mathewhe/aqua_rat huggingface dataset:
Question: If 2^2n + 2^2n + 2^2n + 2^2n = 4^26, then n =
(A) 3
(B) 6
(C) 12
(D) 23
(E) 25
Rationale: 2^2n + 2^2n + 2^2n + 2^2n = 4^26
=> 4 x 2^2n = 4^26 = 2^52
=> 2^2 x 2^2n = 2^52
=> 2^(2n+2) = 2^52
=> 2n+2 = 52=> n =25
So. Answer will be E
Answer: (E) 25
Question: A train 125 m long passes a man, running at 7 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
(A) 35 km/hr
(B) 50 km/hr
(C) 45 km/hr
(D) 52 km/hr
(E) 87 km/hr
Rationale: Speed of the train relative to man
= (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr
= 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed
= (x - 7) km/hr. x - 7 = 45 ==> x = 52 km/hr.
Answer: D
Answer: (D) 52 km/hr
Question: A man's speed with the current is 20 kmph and speed of the current is 2 kmph. The Man's speed
against the current will be
(A) 16 kmph
(B) 12 kmph
(C) 14 kmph
(D) 17 kmph
(E) None of these
Rationale: Explanation:
Speed with current is 20,
speed of the man + It is speed of the current
Speed in sƟll water = 20 - 2 = 18
Now speed against the current will be
speed of the man - speed of the current
= 18 - 2 = 16 kmph
Answer: A
Answer: (A) 16 kmph
Question: A sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is?
(A) 33.8
(B) 33.5
(C) 33.3
(D) 33.9
(E) 33.1
Rationale: Let B = 100
A = 50
C * (150/100) = 50
3C = 100
C = 33.3 then 'C' Cheapest
Answer:C
Answer: (C) 33.3
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 150 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
(A) 28 sec
(B) 16 sec
(C) 39 sec
(D) 18 sec
(E) 17 sec
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 150 = 390 m.
Time taken = 390/10 = 39 sec.
Answer:C
Answer: (C) 39 sec
Question: Mary, Peter, and Lucy were picking chestnuts. Mary picked twice as much chestnuts than Peter. Lucy picked 3 kg more than Peter. Together the three of them picked 27 kg of chestnuts. How many kilograms of chestnuts did Mary, Peter, and Lucy pick respectively?
(A) 6, 9 and 12
(B) 12, 9 and 6
(C) 9, 6 and 12
(D) 12, 6 and 9
(E) 6, 12 and 9
Rationale: M = 2P
L = P+3
M + P + L = 27
2P + P + (P+3) = 27
P = 6, M = 12, L = 9
Therefore, Mary, Peter, and Lucy picked 12, 6, and 9 kg, respectively.
The answer is D.
Answer: (D) 12, 6 and 9
Question: Two members of a club are to be selected to represent the club at a national meeting. if there are 55 different possible selections of the 2 members, how many members does the club have?
(A) 11
(B) 27
(C) 40
(D) 57
(E) 95
Rationale: I have done this problem by substituting numbers
We have n!/2!(n-2)! = 55
or n(n-1)/2 = 110 or n^2-n -110 =0 or n^2-11n+10n-110 =0 or n(n-11) +10(n-11) =0 or (n-11)(n+10)=0
n=11 satisfies the equation
A
Answer: (A) 11
Question: If N = 3^0.15 and N^b = 9, b must equal
(A) 3/80
(B) 3/5
(C) 4
(D) 5/3
(E) 40/3
Rationale: 15/100 = 3/20
N = 3 ^ 3/20
N^b = 3^2
(3^3/20)^b = 3^2
b = 40/3
Answer: E
Answer: (E) 40/3
Question: The ratio of 2 numbers is 5:2 and their H.C.F. is 20. Their L.C.M. is ?
(A) 400
(B) 300
(C) 200
(D) 100
(E) 40
Rationale: Let the numbers be 5x and 2x
Their H.C.F. = 20
so the numbers are 5*20 , 2*20 = 100, 40
L.C.M. = 200
Answer is C
Answer: (C) 200
Question: If 5 men and 2 boys working together, can do four times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time?
(A) 2:5
(B) 2:4
(C) 3:0
(D) 2:1
(E) 2:3
Rationale: 5M + 2B = 4(1M + 1B)
5M + 2B = 4M + 4B
1M = 2B
The required ratio of work done by a man and a boy = 2:1 .Answer: D
Answer: (D) 2:1
Question: The effective annual rate of interest corresponding to a nominal rate of 8% per annum payable half-yearly is?
(A) 6.06%
(B) 8.16%
(C) 6.08%
(D) 6.09%
(E) 6.19%
Rationale: Amount of Rs. 100 for 1 year when compounded half-yearly = [100 * (1 + 4/100)2] = Rs. 108.16 Effective rate = (108.16 - 100) =8.16%
ANSWER:B
Answer: (B) 8.16%
Question: If x is real, find the maximum value of the expression -2x^2 + 5x + 7.
(A) 6.125
(B) 8.125
(C) 10.125
(D) 12.125
(E) 14.125
Rationale: This is an equation of a downward facing parabola.
The maximum value is the top point of the parabola.
-2x^2+5x+7 = (-2x+7)(x+1)
The roots are 7/2 and -1.
The maximum value must be when x is halfway between these two points.
x = 1.25
The maximum value is -2(1.25)^2+5(1.25)+7 = 10.125
The answer is C.
Answer: (C) 10.125
Question: Angelo and Isabella are both salespersons. In any given week, Angelo makes $540 in base salary plus 8 percent of the portion of his sales above $1,000 for that week. Isabella makes 10 percent of her total sales for any given week. For what amount of weekly sales would Angelo and Isabella earn the same amount of money?
(A) 23,000
(B) 24,500
(C) 25,500
(D) 26,500
(E) 27,500
Rationale: Let the weekly sales of both = x
540+(x−1000)8/100=10/100x
x = 23000
ANSWER:A
Answer: (A) 23,000
Question: A thief steals at a car at 2.30 p.m. and drives it at 60 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 90 km/hr. When will he overtake the thief?
(A) 6 p.m
(B) 9 p.m
(C) 4 p.m
(D) 2 p.m
(E) 1 p.m
Rationale: :
Suppose the thief is overtaken x hrs after 2.30 p.m.
Then, distance covered by the owner in (x - 1/2) hrs.
60x = 90(x - 1/2) => x = 3/2 hrs.
So, the thief is overtaken at 4 p.m.'
Answer: C
Answer: (C) 4 p.m
Question: REDO’s manufacturing costs for sets of horseshoes include a $10,500 initial outlay, and $30per set. They can sell the sets $60. If profit is revenue from sales minus manufacturing costs, and the company producessells 1000 sets of horseshoes, what was their profit?
(A) $19500
(B) $15500
(C) $29500
(D) $39500
(E) $1500
Rationale: Total Manufacturing cost = 10500+1000*30 = 40500
Total Selling cost = 1000*60= 60000
Profit = 60000-40500 = 19500
Answer : A
Answer: (A) $19500
Question: The sum of ages of 5 children born at the intervals of 3 years each is 65 years. What is the age of the youngest child?
(A) 3 years
(B) 4 years
(C) 6 years
(D) 7 years
(E) 8 years
Rationale: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 65
5x = 35
x = 7.
Age of the youngest child = x = 7 years.
D)
Answer: (D) 7 years
Question: If x is equal to the sum of the integers from 30 to 50, inclusive, and y is the number of EVEN integers from 30 to 50, inclusive, what is the value of x+y ?
(A) 810
(B) 811
(C) 830
(D) 850
(E) 851
Rationale: Since the integers from 30-50 are consecutive we can use the "median x # of terms formula" to determine x. There are 21 terms and the median is 40. This gives a total of 21x40 = 840. There are 11 even integers from 30-50 = y. Therefore, x+y = 851. Answer: E
Answer: (E) 851
Question: A farmer has a rose garden. Every day he either plucks 7 or 6 or 24 or 23 roses. The rose plants are intelligent and when the farmer plucks these numbers of roses, the next day 37 or 36 or 9 or 18 new roses bloom in the garden respectively. On Monday, he counts 189 roses in the garden. He plucks the roses as per his plan on consecutive days and the new roses bloom as per intelligence of the plants mentioned above. After some days which of the following can be the number of roses in the garden?
(A) 6
(B) 7
(C) 6
(D) 4
(E) 1
Rationale: If he plucks 23, then only 18 grows the next day. This means total roses get decreases by 5. So after n days assume the number of roses got decreased 185 where n = 37, then 4 roses left.
Answer:D
Answer: (D) 4
Question: Find the cost of fencing around a circular field of diameter 30 m at the rate of Rs.5 a meter?
(A) 288
(B) 132
(C) 772
(D) 592
(E) 471.25
Rationale: 2 * 22/7 * 15 = 94.25
94.25 * 5 = Rs.471.25
Answer: E
Answer: (E) 471.25
Question: If y > 0, (9y)/20 + (3y)/10 is what percent of y?
(A) 40%
(B) 50%
(C) 60%
(D) 70%
(E) 75%
Rationale: can be reduced to 9y/20+6y/20 =15y/20=75%
Answer E
Answer: (E) 75%
Question: A code is to be made by arranging 6 letters. Three of the letters used will be the letter A, two of the letters used will be the letter B and one of the letters used will be the letter C . If there is only one way to present each letter, how many different codes are possible?
(A) 230
(B) 360
(C) 420
(D) 840
(E) 5,040
Rationale: we have 6 letters out of which 3 are of one kind, 2 are of another kind..
so total ways = 6!/2!1!=360
ans B
Answer: (B) 360
Question: In five football games thus far this season, Barry has run for 98, 107, 85, 89, and 91 yards. At a minimum, how many yards W will he need to gain this Sunday if he wants to keep his season average above 100 yards?
(A) 101
(B) 116
(C) 130
(D) W=131
(E) W=141
Rationale: Sorry the answer W=141 is D.
Answer: (D) W=131
Question: 120 +520 ÷ 5.00 = ?
(A) 100
(B) 150
(C) 120
(D) 520
(E) None
Rationale: Answer
Given expression = 120 +520 ÷ 5.00
= 120 + 104
= 224
Correct Option: E
Answer: (E) None
Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 4200. What was Simran share in the profit?
(A) s 9500
(B) s 1080
(C) s 1008
(D) s 1820
(E) s 1800
Rationale: Simran : Nanda = (50000 x 36) : (80000 x 30) = 3 : 4.
Simran's share = Rs.4200x 3/7	= Rs. 1,800.
ANSWER :E
Answer: (E) s 1800
Question: Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.
(A) 2:3
(B) 1:1
(C) 3:4
(D) 4:3
(E) 5:5
Rationale: 5/100A+4/100B = 2/3(6/100A+8/100B)
=>1/20A+1/25B= 1/25A+4/75B
=> (1/20-1/25)B= 1/25A+4/75B
(1/20-1/25)A = (4/75-1/25)B
1/100A=1/75B
A/B=100/75=4/3
REQ RATIO = 4:3
ANSWER D
Answer: (D) 4:3
Question: A number consists of two digits. The sum of the digits is 9. If 63 is subtracted from the number, its digits are interchanged. Find the number.
(A) 81
(B) 90
(C) 100
(D) 61
(E) 73
Rationale: Let the ten's digit be x. Then, unit's digit = (9 - x).
Number = l0x + (9 - x) = 9x + 9.
Number obtained by reversing the digits = 10 (9 - x) + x = 90 - 9x.
therefore, (9x + 9) - 63 = 90 - 9x => 18x = 144 => x = 8.
So, ten's digit = 8 and unit's digit = 1.
Hence, the required number is 81.
Answer A)81.
Answer: (A) 81
Question: The number 219 can be written as sum of the squares of 3 different positive integers. What is the difference of these 2 different larger integers?
(A) 6
(B) 2
(C) 3
(D) 5
(E) 4
Rationale: sum of the squares of 3 different positive integers = 219
13^2 + 7^2 + 1^2 = 219
now,
difference of these 2 different larger integers = 13 - 7 = 6
Ans - A
Answer: (A) 6
Question: Brand A coffee costs twice as much as brand B coffee. If a certain blend is 3/4 brand A and 1/4 brand B. what fraction of the cost of the blend is Brand A?
(A) a. 1/3
(B) b. 2/5
(C) 3. 1/2
(D) 4. 2/3
(E) 5. 6/7
Rationale: Assume Cost of A= Ca = 200 , Cost of B = Cb=100
The blend contains 0.75 A and 0.25 B ---> Cost of the blend = Cbl = 0.75*200+0.25*100= 175
Thus fraction of A in the blend = 0.75*200/175 = 6/7.
Answer : E
Answer: (E) 5. 6/7
Question: A car manufacturer produces only red and blue TCS Models which come out of the final testing area at random. What are the odds that five consecutive cars of same color will come through the test area at any one time?
(A) 1 in 16
(B) 1 in 125
(C) 1 in 32
(D) 1 in 25
(E) 1 in 15
Rationale: p(5 consecutive cars of same color)=p(5 red)+p(5 blue)
=1/2^5+1/2^5
=1/16
ANSWER:A
Answer: (A) 1 in 16
Question: In a rectangular coordinate system, what is the area of a quadrilateral whose vertices have the coordinates (2,-2), (2, 6), (14, 2), (14,-5)?
(A) 90
(B) 95
(C) 104
(D) 117
(E) 182
Rationale: By graphing the points, we can see that this figure is a trapezoid. A trapezoid is any quadrilateral that has one set of parallel sides, and the formula for the area of a trapezoid is:
Area = (1/2) × (Base 1 + Base 2) × (Height), where the bases are the parallel sides.
We can now determine the area of the quadrilateral:
Area = 1/2 × (8 + 7) × 12 = 90.
The answer is A.
Answer: (A) 90
Question: Find the income derived from 88 shares of $ 25 each at 5 premium,
brokerage being (1/4) per share and the rate of dividend being 7(1/2)% per annum. Also, find the rate of interest on the investment.
(A) 6.2%
(B) 7.5%
(C) 6.5%
(D) 8.2%
(E) 4.6%
Rationale: Cost of 1 share = $ [25+5+1/4)] = $ (121/4).
Cost of 88 shares = $[(121/4)*88] = $ 2662.
Therefore Investment made = $ 2662.
Face value of 88 shares = $ (88*25) = $ 2200.
Dividend on $ 100 = (15/2).
Dividend on $ 2200 = $ [(15/20*(1/100)*2200] = $ 165.
 Income derived = $ 165.
Rate of interest on investment = [(165/2662)*100] = 6.2 %.
Answer A.
Answer: (A) 6.2%
Question: In 1 kg mixture of iron and manganese 20% of manganese. How much iron should be added so that
the proportion of manganese becomes 10%
(A) 1.5 Kg
(B) 2 Kg
(C) .5 Kg
(D) 1 Kg
(E) None of these
Rationale: Explanation :
By the rule of alligation, we have
Percentage concentration of
manganese in the mixture : 20 Percentage concentration of
manganese in pure iron : 0
Percentage concentration of manganese in the final mixture
10
10 - 0 = 10 20 - 10 = 10
=> Quantity of the mixture : Quantity of iron = 10 : 10 = 1 : 1
Given that Quantity of the mixture = 1 Kg
Hence Quantity of iron to be added = 1 Kg
Answer : Option D
Answer: (D) 1 Kg
Question: A fair white coin with sides marked heads and tails is to be tossed eight times. What is the probability that the coin will land tails side up more than five times?
(A) A)37/256
(B) B)56/256
(C) C)65/256
(D) D)70/256
(E) E)81/256
Rationale: Landing on tails more than 5 times means tails has to hit 6, 7 or 8 times.
8!/6!2! = 7*4 = 28
8!/7!1! = 8
8!/8! = 1
28 + 8 + 1 = 37/256
ans:A
Answer: (A) A)37/256
Question: The owner of a local jewelry store hired four watchmen to guard his diamonds, but a thief still got in and stole some diamonds. On the way out, the thief met each watchman, one at a time. To each he gave 1/4 of the diamonds he had then, and 4 more besides. He escaped with 4 diamonds. How many did he steal originally?
(A) 4384
(B) 3384
(C) 2384
(D) None of these
(E) Cannot be determined
Rationale: Explanation :
Since, thief escaped with 4 diamonds,
Before 4th watchman, he had ( 4 + 4 ) x 4 = 32 diamonds.
Before 3rd watchman, he had (32+ 4 ) x 4 = 144 diamonds.
Before 2nd watchman, he had ( 144 + 4 ) x 4 = 592 diamonds.
Before 1st watchman, he had ( 592 + 4 ) x 4 = 2384 diamonds.
Answer : C
Answer: (C) 2384
Question: 5 + 5 + 5 + 5 +5 + 4 x 5^2 + 4 x 5^3 + 4 x 5^4 + 4 x 5^5 + 4 x 5^6 + 4 x 5^7 + 4 x 5^8 + 4 x 5^9 =
(A)  5^20
(B)  5^18
(C)  5^14
(D)  5^10
(E)  None of above
Rationale: Let's see that 5 + 5 + 5 + 5 +5 is 5^2, then: 5^2 + 4 x 5^2 becomes 5 x 5^2 that is 5^3. You follow with the next element: 5^3 + 4 x 5^3 is equal to 5 x 5^3 that is 5^4. Then is assumed right before 4 x 5^9: 5^9 + 4 x 5^9 becomes 5 x 5^9 that is 5^10. Thus, the correct answer is the option D, 5^10.
Answer: (D)  5^10
Question: A shipment of 1500 heads of cabbage, each of which was approximately the same size, was purchased for $600. The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head. The following day the rest were sold at a price equal to 15% less than the price each head sold for on the day before. What was the total gross profit on this shipment.
(A) $113
(B) b $115
(C) c $125
(D) d $130
(E) e $135
Rationale: Purchase cost = 600/1500= $ 0.4
25% above the cost per head = (125/100)*0.4= $ 0.5
2/3 of the heads were sold means 2/3*1500 =1000 ,Selling amount for 1000 cabbage = 1000 * 0.5 = $ 500
Remaining were sold at a price equal to 15% less than the price each head sold for on the day before i.e , (85/100)*0.5 = $ 0.425
Hence selling cost for the remaining cabbage = 500 * 0.425 = $ 212.5
Total selling cost = 500 + 213 = $ 713
Gross profit = $ 713 - $ 600 = $ 113
Hence Answer is A.
Answer: (A) $113
Question: A rectangular park 60 m long and 40 m wide has 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) 338
(B) 278
(C) 260
(D) 278
(E) 111
Rationale: Answer:B
Answer: (B) 278
Question: Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 5 cm and 4 cm?
(A) 189 cm2
(B) 150 cm2
(C) 127 cm2
(D) 177 cm2
(E) 90 cm2
Rationale: 1/2 * 20(5 + 4)
= 90 cm2
Answer: E
Answer: (E) 90 cm2
Question: If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will be divisible by 11 ?
(A) 4x+6y
(B) x+y+4
(C) X+2
(D) 4X-9Y
(E) Y-5
Rationale: Explanation:
By hit and trial, we put x = 5 and y = 1 so that (3x + 7y) = (3 x 5 + 7 x 1) = 22, which is divisible by 11.
(4x + 6y) = ( 4 x 5 + 6 x 1) = 26, which is not divisible by 11;
(x + y + 4 ) = (5 + 1 + 4) = 10, which is not divisible by 11;
(9x + 4y) = (9 x 5 + 4 x 1) = 49, which is not divisible by 11;
(4x - 9y) = (4 x 5 - 9 x 1) = 11, which is divisible by 11.
ANSWER:D
Answer: (D) 4X-9Y
Question: The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?
(A) 76 Kmph
(B) 68 Kmph
(C) 86 Kmph
(D) 45 Kmph
(E) 56 Kmph
Rationale: Length of the two trains = 600m + 400m
Speed of the first train = X
Speed of the second train= 48 Kmph
1000/X - 48 = 180
1000/x - 48 * 5/18 = 180
50 = 9X - 120
X = 68 Kmph
Answer:B
Answer: (B) 68 Kmph
Question: Mike, Jim and Bob are all professional fisherman. Mike can catch 18 fish in one hour, Jim can catch twice as much and Bob can catch 50% more than Jim. If the three started to fish together and after 40 minutes Mike and Bob left, how many fish did the three fishermen catch in one hour?
(A) 84.
(B) 72.
(C) 86.
(D) 98.
(E) 112.
Rationale: All of them catch fishes in relation to number 18....
2/3*18+2*18+2*1.5*18*2/3=84
Answer is A
Answer: (A) 84.
Question: Two athletes starting from same place walk in the same direction at a rate of 8 km/hr and 6 km/hr. What time will they take to be 10 km apart ?
(A) 10 hours
(B) 15 hours
(C) 5 hours
(D) 4 hours
(E) None of these
Rationale: Explanation :
The relative speed of athletes = 8-6 = 2 km/hr.
Distance between them = 10 km
Time=10/2 = 5 hours
Answer : C
Answer: (C) 5 hours
Question: Using all the letters of the word "NOKIAS", how many words can be formed, which begin with N and end with S?
(A) 24
(B) 80
(C) 160
(D) 80
(E) 100
Rationale: There are five letters in the given word.
Consider 6 blanks ....
The first blank and last blank must be filled with N and S all the remaining three blanks can be filled with the remaining 5 letters in 5! ways.
The number of words = 5! = 120.
Answer: A
Answer: (A) 24
Question: Series till 50 terms: 2+3-5 +2+3-5+.
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 2+3-5 +2+3-5 +2+3-5 +2+3-5 +2+3-5 +2+3-5 +2+3-5 +2+3-5 +2+3-5.........+2+3.
series is repeat +2 +3 -5 continously..
So, till 48th term it will repeat +2+3-5..
49th term = +2
50thterm = +3
ANSWER:A
Answer: (A) 3
Question: Anil brought a scooter for a certain sum of money. He spent 10% of the cost on repairs and sold the scooter for a profit of Rs. 1100. How much did he spend on repairs if he made a profit of 20%?
(A) 220
(B) 420
(C) 250
(D) 700
(E) 500
Rationale: E
C.P. be Rs. x. Then, 20% of x = 1100
20/100 * x = 1100 => x = 5500
C.P. = Rs. 5500, expenditure on repairs = 10%
Actual price = Rs. (100 * 5500)/110 = Rs. 5000
Expenditures on repairs = (5500 - 5000) = Rs. 500.
Answer: (E) 500
Question: The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is
(A) 76.5
(B) 36.5
(C) 46.5
(D) 16.5
(E) 26.5
Rationale: Explanation:
Correct Sum = (36 * 50 + 48 - 23) = 1825.
Correct mean = = 1825/50 = 36.5
Answer: B
Answer: (B) 36.5
Question: The roof of an apartment building is rectangular and its length is 5 times longer than its width. If the area of the roof is 720 feet squared, what is the difference between the length and the width of the roof?
(A) 38.
(B) 40.
(C) 42.
(D) 44.
(E) 48.
Rationale: Answer is E : 48
Let w be the width , so length is 5w. Therefore : w*5w = 720, solving for, w = 12 , so 5w-w = 4w = 4*12 = 48
Answer: (E) 48.
Question: Paul's income is 40% less than Rex's income, Quentin's income is 20% less than Paul's income, and Sam's income is 40% less than Paul's income. If Rex gave 40% of his income to Sam and 60% of his income to Quentin, Quentin's new income would be what fraction of Sam's new income?
(A) 	11/12
(B) 	13/17
(C) 	13/19
(D) 	12/19
(E) 	27/19
Rationale: MAKE R = 10
P = 0.6R = 6
Q = 0.8P = 4.8
S= 0.6P = 3.6
FOR THAT WE GET S = 7.6
AND Q 10.8
SO 10.8/7.6 = 2.7/ 1.9
Ans:E
Answer: (E) 	27/19
Question: Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) 19
(B) 19.7
(C) 21
(D) 23
(E) 24
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
B
Answer: (B) 19.7
Question: A and B together can complete a work in 3 days. They start together but after 2 days,B left the work.If the work is completed after two more days, find the B alone could do the work?
(A) 8
(B) 20
(C) 6
(D) 21
(E) 10
Rationale: A and B(one day work)=1/3 part
(A+B) works 2 days together=2/3 part
Remaining work=1-(2/3) part=1/3 part
1/3 part of the work is completed by A in two days=(1/3)*(1/2)
One day's work of A=1/6 part
One day's work of B=(1/3)-(1/6)=1/6
So,B alone can do the work in 6 days
Answer is option C
Answer: (C) 6
Question: Train C and D, 455 miles apart, are traveling toward each other at constant rates and in the same time zone. If train C left at 4 pm traveling at a speed of 60 miles per hour, and train D left at 5:45 pm and traveling at 45 miles per hour, then at what time would they pass each other?
(A) 9:05 pm
(B) 9:06 pm
(C) 9:07 pm
(D) 9:08 pm
(E) 9:09 pm
Rationale: First, since C has a headstart then in that 1hr45min or 1.75hrs he travels 105 miles
Then remaining distance to be traveled will be 455 - 105 = 350 miles
Now, using relative rates (105)(t) = 350
This gives 10/3 hours
Now 5.45pm + 10/3 hours gives us 9.05pm
Hence answer is A
Answer: (A) 9:05 pm
Question: Find the average of the series : 312, 162, 132, 142 and 122?
(A) 298
(B) 269
(C) 927
(D) 174
(E) 291
Rationale: Average = (312 + 162 + 132 + 142 + 122)/5 = 870/5 = 174.Answer: D
Answer: (D) 174
Question: During one month at a particular restaurant, 1/6 of the burgers sold were veggie burgers and 1/5 of the rest of the burgers sold were double-meat. If x of the burgers sold were double-meat, how many were veggie burgers?
(A) x
(B) x/2
(C) 2x/3
(D) 3x/4
(E) 4x/5
Rationale: T/6 - Veggi
(1/5)[T - (T/6)] = double meat = x = 5T/30
=> Veggie = T/6 = 5x/5=x
Answer is A.
Answer: (A) x
Question: In case M is the only individual sewing on committee B, which among the following shouldserve on committee A?
(A) V and U
(B) V and T
(C) U and S
(D) N and O
(E) T and U
Rationale: N and O should serve on A
ANSWER:D
Answer: (D) N and O
Question: When 2/3 of the garments in the shipment were inspected, 15 of the garments passed inspection and the remaining 5 garments failed. How many of the uninspected garments must pass inspection in order that 80 percent of the garments in the shipment pass?
(A) 10
(B) 9
(C) 8
(D) 7
(E) 5
Rationale: B = 9
2/3x= 20
x=30
for 80% approval we need 24 garments approved.
already approved = 15
we need 9 more.
Answer : B
Answer: (B) 9
Question: If w<0, which of the following must be true?
(A) –100 < w < 100
(B) w ≤ –1
(C) w ≤ 1
(D) w^2 ≥ 1/4
(E) –100 < w < 0
Rationale: w is a negative number.
A. –100 < w < 100w can be a negative number less than -100
B. w ≤ –1w can be a fraction, in which case it would be greater than -1
C. w ≤ 1must be true since 1 is positive and w is negative
D. w^2 ≥ 1/4not true if w is a negative fraction like -1/5
E. –100 < w < 0w can be a negative number less than -100=C
Answer: (C) w ≤ 1