mathewhe/aqua_rat huggingface dataset:
Question: A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is
(A) 3.34
(B) 3.39
(C) 3.37
(D) 3.33
(E) 3.31
Rationale: Area of the path = Area of the outer circle - Area of the inner circle = ∏{4/2 + 25/100}2 - ∏[4/2]2
= ∏[2.252 - 22] = ∏(0.25)(4.25) { (a2 - b2 = (a - b)(a + b) }
= (3.14)(1/4)(17/4) = 53.38/16
= 3.34 sq m
Answer:A
Answer: (A) 3.34
Question: If 40% of a number is equal to two-thirds of another number, what is the ratio of the first number to the second?
(A) 7 : 3
(B) 3 : 7
(C) 2 : 5
(D) 5 : 3
(E) None of these
Rationale: Suppose the first number is x and the second numbery.
Therefore, 40% of x = 2⁄3 of y
∴ x⁄y = 2⁄3 × 100⁄40 = 5⁄3
Answer D
Answer: (D) 5 : 3
Question: Two trains having length of 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions (on parallel tracks). The time which they take to cross each other, is
(A) 10.2
(B) 10.4
(C) 10.6
(D) 10.8
(E) 11.2
Rationale: Distance = 140+160 = 300 m
Relative speed = 60+40 = 100 km/hr = (100×10)/36 m/s
Time = distance/speed = 300 / (100×10)/36 = 300×36 / 1000 = 3×36/10 = 10.8 s
Answer is D.
Answer: (D) 10.8
Question: In a class, the average age of 30 boys is 13 years and the average of 20 girls is 12 years. what is the average age of the whole class?
(A) 11 Years
(B) 12.6 Years
(C) 13 Years
(D) 13.5 Years
(E) 14 Years
Rationale: Total age of 50 students
(30X 13+20 X 12) = 630
Average = 630/50 = 12.6 Years
B)
Answer: (B) 12.6 Years
Question: A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is?
(A) 5768
(B) 5760
(C) 5762
(D) 5766
(E) 5712
Rationale: 1/x - 1/6 = -1/8
x = 24 hrs
24 * 60 * 4 = 5760
Answer: B
Answer: (B) 5760
Question: On his first 4 tests, Rajeev received an average score of X points. If on his fifth test, he exceeds his previous average score by 20 points, what is his average score for his first 5 tests?
(A) X + 5
(B) X + 1
(C) X + 4
(D) X + 2
(E) X + 3
Rationale: Total of 1st 4 tests= 4X
5th test score = X + 20
Total of all 5 tests = 5X + 20
Average = X + 4
Answer : C
Answer: (C) X + 4
Question: One train is traveling 18 kmph and other is at 10 meters a second. Ratio of the speed of the two trains is?
(A) 1:2
(B) 5:6
(C) 5:0
(D) 5:4
(E) 5:1
Rationale: 18 * 5/18 = 10
5:10 => 1:2
Answer: A
Answer: (A) 1:2
Question: What approximate value should come in plce of question mark (?) in the following equations ?
728.038 x 54.978 - 72.016 x 85.250 = ?
(A) 31400
(B) 32700
(C) 33900
(D) 34400
(E) 32400
Rationale: Explanation :
? = 728 x 55 - 72 x 85.25
= 40040 - 6138 = 339900
Answer : Option C
Answer: (C) 33900
Question: A train cruising at 50 km/hr takes 9 seconds to pass a platform. Next, it takes 3 seconds to pass a man walking at 3 km/hr in the same direction. Find the length of the train and that of the platform.
(A) 200/3m175/3m
(B) 40m85m
(C) 50m45m
(D) 100/3 m200/3
(E) none of these
Rationale: A train running at 50 km/hr takes 9 seconds to pass a platform. Next, it takes 3 seconds to pass a man walking at 3 km/hr in the same direction. Find the length of the train and that of the platform.
Distance = Speed*time
It's probably best to convert to meters so we can find the length of the platform.
Distance = 50000 meters/h * 9 seconds*(1/60*60)
Distance =(55000*9 / [3600] ) = 125m
I'm not sure how we take the length of the train into account (if we do at all) to solve this problem. For example, If we were measuring by the time the very front of the train passed one end of the platform to the time the very front of the train passed the other end, the result would be different than if we counted when the very front of the train passed one end of the platform to the time the back side of the train passed the end.
As for the problem involving the man, the man is moving forward at a speed of 3km/h while the train is moving forward at a speed of 50km/h. Therefore, the train is moving past the man at a total speed of 47km/h.
distance = speed * time
distance = 47km/h * 3 seconds
distance (length of train) = 39.16 m
We know the length of the train is roughly 39.16m and the distance covered passing the platform was 125m. However, The platform isn't 125m long - it is 125m minus the length of the train long (or so I think) which is 125-39.16 or roughly 85m. Both of these answers are in A so I think that is the right answer. I am still having a bit of trouble conceptualizing why we have to subtract out the length of the train, however.
ANSWER: B) 40m85m
Answer: (B) 40m85m
Question: What is the area of a regular hexagon with sides 1 in. long?
(A) 1.59 square inch
(B) 2.59 square inch
(C) 3.59 square inch
(D) 4.59 square inch
(E) 2.69 square inch
Rationale: A regular hexagon of side 1 inch can be divided in to 6 equilateral triangle of side 1 inch.
Area of each triangle = (root 3/4)* side^2 = (root 3/4)
Area of 6 triangles = 6*(root 3/4)= 1.5 root 3= 2.59 square inch
ANSWER:B
Answer: (B) 2.59 square inch
Question: In business, A and C invested amounts in the ratio 2:1, whereas the ratio between amounts invested by A and B was 3:2, If Rs 157300 was their profit, how much amount did B receive.
(A) Rs 48000
(B) Rs 47000
(C) Rs 47400
(D) Rs 48400
(E) None of these
Rationale: Explanation:
A:B = 3:2 = 6:4
=> A:C = 2:1 = 6:3
=> A:B:C = 6:4:3
B share = (4/13)*157300
= 48400
Option D
Answer: (D) Rs 48400
Question: Average of 10 matches is 32, How many runs one should should score to increase his average by 6 runs.
(A) A)70
(B) B)76
(C) C)78
(D) D)98
(E) E)88
Rationale: Explanation:
Average after 11 innings should be 38
So, Required score = (11 * 38) - (10 * 32)
= 418 - 320 = 98
Answer: Option D
Answer: (D) D)98
Question: What is the probability of getting a sum 9 from two throws of a dice?
(A) 1/6
(B) 1/8
(C) 1/9
(D) 1/12
(E) None
Rationale: Solution
In two throws of a die, n(S) = (6×6)
= 36.
Let E = event of getting a sum 9= {{3,6),(4,5),(5,4),(6,3)}
P(E)	= n(E) / n(S)
= 4/36
‹=›1/9.
Answer C
Answer: (C) 1/9
Question: The total car population in a Mumbai is 2,94,00 out of which 1,50,00 are made by Honda. Out of every 100 Honda cars, 98 are red in color, but only 53% of the total car population is red. Find the % of non-Honda cars that are red
(A) 5.025%
(B) 5.25%
(C) 6.125%
(D) 7.34%
(E) 8.43%
Rationale: Total Car.29.10 i.e., Honda +non Honda = 29400 Given: Whim. tractor .150W
Now,5346 of 2..00 = Honda +Red Non-Honda 29400 .:4 =15582 Thus...El Mall... 1.0 Now Honda 15582 flow, Non-. Honda =15582 - 15.582-14700=8B2 96 non-Honda =1=1.100 = 6.125%
C
Answer: (C) 6.125%
Question: Three cubes of metal whose edges are 5, 12 and 15 cm respectively, are melted and one new cube is made. Find the edge of the new cube?
(A) 28
(B) 77
(C) 17.3
(D) 18
(E) 99
Rationale: 53 + 123 + 153 = a3 => a
= 17.3
Answer: C
Answer: (C) 17.3
Question: (3x + 4) (2x - 5) = ax^2 + kx + n . What is the value of a - n + k ?
(A) 5
(B) 8
(C) 9
(D) 10
(E) 15
Rationale: Expanding we have 6x^2 -15x + 8x -20
6x^2 - 7x - 20
Taking coefficients, a = 6, k= -7, n = -20
Therefore a - n + k = 6 - (-20) - 11 = 26 - 11 = 15
The answer is E.
Answer: (E) 15
Question: A number is missing from the number series below.
Can you find it ?
84, 155, 258, ? , 584, 819.
(A) 275
(B) 350
(C) 399
(D) 421
(E) 449
Rationale: C
The missing number is 399.
84 = 4^3 + 3^2 + 4
155 = 5^3 + 5^2 + 5
258 = 6^3 + 6^2 + 6
584 = 8^3 + 8^2 + 8
819 = 9^3 + 9^2 + 9
Thus,
399 = 7^3 + 7^2 + 7
Answer: (C) 399
Question: A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40. What is the reduced price/dozen?
(A) 3
(B) 6
(C) 7
(D) 8
(E) 12
Rationale: Sol. lie purchases 6a bananas mere for 4096 of Rs 40 or, Rs 16. Reduced price per do,. 3
A
Answer: (A) 3
Question: If 35% of the 880 students at a certain college are enrolled in biology classes, how many students at the college are NOT enrolled in a biology class?
(A) 110
(B) 330
(C) 572
(D) 430
(E) 880
Rationale: Students enrolled in biology are 35% and therefore not enrolled are 65%. so of 880 is 880*.65 = 572
Answer is C 572
Answer: (C) 572
Question: If a trader sold two cars each at Rs. 325475 and gains 12% on the first and loses 12% on the second, then his profit or loss percent on the whole is?
(A) 1.44%
(B) 1.43%
(C) 1.34%
(D) 4.44%
(E) 1.74%
Rationale: SP of each car is Rs. 325475, he gains 12% on first car and losses 12% on second car.
In this case, there will be loss and percentage of loss is given by = [(profit%)(loss%)]/100 = (12)(12)/100 % = 1.44%
Answer: A
Answer: (A) 1.44%
Question: Eighteen dots are evenly spaced on the circumference of a circle. How many combinations of three dots can we make from these 18 dots that do not form an equilateral triangle?
(A) 792
(B) 798
(C) 804
(D) 810
(E) 816
Rationale: The total number of ways we can choose three dots is 18C3=816.
We can form six equilateral triangles from these eighteen dots.
There are 816 - 6 = 810 combinations which do not form an equilateral triangle.
The answer is D.
Answer: (D) 810
Question: How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 42 kmph?
(A) 21.4 sec
(B) 77 sec
(C) 25 sec
(D) 18 sec
(E) 17 sec
Rationale: D = 100 + 150 = 250
S = 42 * 5/18 = 11.7 mps
T = 250/11.7 = 21.4 sec
Answer:A
Answer: (A) 21.4 sec
Question: What is the smallest positive integer x such that 108x is the cube of a positive integer?
(A) 2
(B) 4
(C) 8
(D) 10
(E) 7
Rationale: Given 108x is a perfect cube
so we will take 216 = 6*6*6
108x = 216
x = 216/108 = 2
correct option is A
Answer: (A) 2
Question: Calculate the sum of first 89 natural numbers.
(A) 2017
(B) 2647
(C) 2147
(D) 2045
(E) 4005
Rationale: Solution
We know that(1+2+3+.....+89)	= n(n+1)/2
Therefore (1+2+3+....+89)	=(89×90 / 2)
= 4005.
Answer E
Answer: (E) 4005
Question: A and B can do a work in 18 days, B and C in 30 days and C and A in 36 days. In how many days will the work be completed, if all three of them work together?
(A) 360/13 days
(B) 350/13 days
(C) 160/13 days
(D) 260/13 days
(E) 960/13 days
Rationale: One day work of A and B = 1/18
One day work of B and C = 1/30
One day work of C and A = 1/36
2(A + B + C) = 1/18 + 1/30 + 1/36
2(A + B + C) = 21/180
(A + B + C) = 13/360
Number of days required = 360/13 days.
ANSWER:A
Answer: (A) 360/13 days
Question: Einstein walks on an escalator at a rate of 5steps per second and reaches the other end in 10 sec. while coming back, walking at the same speed he reaches the starting point in 40secs. What is the number of steps on the escalator?
(A) 22
(B) 80
(C) 28
(D) 17
(E) 11
Rationale: Escalator problems are similar to boats and streams problems. If we assume man's speed as 'a m/s' and escalator speed as 'b m/sec' then while going up man's speed becomes 'a -b' and while coming down 'a + b'.
In this question, Let the speed of escalator be b steps per sec. And length of escalator be L. Einstein's speed = 5 steps/ sec
While going down, L5+x=10L5+x=10 ⇒⇒ L = 50 + 10x
While coming up, L5−x=40L5−x=40 ⇒⇒ L = 200 - 40x
Multiply the first equation by 4, and add to the second, we get L = 80
Answer:B
Answer: (B) 80
Question: If n is a natural number, then (7(n2) + 7n) is always divisible by:
(A) 3 and 7
(B) 14 only
(C) 7 only
(D) 7 and 14
(E) NONE
Rationale: Solution
(7n2 + 7n) = 7n(n + 1), which is always divisible by 7 and 14 both, since n(n + 1) is always even.
Answer D
Answer: (D) 7 and 14
Question: a * b = 2a - 3b + ab, then 3*5 + 5*3 = ?
(A) 20
(B) 21
(C) 22
(D) Bedford is at one end.
(E) Mercedes is at one end.
Rationale: Explanation:
= 2(3)-3(5)+(3*5) + 2(5)-3(3)+(5*3)
= 6-15+15+10-9+15 = 31-9 = 22
Option E
Answer: (E) Mercedes is at one end.
Question: If |y + 5| = 8, what is the sum of all the possible values of y?
(A) -14
(B) -13
(C) -8
(D) -12
(E) -10
Rationale: There will be two cases
y+5 = 8 or y+5 = -8
=> y = 3 or y= -13
sum of both the values will be -13 + 3 = -10
Answer: E
Answer: (E) -10
Question: How many positive integers between 1 and 200 are there such that they are multiples of 17?
(A) 9
(B) 11
(C) 13
(D) 10
(E) 8
Rationale: Multiples of 17= 17,34,51,-----187
Number of multiples of 17 => 17*11= 187
Answer is B
Answer: (B) 11
Question: A discount of 10 percent on an order of goods followed by a discount of 20 percent amounts to
(A) the same as one 45 percent discount
(B) the same as one 38 percent discount
(C) the same as one 36 percent discount
(D) the same as one 30 percent discount
(E) the same as one 28 percent discount
Rationale: 0.9*0.8*x=0.72x from initial value, meaning 0.28 or 36% discount
E
Answer: (E) the same as one 28 percent discount
Question: Divide Rs. 3364 between A and B, so that A's Share at the end of 5 years may equal to B's share at the end of 7 years, compound interest being at 5 percent.
(A) Rs. 1764 and Rs.1600
(B) Rs. 1756 and Rs.1608
(C) Rs. 1722 and Rs.1642
(D) Rs. 1732 and Rs.1842
(E) None of these
Rationale: Explanation: A's share after 5 years = B's share after 7 years
(A's present share)(1+5100)5 = (B's present share)(1+5100)7
=>(A's present share)/(B's present share) = (1+5/100)7/(1+5/100)5 = (1+5/100)(7−5) = (1+5/100)2 =(21/20)2 =441/400
i.e, A's present share : B's present share = 441 : 400
Since the total present amount is Rs.3364, A's share = 3364 × 441/(441 + 400)
= (3364 × 441)/841 = 4 × 441 = Rs. 1764
B's present share = 3364 - 1764 = Rs.1600
Answer: Option A
Answer: (A) Rs. 1764 and Rs.1600
Question: A train passes a station platform in 37 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 328
(B) 255
(C) 240
(D) 288
(E) 231
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 37 = 15
x + 300 = 555
x = 255 m. Answer:B
Answer: (B) 255
Question: A basket of 1430 apples is divided equally among a group of apple lovers. If 45 people join the group, each apple lover would receive 9 apples less. How many Q apples did each person get before 45 people joined the feast?
(A) 20.
(B) 21.
(C) 22.
(D) 23.
(E) 24.
Rationale: Before solving it algebraically, let us prime factorize 1430 = 2*5*11*13.
Since number of apples per person * total persons Q= 1430, the answer should be a factor of 1430. Only C is. And that's your answer.C
Answer: (C) 22.
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
(A) 180 sec
(B) 190 sec
(C) 170 sec
(D) 175 sec
(E) 195 sec
Rationale: Explanation:
L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1900 m
T = D/S
T = 1900/10
T = 190 Sec
ANSWER IS B
Answer: (B) 190 sec
Question: A tank with a volume of 30 cubic feet has one inlet pipe and 2 outlet pipes. The inlet pipe fills water into the tank at the rate of 3 cubic inches/min and the 2 outlet pipes empty it out at the rates of 12 cubic inches/min and 6 cubic inches/min respectively. If all 3 pipes are opened when the tank is full, how many minutes does it take to empty the tank? (1 foot = 12 inches)
(A) 2345
(B) 3456
(C) 4567
(D) 5678
(E) 6789
Rationale: The tank is emptied at this rate: 12 + 6 - 3 = 15 cubic inches/min
The tank has a volume of 30*12*12*12 = 51840 cubic inches.
The time it takes to empty the tank is 51840/15 = 3456 minutes.
The answer is B.
Answer: (B) 3456
Question: In an exam, Libi scored 78 percent, Nibi scored 75 percent and Catherine 85 percent. The maximum score awarded in the exam is 1100. Find the average mark scored by all the three boys?
(A) 874.65
(B) 873.66
(C) 871.22
(D) 872.67
(E) 870.2
Rationale: Average mark scored by all the three boys =
[78/100 (1100) + 75/100 (1100) + 85/100 (1100)] / 3
(858+825+935)/3= 872.67
Answer: D
Answer: (D) 872.67
Question: The ratio of the amount of the oil bill for the month of February to the amount of the oil bill for the month of January was 3:2. If the oil bill for February had been $30 more, the corresponding ratio would have been 5:3. How much was the oil bill for January?
(A) $120
(B) $150
(C) $180
(D) $210
(E) $240
Rationale: 3:2 = 9:6 and 5:3 = 10:6.
An increase in $30 increases the ratio by 1:6.
Therefore, January's bill was 6($30) = $180.
The answer is C.
Answer: (C) $180
Question: A rectangular circuit board is designed to have a width of W inches, a length of L inches, a perimeter of P inches, and an area of B square inches. Which of the following equations must be true?
(A) 2W^2 + PW + 2B = 0
(B) 2W^2 − PW + 2B = 0
(C) 2W^2 − PW − 2B = 0
(D) W^2 + PW + B = 0
(E) W^2 − PW + 2B = 0
Rationale: P = 2(L+W)-----------------1)
B= LW------------------------2)
option A is not possible why ?? because all the terms are positive.
lets try option B , put value of P and B from 1 and 2 we have,
2W^2-2(L+W)W + 2(LW)
2W^2 - 2LW - 2W^2 + 2LW=0.
hence answer is B.
Answer: (B) 2W^2 − PW + 2B = 0
Question: If the milk and water ware added in the ratio 5:4 then how much more water should be added so he gets the ratio of 6:7.
(A) 5/6
(B) 11/6
(C) 7/6
(D) 11/5
(E) 5/11
Rationale: let quantity of water should added be x then
A/Q
5/(4+x)= 6/7
=> 35=24+6x
=> x=11/6
ANSWER:B
Answer: (B) 11/6
Question: If n = 5p, where p is a prime number greater than 2, how many different positiveevendivisors does n have, including n ?
(A)  Two
(B)  Three
(C)  Four
(D)  Six
(E)  Eight
Rationale: This is an interesting question because we are immediately given the option to insert any prime number we wish for p. Since this is a problem-solving question, and there can only be one correct answer, we can select any value for p, as long as it is a prime number greater than 2. We always want to work with small numbers, so we should select 3 for p. Thus, we have:
n = 4 x 3
n = 12
Next we have to determine all the factors, or divisors, of P. Remember the term factor is synonymous with the term divisor.
1, 12, 6, 2, 4, 3
From this we see that we have 4 even divisors: 12, 6, 2, and 4.
If you are concerned that trying just one value of p might not substantiate the answer, try another value for p. Let’s say p = 5, so
n = 4 x 5
n = 20
The divisors of 20 are: 1, 20, 2, 10, 4, 5. Of these, 4 are even: 20, 2, 10 and 4. As we can see, again we have 4 even divisors.
No matter what the value of p, as long as it is a prime number greater than 2, n will always have 4 even divisors.
The answer is D.
Answer: (D)  Six
Question: A wheel makes 1000 revolutions in covering a distance of 88 km. Find the radius of the wheel.
(A) 14
(B) 13
(C) 12
(D) 11
(E) 10
Rationale: Distance covered in one revolution = (88X1000)/1000= 88m.
2 PIE R = 88 = 2X22/7XR =88 R=88X7/44 =14 ANSWER = A
Answer: (A) 14
Question: What is the dividend? The divisor is 17, the quotient is 4 and the remainder is 8.
(A) 76
(B) 67
(C) 176
(D) 671
(E) 0
Rationale: Divided= Divisor * Quotient + Remainder
?= 17 * 4 + 8
68 + 8
76
(e.g. Answer: A)
Answer: (A) 76
Question: Two boys starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time
will they take to be 8.5km apart, if they walk in the same direction?
(A) 15 hours
(B) 16 hours
(C) 17 hours
(D) 18 hours
(E) None of these
Rationale: Explanation:
In this type of questions we need to get the relative speed between them,
The relative speed of the boys = 5.5kmph � 5kmph
= 0.5 kmph
Distance between them is 8.5 km
Time = Distance/Speed
Time= 8.5km / 0.5 kmph = 17 hrs
Answer: C
Answer: (C) 17 hours
Question: A, B, C subscribe Rs. 50000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs.35000 A receives:
(A) Rs. 11900
(B) Rs. 8400
(C) Rs. 14700
(D) Rs. 13600
(E) Rs. 14600
Rationale: Let C = x. Then B = x + 5000 and A + x + 5000 + 4000 = x + 9000
Therefore, x + x + 5000 + x + 9000 = 50000 Û x = 12000.
Therefore, A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12
Therefore, A’s share = Rs (35000 * 21/50) = Rs. 14700
ANSWER:C
Answer: (C) Rs. 14700
Question: An aeroplane covers a certain distance of 670 Kmph in 6 hours. to cover the same distance in 6 1/4 hours, it Must travel at a speed of
(A) 440
(B) 540
(C) 643
(D) 740
(E) 250
Rationale: Speed of aeroplane = 670 Kmph
Distance travelled in 6 hours
= 670 * 6 = 4020 Km
Speed of aeroplane to acver 4020 Km in 25/4
= 4020*4/25 = 643 Km
Answer C.
Answer: (C) 643
Question: Sum of Rs.4000 is given out in 2 pieces, one at 8% S.I. and the other at 10% S.I. If the annual interest is Rs 352, the sum is given at 8% is
(A) 2000
(B) 2200
(C) 2300
(D) 2400
(E) None of these
Rationale: Explanation :
i) Given the total sum = Rs. 4000
If the sum given at 8% be Rs.a
ie) P = a , n=1, R = 8%
(aX18/100) = (8a/100)
If the addition given at 10% be Rs. 4000 – a
P = 4000-a , n=1, R = 10%
(4000 – aX1X10)/(100) = (40000-10a)/100
Given Annual interest is Rs. 352
(8a/100) + (40000-10a)/100 = 352
8a – 10a = 35200 – 40000
-2a = -4800
X = (4800/2)= Rs.2400/-
Answer : D
Answer: (D) 2400
Question: By selling 99 pens, a trader gains the cost of 33 pens. Find his gain percentage?
(A) 33 1/3%
(B) 33 1/6%
(C) 33 3/3%
(D) 34 1/3%
(E) 73 1/3%
Rationale: Let the CP of each pen be Rs. 1.
CP of 99 pens = Rs. 99
Profit = Cost of 33 pens = Rs. 33
Profit% = 33/99 * 100 = 33 1/3%
Answer:A
Answer: (A) 33 1/3%
Question: What no. should be subtracted from x^3+4x2−7x+12x^3+4x^2−7x+12, if it is to be perfectly divisible by x+3x+3?
(A) 38
(B) 42
(C) 46
(D) 49
(E) 62
Rationale: According to remainder theorem when dfracf(x)x+adfracf(x)x+a, then the remainder is f(−a)f(−a).
In this case, as x+3x+3 divides x3+4x2−7x+12–kx3+4x2−7x+12–k perfectly (kk being the number to be subtracted), the remainder is 0 when the value of xx is substituted by -3.
i.e., (−3)3+4(−3)2−7(−3)+12−k=0(−3)3+4(−3)2−7(−3)+12−k=0
or −27+36+21+12=k−27+36+21+12=k
or k=k= 42
B
Answer: (B) 42
Question: A group of 10 representatives is to be selected out of 17 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?
(A) 17C₅ * 10
(B) 17C₇ * 10
(C) 17C12 * ¹⁰C₅
(D) 12 * ¹⁰C₅
(E) None of these
Rationale: Here, five seniors out of 17 seniors can be selected in 17C₅ ways. Also, five juniors out of ten juniors can be selected ¹⁰C₅ ways. Hence the total number of different ways of selection = 17C₅ * ¹⁰C₅ = 17C12 * ¹⁰C₅
since 17C₅ = 17C12
ANSWER:C
Answer: (C) 17C12 * ¹⁰C₅
Question: The mean of 80 observations was calculated as 55. It was found later on that one of the observations was misread as 64 instead of 46. The correct mean is
(A) 39
(B) 54.7
(C) 60.3
(D) 42.7
(E) None of these
Rationale: Explanation :
Correct sum = (55*80 + 46 - 64) = 4382.
Correct mean = 4382/80 = 54.7
Answer : B
Answer: (B) 54.7
Question: On Monday, Lou drives his vehicle with 25-inch tires, averaging x miles per hour. On Tuesday, Lou switches the tires on his vehicle to 32-inch tires yet drives to work at the same average speed as on Monday. What is the percent change from Monday to Tuesday in the average number of revolutions that Lou's tires make per second?
(A) Decrease by 14.3%
(B) Decrease by 22%
(C) Increase by 14.3%
(D) Increase by 12.5%
(E) Cannot be determined with the given information.
Rationale: 800 the LCM
On Tuesday 800/32 =25
On Monday 800/25 = 32
Therefore, 25-32/32= -2/9=-22% decrease
Answer is B
Answer: (B) Decrease by 22%
Question: What approximate value should come in place of the question mark (?) in the following equation?75.22 Ã— 6.12 â€“ 36.85 Ã— 6.54 = (40 + ?) Ã— 2
(A) 65.6737
(B) 69.6737
(C) 61.6737
(D) 68.6737
(E) 60.6737
Rationale: Solve using approximation
Answer B
Answer: (B) 69.6737
Question: If daily wages of a man is double to that of a woman, how many men should work for 25 days to earn Rs.14400? Given that wages for 40 women for 30 days are Rs.21600.
(A) 12
(B) 15
(C) 18
(D) 16
(E) 20
Rationale: Wages of 1 woman for 1 day = 2160040×30
Wages of 1 man for 1 day = 21600×240×30
Wages of 1 man for 25 days = 21600×2×2540×30
Number of men = 14400(21600×2×2540×30)=144(216×5040×30)=1449=16
Answer is D.
Answer: (D) 16
Question: A single discount equivalent to successive discount of 20%, 10% is
(A) 72%
(B) 28%
(C) 32%
(D) 76%
(E) 78%
Rationale: Explanation:
(80 * 90)/100 = Rs. 72/-
Discount = 28 %
Answer: Option B
Answer: (B) 28%