mathewhe/aqua_rat huggingface dataset:
Question: A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is:
(A) 4 mph
(B) 2.5 mph
(C) 3 mph
(D) 2 mph
(E) None of these
Rationale: Explanation :
Speed of the boat in still water = 10 mph
Let speed of the stream be x mph
Then, speed downstream = (10+x) mph
speed upstream = (10-x) mph
Time taken to travel 36 miles upstream - Time taken to travel 36 miles downstream = 90/60 hours
=>36/(10−x) − 36/(10+x) = 3/2
=>12/(10−x) − 12/(10+x) = 1/2
=>24(10 + x) − 24(10 − x) = (10 + x)(10 − x)
=>240 + 24x − 240 + 24x = (100−x2)
=>48x = 100 − x2
=>x2 + 48x − 100 =0
=>(x+50)(x−2)=0
=> x = -50 or 2. Answer : Option D
Answer: (D) 2 mph
Question: The present ages of three persons are in proportions 4:7:9. Seven years ago, the sum of their ages was 79. Find their present ages.
(A) 20, 28
(B) 28, 36
(C) 35, 45
(D) 35, 55
(E) of these
Rationale: Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 7) + (7x - 7) + (9x - 7) = 79
20x = 100 => x = 5
Their present ages are 20, 35 and 45 years respectively.
ANSWER:C
Answer: (C) 35, 45
Question: A bag of blue and green colored marbles has 25% green marbles, with a total of 40 marbles. how many green marbles need to be added to bring their percentage in the bag up to 40%?
(A) 4
(B) 8
(C) 12
(D) 10
(E) 15
Rationale: A bag of 40 marbles which is 25% green marbles means we have 10 green marbles. To get a bag that is 40% green marbles, let's use this expression: (10 + x)/(40 + x) = 0.4 with x representing the amount of green marbles that must be added to get to 40%. The expression thus represents the new number of green marbles over the total new number of marbles in the bag and this fraction should equal 40%. only ten marbles need to be added, as 20/50=0.4 or 40%
choose D
Answer: (D) 10
Question: John can complete a given task in 20 days. Jane will take only 10 days to complete the same task. John and Jane set out to complete the task by beginning to work together. However, Jane was indisposed 5 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) 10
(C) 12
(D) 16
(E) 20
Rationale: In such questions, you need to start from the end. Last 5 days John works alone and completes 5 * (1/20) = 1/4 of the work.
So 3/4 of the work should have been completed by the two of them together before Jane left.
Their combined rate of work is 1/20 + 1/10 = 3/20
Time taken to complete 3/4 of the work = (3/4)/(3/20) = 5 days.
So total number of days taken to complete the work = 5 + 5 = 10 days.
B
Answer: (B) 10
Question: By selling 90 pens, a trader gains the cost of 30 pens. Find his gain percentage?
(A) 33.3%
(B) 32.3%
(C) 31.3%
(D) 30.3%
(E) 29.3%
Rationale: Let the CP of each pen be Rs. 1.
CP of 90 pens = Rs. 90
Profit = Cost of 30 pens = Rs. 30
Profit% = 30/90 * 100 = 33.3%
Answer:A
Answer: (A) 33.3%
Question: In how many ways can 5 arts and 3 science students be arranged in a row so that the arts and the science students are placed alternately?
(A) 2880
(B) 1850
(C) 326
(D) 720
(E) 360*120
Rationale: The five art students can be arranged in those 5 A-slots in 5! = 120 ways.
The three science students can be arranged in those 3 S-slots in 3! = 6 ways.
Total arrangements = 120*6 = 720
Answer =(D)
Answer: (D) 720
Question: What is the year next to 1990 which will have the same calendar as that of the year 1990?
(A) 1992
(B) 2001
(C) 1995
(D) 1996
(E) None of these
Rationale: Explanation :
For a year to have the same calendar with 1990 ,total odd days from 1990 should be 0.
Take the year 1992 from the given choices.
Total odd days in the period 1990-1991= 2 normal years
≡ 2 x 1 = 2 odd days
Take the year 1995 from the given choices.
Number of odd days in the period 1990-1994 = 4 normal years + 1 leap year
≡ 4 x 1 + 1 x 2 = 6 odd days
Take the year 1996 from the given choices.
Number of odd days in the period 1990-1995= 5 normal years + 1 leap year
≡ 5 x 1 + 1 x 2 = 7 odd days ≡ 0 odd days
(As we can reduce multiples of 7 from odd days which will not change anything)
Though number of odd days in the period 1990-1995 is 0, there is a catch here.
1990 is not a leap year whereas 1996 is a leap year.
Hence calendar for 1990 and 1996 will never be the same.
Take the year 2001 from the given choices.
Number of odd days in the period 1990-2000= 8 normal years + 3 leap years
≡ 8 x 1 + 3 x 2 = 14 odd days ≡ 0 odd days
Also, both 1990 and 2001 are normal years.
Hence 1990 will have the same calendar as that of 2001
Answer : Option B
Answer: (B) 2001
Question: The average of 5 consecutive integers starting with m as the first integer is n. What is the average of 11 consecutive integers that start with (m + 2)?
(A) m + 4
(B) n + 6
(C) n + 3
(D) n + 5
(E) n + 4
Rationale: The average of consecutive numbers is the middle number.
Then n = m+2.
The average of 11 consecutive numbers starting from n is n+5.
The answer is D.
Answer: (D) n + 5
Question: Arun and Tarun can do a work in 10 days.After 4 days tarun went to his village.How many days are required to complete the remaining work by Arun alone.Arun can do the work alone in 40 days.
(A) 16 days.
(B) 17 days.
(C) 18 days.
(D) 19 days.
(E) 24 days.
Rationale: They together completed 4/10 work in 4 days.
balance 6/10 work will be completed by Arun alone in 40*6/10 = 24 days.
ANSWER:E
Answer: (E) 24 days.
Question: A train 110 m long is running with a speed of 40 km/hr. In what time will it pass a man who is running at 5 km/hr in the direction opposite to that in which the train is going?
(A) 5
(B) 6
(C) 7.5
(D) 8.8
(E) 9
Rationale: Speed of train relative to man = 40 + 5 = 45 km/hr.
= 45 * 5/18 = 25/2 m/sec.
Time taken to pass the men = 110 * 2/25= 8.8 sec.
Answer: Option D
Answer: (D) 8.8
Question: If a man lost 10% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?
(A) 6.5
(B) 7.5
(C) 7
(D) 8
(E) 2
Rationale: 90% ---- 12
144% ---- ?
90/144 * 12 = 7.50
Answer: B
Answer: (B) 7.5
Question: What is the probability that Abel and Bob will get selected for a job they both applied for in a company, given that their chances of getting selected is 1/5 and 2/3 respectively?
(A) 2/15
(B) 2/11
(C) 2/17
(D) 2/13
(E) 2/19
Rationale: Explanation:
P(Abel) = 1/5
P(Bob) = 2/3
E = {Jamie and Tom both get selected}
P(E) = P(Abel)*P(Bob)
= 1/5 * 2/3
= 2/15
ANSWER: A
Answer: (A) 2/15
Question: If the average of 10x and 8y is greater than 70, and x is twice y, what is the least integer value of x ?
(A) 12
(B) 14
(C) 16
(D) 10
(E) 20
Rationale: Substitution can be used in the following way:
Always start with the equation: x = 2y. It is more straight forward to manage as compared to the inequality.
Substitute y = x/2, not the other way because you need to find the minimum value of x. So you can get rid of y.
Now go on to the inequality. So 8y = 8x/2 = 4x
Now average of 10x and 4x is greater than 70. Average of 10x and 4x is 7x. So,
7x > 70
x > 10
Answer : D
Answer: (D) 10
Question: Gary had an average score of 70 on his first four quizzes. He had an
average score of 75 on his first five quizzes. What score did he receive on
his fifth quiz?
(A) 90
(B) 95
(C) 65
(D) 42
(E) 43
Rationale: The sum of Gary's first 4 scores is 4 Â· 70 and the sum of his first 5 scores is 5 Â· 75, so he received
5 Â· 75 âˆ’ 4 Â· 70 on his 5th quiz. You can do the arithmetic or note that the answer ends in a 5 and eliminate answer C because it is lower than the average. The correct answer is B.
Answer: (B) 95
Question: A is half good a work man as B and together they finish a job in 10 days. In how many days working alone B finish the job?
(A) 23
(B) 22
(C) 15
(D) 36
(E) 48
Rationale: C
15
WC = 1:2
2x + x = 1/10 => x = 1/30
2x = 1/15 => 15 days
Answer: (C) 15
Question: 3x^2-6x+3 = 0 Find the above equation find the value of x
(A) 0
(B) 1
(C) 2
(D) 4
(E) 6
Rationale: a = 3, b = -6, c = 3
x1,2 = (6 ± √( (-6)2 - 4×3×3)) / (2×3) = (6 ± √(36-36)) / 6 = (6 ± 0) / 6
x1 = x2 = 1
B
Answer: (B) 1
Question: Pipe A can fill a tank in 8 hours, pipe B in 10 hours and pipe C in 40 hours. If all the pipes are open, in how many hours will the tank be filled?
(A) 2
(B) 2.5
(C) 3
(D) 4
(E) None
Rationale: Sol.
Part filled by (A + B + C) in 1 hour = (1/8 + 1/10 + 1/40) = 1/4.
âˆ´ All the three pipes together will fill the tank in 4 hours.
Answer D
Answer: (D) 4
Question: If the price of gold increases by 50%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before?
(A) 331/3%
(B) 332
(C) 333
(D) 335
(E) 400
Rationale: Explanation:
100
150
------
150-------50
100-------? => 331/3%
A)
Answer: (A) 331/3%
Question: Valentine day 14 Feb. 2005 was celebrated by Anand and shilpa on Monday. They were very happy. What day of the week would come on 14 Feb. 2010?
(A) monday
(B) tuesday
(C) sunday
(D) wednesday
(E) thursday
Rationale: feb 14 2005 - monday
feb 14 2006 - tuesday
feb 14 2007 - wednesday
feb 14 2008 - thursday
feb 14 2009 - saturday [since 2008 is leap year , 2 days ll go forward]
feb 14 2010 - sunday
ANSWER:C
Answer: (C) sunday
Question: The average of first 20 natural numbers is?
(A) 10.6
(B) 10.5
(C) 10.9
(D) 15.4
(E) 15.1
Rationale: Sum of 20 natural no. = 420/2 = 210
Average = 210/20 = 10.5
Answer:B
Answer: (B) 10.5
Question: A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?
(A) 200
(B) 350
(C) 270
(D) 874
(E) 125
Rationale: Explanation:
The number of ways to select two men and three women = 5C2 * 6C3
= (5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)
= 200
Answer: A
Answer: (A) 200
Question: The radius of a circle is increased by 1%. Find how much % does its area increases?
(A) 2.06%
(B) 2.91%
(C) 9.01%
(D) 2.01%
(E) 3.01%
Rationale: r = 100 r = 101
r2 = 10000 r2 = 10201
10000 ---- 201
100 ---- ? => 2.01%
Answer:D
Answer: (D) 2.01%
Question: What is 120% of 13/24 of 720?
(A) 372
(B) 434
(C) 468
(D) 512
(E) 564
Rationale: 120% * 13/24 * 360 = 1.2 * 13 * 30 = 468
The answer is C.
Answer: (C) 468
Question: In a certain experiment, the data collected is the number of organisms per sample, and this data follows a normal distribution. If the sample of data has a mean of 50 and a standard deviation of 12, which of the following is exactly 1.75 standard deviations more than the mean?
(A) a) 48
(B) b) 60
(C) c) 71
(D) d) 77.5
(E) e) 81
Rationale: Standard Deviation is a relatively rare category in the Quant section, although you're like to be tested on it 1 time on Test Day. You'll never be asked to calculate SD though, so you really just need to learn the basic 'concepts' behind it.
Here, we're told two things about a group of numbers:
1) The average of the group is 50
2) The standard deviation of the group is 12
If you go 1 SDupfrom the average, you hit.....50+12 = 62
If you go 1 SDdownfrom the average, you hit.....50-12 = 38
If you go 2 SDsupfrom the average, you hit.....50+2(12) = 74
If you go 2 SDsdownfrom the average, you hit.....50-2(12) = 26
Etc.
Here, we're asked for the number that is EXACTLY 1.75 SDs above the mean....
1.75 SDsupwould be.....50 + 1.75(12) = 71
C
Answer: (C) c) 71
Question: A contest will consist of n questions, each of which is to be answered eithertrueorfalse. anyone who answers all n questions correctly will be a winner. what is the least value of n for which the probability is less than 1/10000 that a person who randomly guesses the answer to each question will be a winner?
(A) 5
(B) 10
(C) 50
(D) 100
(E) 1000
Rationale: A contest will consist of n questions, each of which is to be answered eithertrueorfalse. anyone who answers all n questions correctly will be a winner. what is the least value of n for which the probability is less than 1/1000 that a person who randomly guesses the answer to each question will be a winner?
A.5
B.10
C.50
D.100
E.1000
Soln: ans is B
Probability that one question is answered right is 1/2.
Now for minimum number of questions needed to take probability less than 1/1000 is
=> (1/2)^n < 1/10000
n = 100 satisfies this.
D
Answer: (D) 100
Question: A palindrome is a number that reads the same forward and backward. For example. 2442 and 111 are palindromes. If 5-digit palindromes are formed using one or more of the digits, 1, 2, 3, how many such palindromes are possible?
(A) 12
(B) 15
(C) 18
(D) 24
(E) 27
Rationale: XYZYX
X can be 1, 2, or 3, thus 3 options.
Y can be 1, 2, or 3, thus 3 options.
Z can be 1, 2, or 3, thus 3 options.
Total 3^3=27.
Answer: E.
Answer: (E) 27
Question: A cylindrical container with 6 meters diameter and a height of 8 meters is filled to capacity with water. If the water is then used to fill several smaller cylinders (2 meters radius and 5 meters height), how many smaller cylinders can be filled to capacity before the larger cylinder becomes empty?
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
Rationale: Calculate the volume of the larger cylinder and divide it by the volume of the smaller cylinder.
volume of cylinder =πr2h
larger cylinder volume=226.19
smaller cylinder volume=62.83
therefore the number of smaller cylinders can be filled to capacity=226.19/62.83=3.6
Answer is C only 3 smaller cylinders can be filled to capacity.
Answer: (C) 3
Question: A committee of three people is to be chosen from 5 married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?
(A) 16
(B) 24
(C) 26
(D) 80
(E) 32
Rationale: One of the approaches:
Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) out of 5 to send only onerepresentativesto the committee:5C3=10.
But each of these 3 couples can send two persons (husband or wife): 2*2*2=2^3=8.
Total # of ways: 5C3*2^3=80.
Answer: D.
Answer: (D) 80
Question: Calculate the distance covered by 350 revolutions of a wheel of radius 25.3 cm.
(A) 558.6 m
(B) 556.6 m
(C) 516.6 m
(D) 156.6 m
(E) 256.6 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 350 resolutions.
=350 * 2 * 22/7 * 25.3 = 55660 cm = 556.6 m
ANSWER:B
Answer: (B) 556.6 m
Question: Find the number of different prime factors of 12800
(A) 4
(B) 2
(C) 3
(D) 5
(E) 6
Rationale: Explanation:
L.C.M of 12800 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5
2, 5
Number of different prime factors is 2.
Answer: Option B
Answer: (B) 2
Question: If f(x)= 5x^2- 2x+6 and g(y)= 3y-3, then g(f(x))
(A) 82x^2-9x+38
(B) 15x^2-6x+15
(C) 58x^2-4x+58
(D) 87x^2-5x+96
(E) 98x^2-7x+94
Rationale: g(f(x))=3(5x^2-2x+6)-3
=15x^2-6x+18-3
=15x^2-6x+15
the answer is B
Answer: (B) 15x^2-6x+15
Question: The parameter of a square is equal to the perimeter of a rectangle of length 40 cm and breadth 20 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)?
(A) 47.14
(B) 45.15
(C) 43.23
(D) 41.44
(E) 41.51
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(40 + 20) = 120 cm Parameter of the square = 120 cm
i.e. 4a = 120
a = 30
Diameter of the semicircle = 30 cm
Circimference of the semicircle
= 1/2(âˆ)(30)
= 1/2(22/7)(30) = 660/14 = 47.14 cm to two decimal places
Answer: A
Answer: (A) 47.14
Question: The average of marks obtained by 120 boys was 35. If the average of marks of passed boys was 39 and that of failed boys was 15, the number of boys who passed the examination is?
(A) 100
(B) 110
(C) 120
(D) 130
(E) 140
Rationale: Let the number of boys who passed = X.
Then, 39 x X + 15 x (120 - X) = 120 x 35
24X = 4200 - 1800
=> X = 2400/24
X = 100.
Hence, the number of boys passed = 100.
ANSWER:A
Answer: (A) 100
Question: The vertices of a rectangle in the standard (x,y) coordinate place are (0,0), (0,4), (8,0) and (8,4). If a line through (1,1) partitions the interior of this rectangle into 2 regions that have equal areas, what is the slope of this line?
(A) 1/3
(B) 2/5
(C) 4/7
(D) 1
(E) 7/4
Rationale: We should know that a rectangle can be divided into two equal areas by a straight line only when the straight line passes through the center of the rectangle.
The center of the rectangle is the point (4,2).
The slope of line passing through points (1,1) and (4,2) = (2-1)/(4-1) = 1/3
The answer is A.
Answer: (A) 1/3
Question: The speed of a train is 72 kmph. What is the distance covered by it in 20 minutes?
(A) 20 kmph
(B) 28 kmph
(C) 25 kmph
(D) 22 kmph
(E) 24 kmph
Rationale: 72 * 20/60
=24 kmph
Answer: E
Answer: (E) 24 kmph
Question: The average number of shirts with Salman, Ambani and Dalmiya is 60, if all of them reached a shopping mall in Delhi and purchased 1 shirts each of them then average number of shirt each of them now has
(A) 66
(B) 63
(C) 62
(D) 64
(E) 61
Rationale: Required average
= Old average + New average
= 60 + 1 = 61
answer :E
Answer: (E) 61
Question: What is the missing number in the series?
4,9,20,43,90,?
(A) 175
(B) 185
(C) 195
(D) 205
(E) 215
Rationale: 4*2+1=9
9*2+2=20
20*2+3=43
43*2+4=90
similarly 90*2+5=185
ANSWER:B
Answer: (B) 185
Question: The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A?
(A) 12
(B) 76
(C) 97
(D) 16
(E) 19
Rationale: (A + B) - (B + C) = 12
A - C = 12
Answer:A
Answer: (A) 12
Question: 337.62+8.591+44.5=?
(A) 448.62
(B) 258.42
(C) 987.63
(D) 390.711
(E) 182.45
Rationale: 337.62
8.591
44.5
----------
390.711
Answer is D
Answer: (D) 390.711
Question: The largest natural number which exactly divides the product of any four consecutive natural numbers is:
(A) 65
(B) 12
(C) 24
(D) 120
(E) 6
Rationale: Required number
= 1*2*3*4
=24
ANSWER:C
Answer: (C) 24
Question: In how many ways 4 boys and 4 girls can be seated in a row so that they are alternate.
(A) 144
(B) 288
(C) 12
(D) 576
(E) None
Rationale: Solution: Let the Arrangement be,
B G B G B G B G
4 boys can be seated in 4! Ways.
Girl can be seated in 4! Ways.
Required number of ways,
= 4!*4! = 576.
Answer: Option D
Answer: (D) 576
Question: Pipe P can fill a tank in 3 hours, pipe Q in 9 hours and pipe R in 24 hours. If all the pipes are open, in how many hours will the tank be filled?
(A) 2 hours
(B) 2.1 hours
(C) 3 hours
(D) 3.5 hours
(E) 4.5 hours
Rationale: Explanation:
Part filled by (P + Q + R) in 1 hour = (1/3 + 1/9 + 1/24) = 35/72
All the three pipes together will fill the tank = 72/35 = 2.1 hours
ANSWER B
Answer: (B) 2.1 hours
Question: Salad dressing P is made up of 30% vinegar and 70% oil, and salad dressing Q contains 10% vinegar and 90% oil. If the two dressings are combined to produce a salad dressing that is 25% vinegar, dressing P comprises what percentage of the new dressing?
(A) 75%
(B) 60%
(C) 40%
(D) 25%
(E) 20%
Rationale: Let x be the percentage of dressing P in the new dressing.
0.3x + 0.1(1-x) = 0.25
0.2x = 0.15
x = 0.75 = 75%
The answer is A.
Answer: (A) 75%
Question: Find value of x: 3x^2+5x+2 = 0
(A) -1
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: a = 3, b = 5, c = 2
x1,2 = (-5 ± √(52 - 4×3×2)) / (2×3) = (-5 ± √(25-24)) / 6 = (-5 ± 1) / 6
x1 = (-5 + 1)/6 = -4/6 = -2/3
x2 = (-5 - 1)/6 = -6/6 = -1
A
Answer: (A) -1
Question: What percent is 150 of 90?
(A) 133 1/3 %
(B) 166 2/3 %
(C) 135 1/3 %
(D) 140 1/3 %
(E) 143 1/3 %
Rationale: 150/90 = 5/3
5/3 × 100 = 500/3 = 166 2/3 %
B
Answer: (B) 166 2/3 %
Question: The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 8% p.a. was Rs.2828.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned.
(A) Rs. 19828.87
(B) Rs. 19828.80
(C) Rs. 19828.81
(D) Rs. 19828.89
(E) Rs. 19828.83
Rationale: Explanation:
Let the sum be Rs.P
P{ [ 1 + 8/100]2 - 1 } = 2828.80
P(8/100)(2 + 8/100) = 2828.80 [a2 - b2 = (a - b) ( a + b)] P = 2828.80 / (0.08)(2.08) = 1360/0.08 = 17000 Principal + Interest = Rs. 19828.80
Answer: B
Answer: (B) Rs. 19828.80
Question: There has been successive increases of 15% and then 10% in the price of gas from the previous month. By what percentage should a driver reduce gas consumption so that the expenditure does not change?
(A) 12%
(B) 15%
(C) 18%
(D) 21%
(E) 24%
Rationale: Let P be the original price per unit of gas.
Let x be the original gas consumption.
Let y be the reduced gas consumption.
y*1.1*1.15*P = x*P
y = x / (1.1*1.15) which is about 0.79x which is a decrease of about 21%.
The answer is D.
Answer: (D) 21%
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.
(A) 150
(B) 388
(C) 266
(D) 299
(E) 261
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9 = 150 meter.Answer: A
Answer: (A) 150
Question: 22 people are there, they are shaking hands together, how many hand shakes possible, if they are in pair of cyclic sequence.
(A) 21
(B) 22
(C) 44
(D) 45
(E) 46
Rationale: n for cyclic hand shake and n-1 for linear handshake.
so here no of hand shake is 22.
ANSWER:B
Answer: (B) 22
Question: a dealer buys 4 varieties of rice costing rs. 40,rs.42,rs.54 and rs.50 per kg in the ratio 6:5:10:9 and mixes all the four varieties and sells at 50% profit. What is the selling price per kg of rice?
(A) 68
(B) 70
(C) 72
(D) 75
(E) 77
Rationale: CP = 40*6+42*5+54*10+50*9=1440
SP = 1.5*1440=2160
Total no.of kgs=6+5+10+9=30
SP per kg=2160/30=72
ANSWER:C
Answer: (C) 72
Question: The population of a town is 7500. It decreases annually at the rate of 10% p.a. What was its population 2 years ago?
(A) 9300
(B) 8000
(C) 8500
(D) 9500
(E) 10000
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
7500 Ã— 100/90 Ã— 100/90 = 9259
A)
Answer: (A) 9300
Question: In 1998 the profits of company N were 10 percent of revenues. In 1999, the revenues of company N fell by 20 percent, but profits were 12 percent of revenues. The profits in 1999 were what percent of the profits in 1998?
(A) 80%
(B) 105%
(C) 96%
(D) 124.2%
(E) 138%
Rationale: 0,096R = x/100*0.1R
Answer C
Answer: (C) 96%
Question: 5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.90 only. Men’s wages are?
(A) 6Rs
(B) 7Rs
(C) 8Rs
(D) 4Rs
(E) 2Rs
Rationale: 5M = xW = 8B
5M + xW + 8B ----- 90 Rs.
5M + 5M + 5M ----- 90 Rs.
15M ------ 90 Rs. => 1M = 6Rs.
Answer: A
Answer: (A) 6Rs
Question: There were two candidates in an election. Winner candidate received 75% of votes and won the election by 500 votes. Find the number of votes casted to the winning candidate?
(A) 228
(B) 744
(C) 750
(D) 199
(E) 231
Rationale: W = 75% L = 25%
75% - 25% = 50%
50% -------- 500
75% -------- ? => 750
Answer: C
Answer: (C) 750
Question: Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007
(A) 1056787
(B) 1076658
(C) 1079767
(D) 1079977
(E) 1083875
Rationale: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 15/100)(1 - 35/100)(1 + 45/100)
= 1083875
E
Answer: (E) 1083875
Question: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer T that must divide n is?
(A) 6
(B) 12
(C) 24
(D) 36
(E) 48
Rationale: Q: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer T that must divide n is:
A 6, B 12, C 24, D 36, E 48
n^2 is divisible by 72, but it must also be greater than 72. If n is an integer, then n^2 must be a perfect square. The factorization of 72 is (8)(9), so if it is multiplied by 2, it will be (2)(8)(9) = (16)(9) = 144, a perfect square. So n^2 must be at least 144 or a multiple of 144, which means that n must be 12 or a multiple of 12.B
Answer: (B) 12
Question: A man leaves a point P at 6 a.m. and reaches the point Q at 10 a.m. another man leaves the point give at 8 a.m. and reaches the point P at 12 noon. At what time do they meet?
(A) 2 a.m
(B) 6 a.m
(C) 9 a.m
(D) 5 a.m
(E) 1 a.m
Rationale: 9 a.m.
Answer:C
Answer: (C) 9 a.m