: Let the initial investments of A, Band C be Rs. 3x, Rs. 2x and Rs. 4x respectively. Then,
(3x x 36) : [(2x x 12) + (2x + 270000) x 24] : [(4x x 24) + (4x +270000) x 12]=3:4:5
1O8x : (72x + 6480000) : (144x + 3240000) = 3 : 4 : 5
108x /(72x+6480000)=3/4  432x = 216x + 19440000
=216x = 19440000
=x=90000
Hence, A’s initial investment = 3x = Rs. 2,70,000;
B's initial investment = 2x = Rs. 1,80,000;
C's initial investment = 4x = Rs. 3,60,000.
Answer is B.
Answer: (B) 270000;180000;360000
Question: The average of a couple was 28Yrs when they were married 15Yrs ago.The avg age of
the couple and a child, who was born during the interval, is 31Yrs now. How old is the
child now ?
(A) 2 Yrs
(B) 7 Yrs
(C) 3 Yrs
(D) 1 Yrs
(E) None of these
Rationale: (a+b-15-15)/2=28;
a+b=86;
a+b+c/3=31;
solving both c=7
ANSWER:B
Answer: (B) 7 Yrs
Question: When n is divided by 19, the remainder is 6. When n is divided by 11, the quotient is equal to Z, and the remainder is equal to 6. Z must be divisible by which of the following numbers?
(A) 3
(B) 7
(C) 10
(D) 13
(E) 19
Rationale: N = 19 q + 6
N = 11 z + 6
Equating
19 Q + 6 = 11z+6
11z=19q
11z/19 = q
since q is an integer Z must be divisible by 19.
ANSWER:E
Answer: (E) 19
Question: Rahim went to a shop and bought things worth Rs. 35, out of which 50 Paise went on sales tax on taxable purchases. If the tax rate was 5%, then what was the cost of the tax free items?
(A) 18.5
(B) 21.5
(C) 24.5
(D) 23.5
(E) 22.5
Rationale: Total cost of the items he purchased = Rs.35
Given that out of this Rs.35, 50 Paise is given as tax
=> Total tax incurred = 50 Paise = Rs.50/100
Let the cost of the tax free items = x
Given that tax rate = 5%
∴ (35−50/100−x)5/100 = 50/100
⇒ 5(35 −0.5−x) = 50
⇒ (35 − 0.5 − x) = 10
⇒ x = 35 − 0.5 − 10= 24.5
C)
Answer: (C) 24.5
Question: In a games hour 4 different types of players came to the ground? cricket 10, hokey 12, football 16, softball 13. How many players are present in the ground?
(A) 70
(B) 52
(C) 51
(D) 49
(E) 50
Rationale: total number of players= 10+12+16+13= 51
Answer is C
Answer: (C) 51
Question: If 36 men can do a piece of work in 25 hours, in how many hours will 12 men
do it ?
(A) 65 hours
(B) 75 hours
(C) 30 hours
(D) 62 hours
(E) 66 hours
Rationale: Let the required number of hours be x. Then,
Less men, More hours	(Indirect Proportion)
12 : 36 : : 25 : x	(12 x x) = (36 x 25)	(36 x 25)/12 = 75
Hence, 15 men can do it in 60 hours.
Answer is B.
Answer: (B) 75 hours
Question: A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
(A) 230
(B) 88
(C) 77
(D) 26
(E) 22
Rationale: Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 270)/9 = 500/9 => x = 230.
Answer: A
Answer: (A) 230
Question: Divide $1000 among A,B in the ratio 1:4. How many $ that B get?
(A) $500
(B) $800
(C) $1000
(D) $200
(E) $750
Rationale: Sum of ratio terms = 1+4 = 5
A = 1000*4/5 = $800
Answer is B
Answer: (B) $800
Question: John is building a rectangular fence around a garden. The length will be 5 feet shorter than its width. If the total area of the garden is 176 square feet, what is the length of the diagonal (in feet)?
(A) Between 18 and 19
(B) Between 19 and 20
(C) Between 20 and 21
(D) Between 21 and 22
(E) Between 22 and 23
Rationale: To solve this, we first need to set up an equation for the area of the garden. If x is the width, then we have
x(x - 5) = 176. By putting the equation in standard form, we get x^2-5x-176=0. By using the quadratic formula, we get roots of -11 and 16. We know that x is the width, and x-5 is the length, so by using the roots, we get 16 as the width (x), and 11 as the length (x-5).
Once we have this, we can use the Pythagorean Theorem to solve for the diagonal. Plugging in the length and width, we will get d^2=16^2+11^2
=256+121
=377
The square root of 377 is less than 20, since 20^2 = 400. Going down a number, we can compute 19^2 = 361 < 377. Therefore, the length of the diagonal must be between 19 and 20.
The correct answer is B.
Answer: (B) Between 19 and 20
Question: There is a single elimination lacrosse tournament, meaning when one player loses, they are out of the tournament. There are 10 teams in the tournament, how many games are played?
(A) 10
(B) 5
(C) 2
(D) 9
(E) 7
Rationale: D
The number of games always adds up to one less than the number of teams in a single elimination tournament. You may calculate it any way. Therefore, 9 games were played.
Answer: (D) 9
Question: x, a, z, and b are single digit positive integers. x = ¼ a. z = ¼ b.2*( (10a + b) – (10x + z) )could NOT equal
(A) 66
(B) 72
(C) 48
(D) 126
(E) 132
Rationale: 1) firstly we are not given that all are different integers..
2) since each is a positive single digit integer and x=a/4... a can take only 4 and 8 as value, and x can take 1 and 2..
3) same as 2) for b and z.
so in 2*((10a + b) – (10x + z)) ..
10a+b can be
44,48,84,88..
10x+z can be
11,12,21,22..
lets see teh choices
ans C
Answer: (C) 48
Question: The average of 5 numbers is 6.8. If one of the numbers is multiplied by a factor of 2, the average of the numbers increases to 9.2. What number is multiplied by 2?
(A)  12.0
(B)  30.0
(C)  30.9
(D)  40.0
(E)  60.0
Rationale: The average of 5 numbers is 6.8
The sum of 5 numbers will be 6.8 x 5 = 34
The average of 5 number after one of the number is multiplied by 2 is 9.2
The sum of the numbers will now be 9.2 x 5 = 46
So the sum has increased by 46-34 = 12
Let the number multiplied by 2 be n
Then,
2n = n+12
or n = 12
Answer:- A
Answer: (A)  12.0
Question: A certain rectangular crate measures 8 feet by 12 feet by 14 feet. A cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces. What should the radius of the tank be if it is to be of the largest possible volume?
(A) 6
(B) 5
(C) 6
(D) 8
(E) 10
Rationale: Ans is "B".
For max volume of cylinder (pi*r^2*h) we need to max out r^2*h. We don't know what the dimensions of the crate refer to. So to maximize the above eqn, radius may be of 9,10,12 one of the base area( 8x12, 14x12 or 8 x14) r is maximum for base 14x12 and 12 can be maximum value so r = 10/2 =6
A
Answer: (A) 6
Question: Which is the least number, which, when divided by 12 and 16, leave the same remainder, but is exactly divisible by 11?
(A) 55
(B) 27
(C) 29
(D) 12
(E) 01
Rationale: Explanation:
No explanation is available for this question!
ANSWER: A
Answer: (A) 55
Question: In an examination, 300 students appeared. Out of these students; 28 % got first division, 54 % got second division and the remaining just passed. Assuming that no student failed; find the number of students who just passed.
(A) 33
(B) 37
(C) 54
(D) 99
(E) 01
Rationale: The number of students with first division = 28 % of 300 = 28/100 × 300 = 8400/100 = 84
And, the number of students with second division = 54 % of 300
= 54/100 × 300
=16200/100
= 162
Therefore, the number of students who just passed = 300 – (84 + 162) = 54
Answer:C
Answer: (C) 54
Question: If Z = 52 and ACT = 48, then BAT will be equal to
(A) 33
(B) 88
(C) 77
(D) 46
(E) 99
Rationale: Explanation:
In the given code, A = 2, B = 4, C = 6,.... , Z = 52.
So, ACT = 2 + 6 + 40 = 48 and
BAT = 4 + 2 + 40 = 46
Answer: D) 46
Answer: (D) 46
Question: What is the lowest positive integer that is divisible by 1 through 3, inclusive?
(A) 12
(B) 6
(C) 8
(D) 18
(E) 33
Rationale: The integer should be divisible by: 1, 2, and 3. The least common multiple of these integers is LCM=1*2*3=6
Answer: B
Answer: (B) 6
Question: A train 240 m in length crosses a telegraph post in 16 seconds. The speed of the train is?
(A) 22
(B) 21
(C) 54
(D) 28
(E) 32
Rationale: S = 240/16 * 18/5 = 54 kmph.Answer:C
Answer: (C) 54
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 Q per 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: A librarian has a set of eight books, including four different books about Abraham Lincoln. The librarian wants to put the eight books on a shelf with the four Lincoln books next to each other, somewhere on the shelf among the other four books. How many different arrangements of the eight books are possible?
(A) (8!)/(4!)
(B) (4!)(4!)
(C) (4!)(5!)
(D) (4!)(8!)
(E) (4!)(4!)(8!)
Rationale: You can club the four Lincoln books as one, which leaves us with four other books plus this one to think about. So, these five items can be arranged in 5! ways, and since the four books can be moved around among themselves with each combination giving us a new overall combination, we have an additional 4! ways. Therefore, the answer would be 5!*4!, which is C.
Answer: (C) (4!)(5!)
Question: The variables a and b are non-zero integers B. If a = 2b^3/c, what happens to c when a is halved and b is doubled?
(A) c is not changed.
(B) c is halved.
(C) c is doubled.
(D) c is multiplied by 4.
(E) c is multiplied by 16.
Rationale: a =2b^3/c
c =2b^3/a
when a is halved and b is doubled
c=2(2b)^3/(a/2)
c= 16*2b^3/a
Ans. E c is multiplied by 16.
Answer: (E) c is multiplied by 16.
Question: The sequence of numbers a1, a2, a3, ..., an is defined by an = 1/n - 1/(n+2) for each integer n >= 1. What is the sum of the first 50 terms of this sequence?
(A) (1+1/2) – (1/51 +1/ 52)
(B) (1/51 +1/ 52)
(C) (1+1/2) +(1/51 +1/ 52)
(D) (1+1/2) – 1/51
(E) (1+1/2) – 1/52
Rationale: The answer would most certainly be[A]. But the question needs a slight modification.n>=1, since the answer does consider a1 under the sum.
The sequence is :
a1 = 1-1/3
a2 = 1/2 - 1/4
a3 = 1/3 - 1/5....
We can observe that the third term in the sequence cancels the negative term in the first. A similar approach can be seen on all the terms and we would be left with 1 + 1/2 from a1 and a2 along with -1/52 and -1/51 from a50 and a49 term which could not be cancelled.
Hence the sum = (1+1/2) – (1/51 +1/ 52)
Answer : A
Answer: (A) (1+1/2) – (1/51 +1/ 52)
Question: ((7^1/2)^2)
(A) 49^1/2
(B) 49^1/4
(C) 7^1/2
(D) 7^1/4
(E) 7^1/3
Rationale: ((7^1/2)^2)
=7^(1/2*2)
=7^1
=7
=49^1/2
ANSWER:A
Answer: (A) 49^1/2
Question: An article costing rs.160 is sold at 10% discount on a mark-up price. What is the selling price after
discount?
(A) 106
(B) 116
(C) 126
(D) 136
(E) 144
Rationale: 160*90/100=144
ANSWER:E
Answer: (E) 144
Question: All the stocks on the over-the-counter market are designated by either a 3 letter or 4 letter codes that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
(A) 2(26^5)
(B) 26(26^4)
(C) 27(26^3)
(D) 26(26^5)
(E) 27(26^5)
Rationale: with 3 letters: 26^3
with 4 letters: 26^4
26^3 + 26^4 = 27*(26^3)
C
Answer: (C) 27(26^3)
Question: A courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof. What could be the weight in grams of a package for which the charge is $2.05?
(A) 980
(B) 1130
(C) 1440
(D) 1610
(E) 1820
Rationale: The charge is 65 cents for the first 250 grams.
This leaves a charge of $2.05 - $0.65 = $1.40
The charge for the next 1300 grams is $1.30 which leaves a charge of $0.10
The weight is somewhere between 1550 and 1650.
The answer is D.
Answer: (D) 1610
Question: If 1/2 of the air in a tank is removed with each stroke of a vacuum pump, what fraction of the original amount of air has been removed after 3 strokes ?
(A) 15/16
(B) 7/8
(C) 1/4
(D) 1/8
(E) 1/16
Rationale: Left After 1st stroke = 1/2
Left After 2nd stroke = 1/2 * 1/2 = 1/4
Left After 3rd stroke = 1/2 * 1/4 = 1/8
So removed = 1- 1/8 = 7/8=B
Answer: (B) 7/8
Question: 30 men can do a work in 40 days. When should 14 men leave the work so that the entire work is completed in 40 days after they leave the work?
(A) 87 days
(B) 16 days
(C) 55 days
(D) 44 days
(E) 22 days
Rationale: Total work to be done = 30 * 40 = 1200
Let 14 men leave the work after 'P' days, so that the remaining work is completed in 40 days after they leave the work.
40P + (14 * 40) = 1200
40P = 640 => P = 16 days
Answer:B
Answer: (B) 16 days
Question: In the coordinate plane, Line A has a slope of -1 and an x-intercept of 1. Line B has a slope of 4 and a y-intercept of -4. If the two lines intersect at the point (a,b), what is the sum a+b?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: The equation of Line A is y = -x + 1
The equation of Line B is y = 4x - 4
4x - 4 = -x + 1
x = 1
y = 0
The point of intersection is (1,0) and then a+b = 1.
The answer is B.
Answer: (B) 1