mathewhe/aqua_rat huggingface dataset:
Question: Which of the following leads to the correct mathematical solution for the number of ways that the letters of the word SUCCESS could be arranged to create a seven-letter code?
(A) 6!
(B) 6! − (3! + 2!)
(C) 7!/(3! × 2!)
(D) 7!/(3! + 2!)
(E) 8!/(2! x 2!)
Rationale: Number of letters in word 'SUCCESS' = 7.
The letters 'S' and 'C' appear 3 times and 2 times respectively in the word 'SUCCESS'.
Therefore the mathematical solution for number of ways that the letters of the word SUCCESS can be arranged to create seven-letter code
= 7!/(3!*2!)
Answer:C
Answer: (C) 7!/(3! × 2!)
Question: The average of first 32 natural numbers is?
(A) 16.5
(B) 17.5
(C) 18.4
(D) 15.4
(E) 15.1
Rationale: Sum of 32 natural no. = 1056/2 = 55
Average = 528/32 = 16.5
Answer:A
Answer: (A) 16.5
Question: A boat ma goes 2km against the current of the stream in 1 hr and goes 1 km along the current in 10 min. how long will it take to go 8 km in stationary water
(A) 40 min
(B) 1hr
(C) 1hr 15 min
(D) 1hr 30 min
(E) 2 hr
Rationale: rate down stream=(1/10*60)km/hr=6km/hr
rate up stream=2km/hr
speed still water =1/2(6+2)=4km/hr
required time =(8/4)=3 hr
Answer(E)
Answer: (E) 2 hr
Question: A rectangular lawn of length 50 m and breadth 35 m is to be surrounded externally by a path which is 2 m wide. Find the cost of turfing the path at the rate of $3 per m².
(A) $1008
(B) $1031
(C) $1028
(D) $1068
(E) $1088
Rationale: Length of the lawn = 50 m
Breadth of the lawn = 35 m
Area of the lawn = (50 × 35) m²
= 1750 m²
Length of lawn including the path = [50 + (2 + 2)] m = 54 cm
Breadth of the lawn including the path = [35 + (2 + 2)] m = 39 m
Area of the lawn including the path = 54 × 39 m² = 2106 m²
Therefore, area of the path = (2106 - 1750) m² = 356 m²
For 1 m², the cost of turfing the path = $ 3
For 356 m², the cost of turfing the path = $3 × 356 = $1068
ANSWER : D
Answer: (D) $1068
Question: A boy can reach a certain place in 45 hours. If he reduces his speed by 1/30th, he goes 3 km less in that time. Find his speed.
(A) 2 km/hr.
(B) 6 km/hr
(C) 8 km/hr
(D) 14 km/hr
(E) None of these
Rationale: Explanation :
Solution: Let the speed be x km/hr. then,
45x - (45 * 29x/30) = 3
=> 3/2X =3
X=2
A
Answer: (A) 2 km/hr.
Question: One-fourth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/20 of the non defective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?
(A) 4.4%
(B) 5.5%
(C) 6.6%
(D) 11.3%
(E) 16.2%
Rationale: 1/4 of the switches are defective.
The defective switches that are not rejected are 1/5*1/4 = 1/20 = 4/80 of all switches.
The non defective switches that are sold are 3/4*19/20 = 57/80 of all switches.
The percent of switches sold that are defective is 4/61 = 6.6%
The answer is C.
Answer: (C) 6.6%
Question: If P(A) = 2/15, P(B) = 4/15, and P(A âˆª B) = 6/15 Find P(B|A)
(A) 1/2
(B) 2/3
(C) 3
(D) 4/5
(E) 4/7
Rationale: P(B|A) = P(A âˆª B)/P(A)
P(B|A) = (6/15)/(2/15) = 3.
C
Answer: (C) 3
Question: A train running at the speed of 60 km/hr crosses a pole in 12 seconds. Find the length of the train.
(A) 150
(B) 278
(C) 179
(D) 200
(E) 191
Rationale: :
Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 12 = 200 meter
Answer:D
Answer: (D) 200
Question: The average number of visitors of a library in the first 4 days of a week was 58. The average for the 2nd, 3rd, 4th and 5th days was 60.If the number of visitors on the 1st and 5th days were in the ratio 7:8 then what is the number of visitors on the 5th day of the library?
(A) 17
(B) 17
(C) 64
(D) 19
(E) 01
Rationale: If number of visitors on 1st, 2nd, 3rd, 4th & 5th day are a, b, c, d & e respectively, then
a + b + c + d = 58 × 4 = 232 ----(i) &
b + c + d + e = 60 × 4 = 240 ----(ii)
Subtracting (i) from (ii), e – a = 8 ---(iii)
Given
a/e=7/8 ---(iv)
So from (iii) & (iv) a=56, e=64
Answer:C
Answer: (C) 64
Question: A computer manufacturer produces a certain electronic component at a cost of $70 per component. Shipping costs for delivering the components are $4 per unit. Further, the manufacturer has costs of $14,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 250 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?
(A) 132
(B) 138
(C) 144
(D) 128
(E) 116
Rationale: $14500 is a fixed cost
Each component is $74 ($70 to produce, $4 to ship)
Manufacturer will be producing and selling 250 components
so therefore the equation to find price would be
250*p = 14500+(250*70)+(250*4)
p = (14500+17500+1000)/250
p = 132
Answer:A
Answer: (A) 132
Question: The sum of three consecutive even numbers is 30. Find the middle number of the three?
(A) 14
(B) 16
(C) 18
(D) 25
(E) 34
Rationale: Three consecutive even numbers (2P - 2), 2P, (2P + 2).
(2P - 2) + 2P + (2P + 2) = 30
6P = 30 => P = 5.
The middle number is: 5P = 25.
ANSWER:D
Answer: (D) 25
Question: If p is a positive integer and 10p/96 is an integer, then the minimum number of unique prime factors p could have is L:
(A) L=1
(B) L=2
(C) L=3
(D) L=4
(E) 5
Rationale: 10p/96 should resolve to a integer => 5p/48 should resolve to an integer.
Hence p/48 should resolve to a integer.
48 -- > 2^4 * 3.
Hence p should have atleast 2^4*3 for p/48 to resolve to a int.
The unique prime factors in 2^4 * 3 is 2, 3 and hence the answer is B(2).
Answer: (B) L=2
Question: The original price of a camera was displayed as a whole dollar amount. After adding sales tax of 15 percent, the final price was also a whole dollar amount. Which of the following could be the final price of the camera?
(A) $207
(B) $210
(C) $230
(D) $213
(E) $215
Rationale: Final price = (1+15/100) * Original Price
= 1.15 * Original Price
From options given only 230 is divisible by 1.10 as it is stated OP is whole dollar amount.
Hence C
Answer: (C) $230
Question: How many positive three-digit integers are divisible by both 3 and 7?
(A) 43
(B) 45
(C) 47
(D) 50
(E) 52
Rationale: A number to be divisible by both 3 and 7 should be divisible by the least common multiple of 3 and 7 so by 21.
Multiples of 21 between 100 and 999, inclusive is
(last-first)/multiple+1=(987-105)/21+1=42+1=43
Answer: A.
Answer: (A) 43
Question: Three partners A,B,C start a business.A invested 3000 for 8 month,B invested
4000 for 9 month.and C invested 5000 for 1 years.at the end of year there is total profit of 15000 rs.what is profit share of B?
(A) 3000
(B) 4500
(C) 4000
(D) 4200
(E) 3500
Rationale: ratio of A,B,C investment=(3000*8):(4000*9):(5000*12)
=24000:36000:60000=2:3:5.
Total annual profit=15000 rs.
profit share of B=15000*3/10=4500rs.
answer B
Answer: (B) 4500
Question: If p/q = 5/4 , then 2p+q= ?
(A) 12
(B) 14
(C) 13
(D) 15
(E) 16
Rationale: let p=5, q=4 then 2*5+4=14
so 2p+q=14.
ANSWER:B
Answer: (B) 14
Question: A sum of money at simple interest amounts to $ 815 in 3 years and to $854 in 4 years. The sum is:
(A) $153
(B) $698
(C) $398
(D) $549
(E) $675
Rationale: B
$698
S.I. for 1 year = $(854 - 815) = $39.
S.I. for 3 years = $(39 x 3) = $117.
Principal = $(815 - 117) = $698.
Answer: (B) $698
Question: When n is divided by 19, the remainder is 7. Find thee difference between previous remainder and the remainder when 18n is divided by 9 ?
(A) 7
(B) 5
(C) 0
(D) 3
(E) 9
Rationale: Let n=7 (leaves a remainder of 7 when divided by 19)
18n = 18(7) =126, which leaves a remainder of 0 when divided by 9.
difference = 7 - 0 = 7.
Answer A
Answer: (A) 7
Question: There are 437 doctors and nurses in a hospital. If the ratio of the doctors to the nurses is 8 : 11, then how many nurses are there in the hospital?
(A) 152
(B) 253
(C) 57
(D) 171
(E) 181
Rationale: Given,
The ratio of the doctors to the nurses is 8 : 11
Number of nurses = 11/19 x 437 = 253
ANSWER:B
Answer: (B) 253
Question: In how many ways can live boys and three girls sit in a row such that all boys sit together?
(A) 3877
(B) 2778
(C) 2880
(D) 2987
(E) 1231
Rationale: Explanation:
Treat all boys as one unit. Now there are four students and they can be arranged in 4! ways. Again five boys can be arranged among themselves in 5! ways.
Required number of arrangements = 4! * 5! = 24 * 120 = 2880.
Answer: C
Answer: (C) 2880
Question: What is the median of a set of consecutive integers if the sum of nth number from the beginning and nth number from the end is 150?
(A) 10
(B) 25
(C) 50
(D) 75
(E) 100
Rationale: Surprisingly no one answered this easy one.
property of a set of consecutive integerz.
mean=median=(first element+last element)/2 = (second element+last but one element)/2 =(third element+ third last element)/2 Etc. Etc.
So mean=median=150/2=75
Answer is D
Answer: (D) 75
Question: Kiran has 85 currency notes in all, some of which were of Rs. 100 denomination and the
remaining of Rs. 50 denomination. The total amount of all these currency notes was Rs.
5000. How much amount did she have in the denomination of Rs. 50?
A. B. C. None of these D.
Answer: Option B
Explanation:
(A) 1900
(B) 3500
(C) 4000
(D) 2000
(E) 2500
Rationale: Let the number of 50 – rupee notes be x.
Then, the number of 100-rupee notes = (85 – x)
50x + 100(85 – x) = 5000
x + 2 (85 – x) = 100 = x=70
So, required amount = Rs. (50 x 70) = Rs. 3500 ANSWER :B
Answer: (B) 3500
Question: If 4 is the remainder when m is divided by 10, what is the remainder when 4m is divided by 10?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 0
Rationale: We can put m=10*k+4.
So 4*m=40*k+16 ---> 40*k+16 = 10*(4*m+1) +6 ---> The remainder is 6.
The answer is, therefore, (C).
Answer: (C) 6
Question: If the area of circle O is 16π, what is the length of an arc on the circle formed by a central angle measuring 45 degrees?
(A) π
(B) 3π/2
(C) 2π
(D) 5π/2
(E) 8π
Rationale: Area = 16π
Radius = 4
Circumference = 2 x 4 x π = 8π
Angle forming the arc = 45 degrees. 45/360 = 1/8.
Therefore length of arc = 1/8 * 8π = π - Answer choice A.
Answer: (A) π
Question: A number when divided by 296 leaves 75 as remainder. When the same number is divided by 37, the remainder will be:
(A) 1
(B) 5
(C) 3
(D) 4
(E) 11
Rationale: Let x = 296q + 75
= (37 x 8q + 37 x 2) + 1
= 37 (8q + 2) + 1
Thus, when the number is divided by 37, the remainder is 1.
ANSWER A
Answer: (A) 1
Question: Find the fourth proportional to 2.4, 4.6 and 7.6?
(A) 14
(B) 14.56
(C) 15.14
(D) 15.17
(E) 15.26
Rationale: Formula = Fourth proportional = (b × c)/a
A = 2.4 , B = 4.6 and C = 7.6
(4.6 × 7.6)/2.4 = 14.56
B
Answer: (B) 14.56
Question: Two goods trains each 250 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 24
(B) 45
(C) 48
(D) 51
(E) 44
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 250 + 250 = 500 m.
Required time = 500 * 6/125 = 24 sec.
Answer: Option A
Answer: (A) 24
Question: Find the sum of all 2 digit numbers divisible by 3.
(A) 1565
(B) 1665
(C) 1300
(D) 1448
(E) 1465
Rationale: All 2 digit numbers divisible by 3 are 12,15,18,21,……….. 99
This is an A.P with a = 12, and d = 3, Let it contain n terms
Then, 12 + (n – 1 ) *3 = 99, or n = ( 99-12) /3 + 1 = 30
Required sum = 30/2*( 12 + 99 ) = 15*111 = 1665
ANSWER:B
Answer: (B) 1665
Question: A restaurant serves 600 bowls of noodles for Rs. 12000 at a loss of Rs. 2 per bowl. Find the cost price for one bowl?
(A) 12
(B) 18
(C) 22
(D) 35
(E) 26
Rationale: SP per bowl = 12000/600 = Rs. 20 Loss per bowl = Rs. 2 CP per bowl = 20 + 2= Rs. 22Answer: C
Answer: (C) 22
Question: Entry fee is Re.1.there are 3 rides each is of Re.1. total boys entering are 3000.total income is Rs.7200. 800 students do all 3 rides. 1400 go for atleast 2 rides.none go the same ride twice. then no of students who do not go any ride is?
(A) 1328
(B) 1000
(C) 2378
(D) 8287
(E) 1872
Rationale: Total entries are 3000 So fee collected through entry fee = 3000 x 1 = Rs.3000
Income generated through rides = 7200 - 3000 = 4200
Now 800 went for 3 rides so total fee paid by these 800 = 800 x 3 = 2400
(1400 - 800) went for 2 rides so fee paid by these 600 = 600 x 2 = 1200
Assume K went for exactly 1 ride
Then K x 1 + 1200 + 2400 = 4200 ⇒⇒ K = 600
So number of boys who did not go for any ride = 3000 - (600 + 600 + 800 ) = 1000
Answer:B
Answer: (B) 1000
Question: A can do a piece of work in 80 days. He works at it for 10 days & then B alone finishes the remaining work in 42 days. In how much time will A and B, working together, finish the work?
(A) 30 days
(B) 20 days
(C) 25 days
(D) 35 days
(E) 45 days
Rationale: Work done by A in 10 days = 10/80 = 1/8
Remaining work = (1 - (1/8)) = 7/8
Now, work will be done by B in 42 days.
Whole work will be done by B in (42 x 8/7) = 48 days
Therefore, A’s one day’s work = 1/80
B’s one day’s work = 1/48
(A+B)’s one day’s work = 1/80 + 1/48 = 8/240 = 1/30
Hence, both will finish the work in 30 days.
ANSWER:A
Answer: (A) 30 days
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) 36.6
(B) 36.1
(C) 36.5
(D) 36.2
(E) 36.9
Rationale: Correct sum
= (36 * 50 + 48 - 23)
= 1825.
Correct mean
= 1825/50 = 36.5
Answer:C
Answer: (C) 36.5
Question: If Greg buys 3 shirts, 4 trousers and 2 ties, the total cost is $40. If Greg buys 7 shirts, 2 trousers and 2 ties, the total cost is $60. How much will it cost him to buy 3 trousers, 5 shirts and 2 ties?
(A) $50
(B) $64
(C) $75
(D) $96
(E) Cannot be determined
Rationale: Solution: 3x+4y+2z=40 7x+2y+2z=60
adding both the equations= 10x+6y+4z=100
5x+3y+2z=50
ans A
Answer: (A) $50
Question: How many combinations of three letters taken from letters (a, b, b, c, c, d,d) are possible?
(A) 4C3+4
(B) 4C3+9
(C) 4C3+2
(D) 4C3
(E) 4C3+6
Rationale: So 4C3 for abcd - 4 choices
3 more for dd(b,c or a)
3 more for bb(a,c or d)
3 more for cc(a,b or d)
total 4C3+9
Ans : B
Answer: (B) 4C3+9
Question: In how many ways can you seat 6 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end?
(A) 360
(B) 1720
(C) 2880
(D) 5040
(E) 10080
Rationale: Since Rohit does not want to sit on the middle seat or at either end (3 chairs), then he can choose 3 chairs to sit. The remaining 5 people can sit in 5! ways. Thus the # of arrangements is 3*5! = 360.
Answer: A.
Answer: (A) 360
Question: The area of a triangle is with base 8.4m and height 5.8m?
(A) 11.36 m2
(B) 10.36m2
(C) 18.36 m2
(D) 19.36 m2
(E) 24.36 m2
Rationale: 1/2 * 8.4 * 5.8
= 24.36 m2
Answer: E
Answer: (E) 24.36 m2
Question: 8 fruits are tpo kept on a table. A pair of oranges and apples must be kept together. in how many arrangements can the fruits be arranged?
(A) A.1296
(B) B.1850
(C) C.4200
(D) D.3546
(E) E.2880
Rationale: Glue pair of oranges and apples together: {AB}, {CD}.
6 units {AB}, {CD}, {E}, {F}, {G}, {H} can be arranged in 6! ways. Each couple within their unit can be arranged in 2! ways.
Therefore the final answer is 6!*2!*2!=2,880.
Answer: E.
Answer: (E) E.2880
Question: What is the perimeter of a rectangular field whose diagonal is 5m and length is 4m ?
(A) 20 m
(B) 15 m
(C) 14 m
(D) 10 m
(E) 25 m
Rationale: Sol:
Breadth of the rectangular plot is=5^2-4^2=3m
Therefore,
Perimeter of the rectangular plot= 2(4+3)=14m
C) 14m
Answer: (C) 14 m
Question: The average (arithmetic mean) of four different positive integers is 16. If the first of these integers in 3 times the second integer and the second integer is 2 less than the third integer, what is the least possible value of the fourth integer?
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
Rationale: Let the second integer be x and the fourth be a.
Then [3x + x + (x+2) + a]/4 = 16
=> 5x + 2 + a = 64
=> 5x + a = 62
=> a = 62 - 5x
From the above equation we can see that a is minimum when x is maximum, provided both are positive
The maximum value that x can take in the above equation while still keeping a positive is x=12
This gives us a= 62 - 60 = 2
Therefore the minimum value that the fourth integer can have is 2. Option D.
Answer: (D) 2
Question: John and Amanda stand at opposite ends of a straight road and start running towards each other at the same moment. Their rates are randomly selected in advance so that John runs at a constant rate of 3, 4, or 5 miles per hour and Amanda runs at a constant rate of 4, 5, 6, or 7 miles per hour. What is the probability that John has traveled farther than Amanda by the time they meet?
(A) 1/16
(B) 1/12
(C) 1/8
(D) 1/6
(E) 1/3
Rationale: John will run farther if he runs at 5 mph and Amanda runs at 4 mph.
P(John runs farther) = 1/3 * 1/4 = 1/12
The answer is B.
Answer: (B) 1/12
Question: Amber works 20 days a month at d dollars per day for m months out of the year. Which of the following represents her monthly pay?
(A) m/(20d)
(B) 20d
(C) 10md/6
(D) 20d/m
(E) 20md
Rationale: Total income of Amber in a year = d*20*m dollars.
Now Monthly income = Total/12 = d*20*m / 12 = 10md/6
Answer is C
Answer: (C) 10md/6
Question: Find the set of all points (x, y) such that the area of the triangle with vertices (0, 0), (6, 4) and (x, y) is 4.
(A) 3
(B) 9
(C) 7
(D) 8
(E) 2
Rationale: Explanation:
Area of a triangle if one of the point is (0, 0) = 12|(x1y2−x2y1)|12|(x1y2−x2y1)|
⇒ 12|(6×y−4×x)|12|(6×y−4×x)| = 4
⇒ 6y – 4x = 8
Answer: D
Answer: (D) 8
Question: In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?
(A) 2/7
(B) 3/7
(C) 4/8
(D) 9/2
(E) 3/8
Rationale: P (getting a prize) =	10/(10 + 25)= 10/35 =2/7	.
A
Answer: (A) 2/7
Question: The average of six numbers is S and the average of three of these is T.If the average of the remaining three is U, then
(A) S= T + U
(B) 2S= T + U
(C) S= 2T + 2U
(D) None of these
(E) Cannot ne determined
Rationale: Explanation :
Clearly, we have S =(3T+3U/6)
or 2S= T + U
Answer : B
Answer: (B) 2S= T + U
Question: 3889 + 15.952 - ? = 3854.002
(A) 47.95
(B) 50.95
(C) 45.97
(D) 47.59
(E) 45.79
Rationale: Let 3889 + 15.952 - x = 3854.002.
Then x = (3889 + 15.952) - 3854.002
= 3904.952 - 3854.002
= 50.95.
Answer is B
Answer: (B) 50.95
Question: October 9, 2012, fell on a Tuesday. On which day of the week did June 25, 2013, fall? (Note: 2012 was a leap year.)
(A) Sunday
(B) Monday
(C) Tuesday
(D) Wednesday
(E) Thursday
Rationale: The date range contains a partial year. The number of days in the partial year is:
October - 22, February - 28, November and April - 30, December, January, March, and May - 31, and June - 25.
22 + 28 + (2 * 30) + (4 * 31) + 25 = 259 total days in the date range.
Divide by 7 to determine how much the day of the week advances: 259 / 7 = 37 remainder 0.
Since the remainder is 0 the second date has the same day of the week as the first date.
Even though 2012 is a leap year, with 366 days, the extra day does not come into play unless the date range contains February 29. Since this did not occur, the extra day had no effect on the day of the week.
The answer is C.
Answer: (C) Tuesday
Question: When positive integer x is divided by 11, the quotient is y and the remainder is 4. When 2x is divided by 5, the quotient is 3y and the remainder is 4. What is the value of 4y – x ?
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
Rationale: (1) x = 11y + 4
(2) 2x = 15y + 4
Let's subtract equation (1) from equation (2).
4y = x
4y - x = 0
The answer is C.
Answer: (C) 0
Question: Two sides of a triangle have lengths q and y and meet at a right angle. If the perimeter of the triangle is 4q, what is the ratio of q to y ?
(A) a) 2 : 3
(B) b) 3 : 4
(C) c) 4 : 3
(D) d) 3 : 2
(E) e) 2 : 1
Rationale: Ahhhh....my bad. Thank you, you're correct. 8q = 6y --> q/y = 3/4.
Actually B is the right answer.
Answer: (B) b) 3 : 4
Question: If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players?
(A) 1243
(B) 1345
(C) 1788
(D) 1346
(E) 1365
Rationale: A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players.
=. Required number of ways = 14C10 = 14C4
= 14!/4!x19! = 1365
E
Answer: (E) 1365
Question: What is the minimum value of |x-4| + |x+2| + |x-5| ?
(A) -3
(B) 3
(C) 5
(D) 7
(E) 8
Rationale: A cannot be the answer as all the three terms are in modulus and hence the answer will be non negative.
|x-4| >= 0 --> Minimum occurs at x = 4
|x+2| >= 0 --> Minimum occurs at x = -2
|x-5| >= 0 --> Minimum occurs at x = 5
x = -2 --> Result = 6 + 0 + 7 = 13. Also any negative value will push the combined value of |x-4| + |x-5| to a value > 9.
x = 4 --> Result = 0 + 6 + 1 = 7
x = 5 --> Result = 1 + 7 + 0 = 8
x = 2 --> Result = 2 + 4 + 3 = 9
So minimum value of the expression occurs at x = 4 and the resultant value = 7
Answer: D
Answer: (D) 7
Question: Which of the following ratios is greatest ?
(A) 7 :15
(B) 15 :23
(C) 17 :25
(D) 21 :29
(E) 1 : 2
Rationale: 7/15 = 0.466,
15/23 = 0.652,
17/25 = 0.68
21/29 = 0.724
Clearly, 0.724 is greatest
therefore, 21 : 29 is greatest
ANSWER:D
Answer: (D) 21 :29
Question: If f(a)=a^2, what is the value of (f(a-b)−f(a))/b ?
(A) a
(B) b
(C) 2a
(D) -2a + b
(E) 2b - a
Rationale: start with f(a+b) before start calculations: f(a-b)=(a-b)^2= a^2-2ab+b^2
a^2-2ab+b^2 - a^2/b = (simplify a^2)
-2ab+b^2/b = (cancel b's)
= -2a+b
Ans : D
Answer: (D) -2a + b
Question: 36.	A 240 m long train crosses a platform of equal length in 27 s. What is the speed of the train in km/h?
(A) 48
(B) 60
(C) 56
(D) 64
(E) 68
Rationale: By the formula, speed= Distance/ Time
= (240 + 240)/27 x (18/5)
= 480/27 x 18/5 = 64 km/h
Answer :D
Answer: (D) 64
Question: A vessel of capacity 2 litre has 20% of alcohol and another vessel of capacity 6 litre had 40% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. What is the new concentration of Mixture?
(A) 31%.
(B) 71%.
(C) 49%.
(D) 29%.
(E) 28%.
Rationale: 20% of 2 litres = 0.4 litres
40% of 6 litres = 2.4 litres
Therefore, total quantity of alcohol is 2.8 litres.
This mixture is in a 10 litre vessel. Hence, the concentration of alcohol in this 10 litre vessel is 28%
ANSWER:E
Answer: (E) 28%.
Question: Smita Was Making A Cube With Dimensions 5*5*5 Using 1*1*1 Cubes. What Is The Number Of Cubes Needed To Make A Hollow Cube Looking Of The Same Shape?
(A) 98
(B) 104
(C) 100
(D) 61
(E) 51
Rationale: cube use to make perfect 5 * 5 * 5 = 125
No need of cube to make hollow=(5-2)*(5-2)*(5-2)=27
so total cube need to make hollow cube is=125-27 =98
ANSWER:A
Answer: (A) 98
Question: Working alone, printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 15, 10, and 20 hours, respectively. What is the ratio of the time it takes printer X to do the job, working alone at its rate, to the time it takes printers Y and Z to do the job, working together at their individual rates?
(A) 5/2
(B) 8/3
(C) 9/4
(D) 10/3
(E) 12/5
Rationale: The time it takes printer X is 15 hours.
The combined rate of Y and Z is 1/10 + 1/20 = 3/20
The time it takes Y and Z is 20/3
The ratio of times is 15 / (20/3) = 3*15/20 = 9/4
The answer is C.
Answer: (C) 9/4
Question: Alice walked for 3 days. She walked 18 miles on the first day, walking 3 miles per hour. On the second day she walked for one less hour but she walked one mile per hour, faster than on the first day. On the third day she walked the same number of hours as on the first day, but at the same speed as on the second day. How many miles in total did she walk?
(A) 24
(B) 44
(C) 58
(D) 60
(E) 62
Rationale: Alice walked 18 miles on the first day, walking 3 miles per hour i.e. total time of walk on Day-1 = 18/3 = 6 Hours
Second day time of walk = 6-1 = 5 hours and Speed = 3+1=4 miles per hour i.e. Distance walked on second day = 5*4 = 20 miles
Third day time of walk = 6 hours and Speed = 4 miles per hour i.e. Distance walked on second day = 6*4 = 24 miles
Total Distance travelled on three days = 18+20+24 = 62
Answer: Option E
Answer: (E) 62
Question: A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?
(A) 2500
(B) 3000
(C) 3500
(D) 4000
(E) 4500
Rationale: A:B:C = 2/3:1/6:1/6 = 4:1:1
x * 2/100 * 2/3 = 200
B capital = 15000*1/6 = 2500
ANSWER A
Answer: (A) 2500