mathewhe/aqua_rat huggingface dataset:
Question: x and y are positive integers. When x is divided by 9, the remainder is 2, and when x is divided by 7, the remainder is 4. When y is divided by 11, the remainder is 3, and when y is divided by 13, the remainder is 12. What is the least possible value of y - x?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: When x is divided by 9, the remainder is 2: So, the possible values of x are: 2, 11, 21, 29, etc.
When x is divided by 7, the remainder is 4: So, the possible values of x are: 4,11,18,... STOP. Since both lists include 11, the smallest possible value of x is 11.
When y is divided by 11, the remainder is 3: So, the possible values of y are: 3, 14, 25, etc.
When y is divided by 13, the remainder is 12: So, the possible values of y are: 12, 25, ...STOP. Since both lists include 25, the smallest possible value of y is 25
Since the smallest possible values of x and y are 11 and 25 respectively, the smallest possible value of y - x is 14. So,C is the correct answer to the original question.
Answer: (C) 14
Question: A necklace is made by stringing N individual beads together in the repeating pattern yellow bead, green bead, red bead, white bead, and blue bead. If the necklace design begins with a yellow bead and ends with a red bead, then N could equal
(A) 45
(B) 55
(C) 35
(D) 65
(E) 68
Rationale: Recognize that we are going to have to look for an answer thats a multiple of 5, plus 3.
Mutliple of 5 because there are 5 beads in the pattern, and plus 3 because the bead ends on red, which is 3 into the pattern.
I just went through all the answer choices, and only E fits. 5x13 = 65, and 65+3=68
Answer : E
Answer: (E) 68
Question: Aryan runs at a speed of 40 metre/minute. Rahul follows him after an interval of 5 minutes and runs at a speed of 50 metre/minute. Rahul's dog runs at a speed of 60 metre/minute and start along with Rahul. The dog reaches Aryan and then comes back to Rahul, and continues to do so till Rahul reaches Aryan. What is the total distance covered by the dog?
(A) 1100 meters
(B) 1200 meters
(C) 1250 meters
(D) 1300 meters
(E) 1400 meters
Rationale: Let X = Minutes
And Y = Aryan runs speed = 40 meter per X
And Z = Rahul runs speed = 50 meter per X (i.e., 200 + 50x)
And D = Total distance covered by the dog = X* 60meters
Y = Z
40x = 200 + 50x
200 = 10x
x = 200/10
x = 20
So, by 20minutes, both Aryan and Rahul meets.(Rahul reaches Aryan.)
So, dog covered distance, D = X * 60 meters = 20*60 = 1200 meters
ANSWER:B
Answer: (B) 1200 meters
Question: Andrew purchased 11kg of grapes at the rate of 98 per kg and 7 kg of mangoes at the rate of 50 per kg. How much amount did he pay to the shopkeeper?
(A) 1000
(B) 1055
(C) 1428
(D) 1500
(E) 1080
Rationale: Cost of 11 kg grapes = 98 × 11 = 1078.
Cost of 7 kg of mangoes = 50 × 7 = 350.
Total cost he has to pay = 1078 + 350= 1428
C
Answer: (C) 1428
Question: Amith was 3 times as old as Harsh 6 years back. Amith will be 5/3 times as old as Harsh 6 years hence. How much old is Harsh today?
(A) 12
(B) 11
(C) 15
(D) 16
(E) 18
Rationale: A
12
Let Harsh’s age 6 years back = A
Then, Amith’s age 6 years back = 32.
Then 5/3 (A + 6 + 6) = (3A + 6 + 6)
5(A + 12) = 3 (3A + 12)
4A = 24
A = 6
Harsh’s age today = (A + 6) years
= 12 years.
Answer: (A) 12
Question: If (x/y)=(9/5), find the value (x^2+y^2)/(x^2-y^2)
(A) 53/28
(B) 59/11
(C) 51/77
(D) 41/11
(E) None of them
Rationale: = (x^2+y^2)/(x^2-y^2) = ( x^2 /y^2+ 1)/ ( x^2 /y^2-1) = [(9/5)^2+1] / [(9/5)^2-1]
= [(81/25)+1] / [(81/25)-1] = 53/28
Answer is A.
Answer: (A) 53/28
Question: A motor pool has 300 vehicles of which 40 percent are trucks. 20 percent of all the vehicles in the motor pool are diesel, including 15 trucks. What percent of the motor pool is composed of vehicles that are neither trucks nor diesel?
(A) 45%
(B) 90%
(C) 65%
(D) 55%
(E) 10%
Rationale: Trucks = 40% of 300 = 120
Other Vehicles (Excluding Trucks) = 300-120 = 180
Diesel Vehicle = 20% of 300 = 60 (Including 15 Trucks)
Other Diesel Vehicles (Excluding Trucks) = 60-15 = 45
Trucks that are NOT diesel = 120 - 15 = 105
Other Vehicles that are NOT diesel Vehicles = 180-45 = 135
Required % = (135/300)*100 = 45%
Answer: option A
Answer: (A) 45%
Question: P is three times as fast as Q and working together, they can complete a work in 9 days. In how many days can Q alone complete the work?
(A) 16 days
(B) 17 days
(C) 19 days
(D) 12 days
(E) 10 days
Rationale: P = 3Q
P + Q = 3Q + Q = 4Q
These 4Q people can do the work in 9 days, which means Q can do the work in 48 days.
Hence, P can do the work in 12 days.
Answer:D
Answer: (D) 12 days
Question: A larger cube has 64 cubic inch as a volume and in the cube there are 64 smaller cubes such that their volume is 1 cubic inch. What is the difference between the surface areas’ sum of the 64 smaller cubes and the surface area of the larger cube, in square inch?
(A) 54
(B) 64
(C) 81
(D) 288
(E) 120
Rationale: Volume of larger cube = 64 = 4^3
Side of larger cube = 4
Volume of smaller cube = 1 --> Side of smaller cube = 1
Surface area of larger cube = 6 * 4^2 = 96
Surface area of 27 smaller cubes = 64 * 6 * 1 = 384
Difference = 384 - 96 = 288
Answer: D
Answer: (D) 288
Question: Calculate the largest 5 digit number which is exactly divisible by 77?
(A) 99111
(B) 99946
(C) 99869
(D) 99792
(E) 99654
Rationale: Largest 4 digit number is 99999
After doing 99999 ÷ 77 we get remainder 53
Hence largest 5 digit number exactly divisible by 77 = 99999 - 53 = 99946
B
Answer: (B) 99946
Question: There are some pigeons and hares in a zoo. If heads are counted, there are 200. If legs are counted, there are 580. The number of hares in the zoo is?
(A) 17
(B) 26
(C) 90
(D) 27
(E) 21
Rationale: 200*2 = 400
580
-----
180
1----2
?----180 = 90
Answer: C
Answer: (C) 90
Question: In a group of 5 boys and 3 girls, four children are to be selected. In how many different ways can they be selected such that at least one girl is included?
(A) 65
(B) 50
(C) 80
(D) 35
(E) 120
Rationale: The total number of ways to choose 4 children is 8C4 = 70
The number of ways to choose only boys is 5C4 = 5
The number of groups which include at least one girl is 65.
The answer is A.
Answer: (A) 65
Question: The value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is :
(A) Rs. 118
(B) Rs. 120
(C) Rs. 124.75
(D) Rs. 131
(E) Rs. 124.75
Rationale: For an income of Rs.756, investment = Rs.9000
For an income of Rs., investment = = Rs.125
For a Rs.100 stock, investment = Rs.125.
Market value of Rs. 100 stock = = Rs. 124.75
C
Answer: (C) Rs. 124.75
Question: A university cafeteria offers 1 flavors of pizza - pepperoni. If a customer has an option (but not the obligation) to add extra cheese, mushrooms or both to any kind of pizza, how many different pizza varieties are available ?
(A) 4
(B) 8
(C) 12
(D) 1
(E) 32
Rationale: 1 flavours * 1 choices = 1C1*1C1 = 1*1=1=D
Answer: (D) 1
Question: The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $350, by what percent is the price to be reduced?
(A) 70%
(B) 15%
(C) 20%
(D) 25%
(E) 30%
Rationale: price of a coat in a certain store = $500
the price of the coat is to be reduced by $350
% change = (Final Value - Initial Value)*100 / Initial Value
% Reduction= (Reduction in Price)*100 / Initial Value
i.e. % Reduction= (350)*100 / 500 = 70%
Answer: Option A
Answer: (A) 70%
Question: A team consists of 4 boys and 3 girls. If you pick two persons at the same time, what's the probability that one person is boy and other one is girl ?
(A) 2/7
(B) 5/7
(C) 4/7
(D) 3/7
(E) 1/2
Rationale: P(1st b, 2nd g) = 4/7*3/6 = 4/14;
P(1st g, 2nd b) = 3/7*4/6 = 4/14.
P = 4/14 + 4/14 = 4/7.
Answer: C.
Answer: (C) 4/7
Question: A certain article of clothing was discounted during a special sale to 2/5 of its original retail price. When the clothing didn't sell, it was discounted even further to 1/2 of its original retail price during a second sale. By what percent did the price of this article of clothing decrease from the first sale to the second sale?
(A) 50%
(B) 33.33%
(C) 25%
(D) 16.66%
(E) 12.5%
Rationale: Say the original retail price of the item was $200.
The price after the first sale = 3/5 * $200 = $120.
The price after the second sale = 1/2 * $200 = $100.
The percent change from the first sale to the second = (120 - 100) / 120 = 1/3 = 16.66%.
Answer: D.
Answer: (D) 16.66%
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 48, the dividend is:
(A) 5808
(B) 5336
(C) 5343
(D) 5345
(E) 5350
Rationale: Divisor = (5 * 48) = 240
= 10 * Quotient = Divisor
=> Quotient = 240/10 = 24
Dividend = (Divisor * Quotient) + Remainder
Dividend = (240 * 24) + 48 = 5808.
A
Answer: (A) 5808
Question: In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
(A) 8/21
(B) 7/11
(C) 5/27
(D) 11/32
(E) 1/4
Rationale: Total number of balls = 8+7+6 = 21
E = event that the ball drawn is neither red nor green
= event that the ball drawn is red
n(E) = 8
P(E) = 8/21
Answer is A
Answer: (A) 8/21
Question: After working for 6 days, David was joined by Moore. Together they completed the remaining job in 3 days. How many days will it take both of them to complete the entire job, given that it would have taken David 12 days to complete the job alone?
(A) 7
(B) 4
(C) 6
(D) 2
(E) 7
Rationale: Explanation:
David and Moore complete half work in 3 days
=> they can complete whole work in 6 days
Answer: Option C
Answer: (C) 6
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 25 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 877 m
(B) 165 m
(C) 167 m
(D) 887 m
(E) 265 m
Rationale: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train
= (15 x 25)m = 375 m. Let the length of the platform be x meters. Then, (x + 375)/36 = 15
==> x + 375 = 540 ==> x
= 165 m.
Answer: B
Answer: (B) 165 m
Question: In a rectangular coordinate system, what is the area of a rectangle whose vertices have the coordinates (-8, 1), (1, 1), (1, -7 and (-8, -7)?
(A) 144
(B) 36
(C) 72
(D) 56
(E) 112
Rationale: Length of side 1= 8+1=9
Length of side 2= 7+1= 8
Area of rectangle= 9*8= 72
C is the answer
Answer: (C) 72
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
(A) 2/29
(B) 2/17
(C) 2/21
(D) 2/28
(E) 2/11
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³C₂/¹⁵C₂ = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = ²C₂/¹⁵C₂ = (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow = (³C₁ * ²C₁)/¹⁵C₂ = (2 * 3 * 2)/(15 * 14) = 2/35
Required probability = 1/35 + 1/105 + 2/35
= 3/35 + 1/105 = 1/35(3 + 1/3)
= 10/(3 * 35) = 2/21
Answer: C
Answer: (C) 2/21
Question: A discount of 20 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 40 percent discount
(C) the same as one 36 percent discount
(D) the same as one 30 percent discount
(E) the same as one 25 percent discount
Rationale: Say initial order = 100
Discount 20% = 20
Value = 100 - 20 = 80
Again discount 20% =80∗20100=16=80∗20100=16
Value = 80-16 = 64
Total discount = 20+16 = 36
Answer = C) the same as one 36 percent discount
Answer: (C) the same as one 36 percent discount
Question: In the set of positive integers from 1 to 90, what is the sum of all the odd multiples of 5?
(A) 180
(B) 245
(C) 320
(D) 405
(E) 450
Rationale: reduce 1 - 90
5 - 15 - 25 - 35 - 45--55--65--75--85 are valid multiples. Add them --> 405
D
Answer: (D) 405
Question: A car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 9 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city?
(A) 14
(B) 16
(C) 21
(D) 24
(E) 27
Rationale: I treat such problems as work ones.
Work=Rate*Time
Mileage(m)=Rate(mpg)*Gallons(g)
X gallons is a full tank
{462=RX
{336=(R-9)X solve for R, R=33
33-9=24 mpg
D
Answer: (D) 24
Question: A metallic sheet is of rectangular shape with dimensions 30 m x 25 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 6 m, the volume of the box (in m cube) is:
(A) 920 m cube
(B) 840 m cube
(C) 1000 m cube
(D) 120 m cube
(E) None of these
Rationale: Explanation:
l = (30-12)m = 20 m, [because 6+6 = 12]
b = (25-12)m = 13 m,
h = 6 m.
Volume of the box = (12X13X6) m cube
= 936 m cube.
Option E
Answer: (E) None of these
Question: A large tanker can be filled by two pipes A and B in 60 and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?
(A) 15 min
(B) 20 min
(C) 27.5 min
(D) 30 min
(E) 25 min
Rationale: Part filled by (A + B) in 1 minute = (1/60 + 1/40) = 1/24
Suppose the tank is filled in x minutes.
Then, x/2(1/24 + 1/40) = 1
x/2 * 1/15 = 1 => x = 30 min
ANSWER:D
Answer: (D) 30 min
Question: One side of a rectangle is 3 cm shorter than the other side. If we increase the length of each side by 1 cm, then the area of the rectangle will increase by 14 cm2. Find the lengths of all sides.
(A) 10 and 3
(B) 7 and 10
(C) 10 and 7
(D) 3 and 10
(E) 8 and 5
Rationale: Let x be the length of the longer side x>3, then the other side's length is x−3 cm. Then the area is S1 = x(x - 3) cm2. After we increase the lengths of the sides they will become (x+1) and (x−3+1)=(x−2) cm long. Hence the area of the new rectangle will be A2=(x+1)⋅(x−2) cm2, which is 14 cm2 more than the first area. Therefore
A1+14=A2
x(x−3)+14=(x+1)(x−2)
x2−3x+14=x2+x−2x−2
2x=16
x=8. So, the sides of the rectangle are 8 cm and (8−3)=5 cm long.
So answer is E.
Answer: (E) 8 and 5
Question: The ratio of the volumes of two cubes is 729 : 1000. What is the ratio of their total surface areas?
(A) 81 : 100
(B) 9 : 11
(C) 729 : 1331
(D) 27 : 121
(E) None of these
Rationale: Ratio of the sides = Â³âˆš729 : Â³âˆš1000 = 9 : 10
Ratio of surface areas = 9^2 : 10^2 = 81 : 100
ANSWER:A
Answer: (A) 81 : 100
Question: A train running at the speed of 60 km/hr crosses a pole in 21 seconds. What is the length of the train?
(A) 350 m
(B) 278 m
(C) 876 m
(D) 150 m
(E) 267 m
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train
= (Speed x Time)
= (50/3 * 21) m
= 350 m.
Answer: A
Answer: (A) 350 m
Question: A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 20 percent of the drive from the center, what percent of the round-trip has the technician completed?
(A) 5%
(B) 10%
(C) 60%
(D) 40%
(E) 50%
Rationale: The complete round trip consists of driving to the service center and then back home again.
So, once the technician drives to the service center he/she has already competed 50% of the entire trip.
Since the technician completes a portion of the trip back home,the correct answer must be greater than 50%
Only one answer choice works.
Answer:
C
Answer: (C) 60%
Question: An amount of Rs.95000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 3/4 %, then the amount invested in each share was?
(A) s. 52500; Rs. 47500
(B) s. 59375; Rs. 35625
(C) s. 72500; Rs. 27500
(D) s. 82500; Rs. 17500
(E) s. 72500; Rs. 17500
Rationale: Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (95000 - x). Then,
(x * 9 * 1)/100 + [(95000 - x) * 11 * 1]/100 = (95000 * 39/4 * 1/100)
(9x + 1045000 - 11x)/100 = 39000/4 = 18525/2
x = 59375
Sum invested at 9% = Rs. 59375
Sum invested at 11% = Rs. (95000 - 59375) = Rs. 35625.
ANSWER:B
Answer: (B) s. 59375; Rs. 35625
Question: If r = 199,999 and s = 991,999, which of the following is the units digit of r^5 + s^4?
(A) 0
(B) 1
(C) 2
(D) 8
(E) 9
Rationale: The exponents of 9 cycle between 9 (odd exponents) and 1 (even exponents).
Then the sum of r^5+s^4 will have the units digit of 9+1 = 10 as a units digit.
The answer is A.
Answer: (A) 0
Question: At present, the ratio between the ages of Arun and Deepak is 4:5. After 5 years, Arun's age will be 25 years. What is the age of Deepak at present?
(A) 18
(B) 20
(C) 25
(D) 23
(E) 22
Rationale: Let the present ages of Arun and Deepak be 4x and 3x years respectively.
Then, 4x + 5 = 25 => x = 5
Deepak's age = 5x = 25 years.
Answer: C
Answer: (C) 25
Question: Mr. Kramer, the losing candidate in a two-candidate election, received 942,568 votes, which was exactly 47 percent of all votes cast. Approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast?
(A) 10%
(B) 6%
(C) 15%
(D) 17%
(E) 20%
Rationale: Let me try a simpler one.
Lets assume that candidate got 47% votes and total votes is 100.
Candidate won = 47
Remaining = 53
To get 50%, candidate requires 3 votes from 100 which is 3% and 3 votes from 53.
3/53 = .056= 5.6%
Which is approx 6%. Hence the answer is B.
Answer: (B) 6%
Question: Find the value of c from (8)^3 x 9^3 Ã· 679 = c.
(A) 249.7
(B) 529.7
(C) 549.7
(D) 594.7
(E) 119.7
Rationale: Given Exp. =(8)^3 x 9^3 Ã· 679 = c
= 512 x 729 Ã· 679
= 549.7
C
Answer: (C) 549.7
Question: Sixty percent of a number is 21 less than four fifth of that number. What is the number ?
(A) 240
(B) 140
(C) 230
(D) 130
(E) 105
Rationale: Let the number be x.
Then, 4*x/5 â€“(60% of x) = 21
4x/5 â€“ 60x/100 = 21
x = 105.
Answer E.
Answer: (E) 105
Question: Two trains 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 46 kmph respectively. In how much time will they cross each other, if they are running in the same direction?
(A) 72 sec
(B) 210 sec
(C) 192 sec
(D) 252 sec
(E) None
Rationale: Solution
Relative Speed	= (46 - 40 ) Kmph
= 6 kmph
=(6 x 5 / 18)m/sec
= (30 / 18 ) m/sec
Time taken	= (350 x 18 / 30) sec
= 210 sec.
Answer B
Answer: (B) 210 sec
Question: How many 3-digit even numbers are possible such that if one of the digits is 4, the next/succeeding digit to it should be 7?
(A) 305
(B) 5
(C) 365
(D) 405
(E) 495
Rationale: 470, 472, 474, 476, and 478, so total 5. Hence Option B.
Answer: (B) 5
Question: What is the next number of the following sequence
10, 7, 12, 10, 14, __ ?
(A) 13
(B) 14
(C) 15
(D) 16
(E) 17
Rationale: combine two series:
1st series is:10 12 14
10+2=12
12+2=14
14+2=16
2nd series is:7 10
means its 7+3=10
10+3=13
ANSWER:A
Answer: (A) 13
Question: A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?
(A) 1350
(B) 277
(C) 299
(D) 266
(E) 29912
Rationale: Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 2 = Rs.1350
Answer:A
Answer: (A) 1350
Question: In how many different number of ways 7 men and 2 women can sit on a shopa which can accommodate persons?
(A) A)160
(B) B)170
(C) C)190
(D) D)15120
(E) E)230
Rationale: 9p5 = 9 x 8 x 7 × 6 × 5 = 15120
Option 'D'
Answer: (D) D)15120
Question: The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%?
(A) 16 2/3%
(B) 16 2/8%
(C) 16 7/3%
(D) 16 5/3%
(E) 16 6/3%
Rationale: 15 CP = 18 SP
18 --- 3 CP loss
100 --- ? => 16 2/3% loss
Answer: A
Answer: (A) 16 2/3%
Question: If the L.C.M of two numbers is 750 and their product is 18750, find the H.C.F of the numbers
(A) 23
(B) 28
(C) 48
(D) 25
(E) 99
Rationale: Explanation:
H.C.F = (Product of the numbers) / (Their L.C.M) = 18750/750 = 25.
Answer: D
Answer: (D) 25
Question: On January 1, 2004 two new societies, S1 and S2, are formed, each with n members. On the first day of each subsequent month, S1 adds b members while S2 multiplies its current number of members by a constant factor r. Both the societies have the same number of members on July 2, 2004. If b = 10.5n, what is the value of r?
(A) 2
(B) 9
(C) 1.8
(D) 1.7
(E) None
Rationale: Explanation :
Jan 1 – S1 and S2 has n members. Till july 2nd, there are 6 more months, and hence 6 more additions.
In S1, b members are added each month. So after 6 months, S1 has n + 6b.
In S2, r members are multiplied each month. So after 6 months, S2 has n * r6.
After 6 months, both are same, hence
=> n + 6b = nr6. ----------------- (1)
=> b = 10.5 n. (given)
=> 6b = 63n hence.
Substituting in (1)
So, 64n = nr6. Cancelling n on both sides, we have r6 = 64 or r = 2.
Answer : A
Answer: (A) 2
Question: A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400.
(A) 1999
(B) 1900
(C) 19077
(D) 19055
(E) 19012
Rationale: 65 * 6 : 84 * 5 : 100 * 3
26:28:20
C share = 74000 * 95/100 = 7030 * 20/74 => 1900
Answer: B
Answer: (B) 1900
Question: Seven different books (A, B, C, D,E,F and G) are to be arranged on a shelf. Books A , B and C are to be arranged first and second starting from the right of the shelf. The number of different orders in which books D,E, F and G may be arranged is
(A) 4!
(B) 15!
(C) 16!
(D) 28!
(E) 42!
Rationale: Solution
Since books A,B and C are arranged first and second, only books D, E,F and G will change order. Therefore it an arrangement problem involving 4 items and the number of different order is given by
4!
Answer A
Answer: (A) 4!
Question: The H.C.F. of two numbers is 18 and the other two factors of their L.C.M. are 11 and 15. The larger of the two numbers is:
(A) 270
(B) 300
(C) 299
(D) 322
(E) 345
Rationale: the numbers are (18 x 11) and (18 x 15).
Larger number = (18 x 15) = 270.
ANSWER :A
Answer: (A) 270
Question: Pipe A fills a swimming pool in 4 hours. Pipe B empties the pool in 6 hours. If pipe A was opened at 9:00 am and Pipe B at 10:00 am, at what time will the pool be full?
(A) 19:00
(B) 17:00
(C) 16:00
(D) 18:00
(E) 20:00
Rationale: Pipe A fills the pool in 4 hrs.
1 hour's work : 1/4
Pipe B empties the pool in 6 hrs.
1 hour's work : 1/6
Together if they work, 1 hour's work = 1/4 -1/6 = 1/12
Given : Pipe A started at 9:00 a.m and Pipe B at 10:00 a.m
Pool filled after 1 hour by Pipe A : 1/4 or 3/12
After 10:00 a.m
Pool filled after 1 hour with both the pipes on : 1/12
Pool filled after 9 hours with both pipes on : 9/12
Pool filled in 1 hour + Pool filled in 9 hours = 3/12 +9/12 =1
Therefore, it takes 10 hrs to fill the pool
As Pipe A started at 9:00 a.m, pool is full at 19:00 hrs
Answer : A
Answer: (A) 19:00
Question: Sum of ages of two friends is 25 while difference is 3 then their ages are
(A) 15 years, 17 years
(B) 11 years, 14 years
(C) 16 years, 20 years
(D) 10 years, 16 years
(E) None
Rationale: 11,14
ANSWER:B
Answer: (B) 11 years, 14 years
Question: If x is even and y is odd, which of the following is odd?
(A) xy
(B) 5xy
(C) 6(x^2)y
(D) 5x + 6y
(E) 6x + 5y
Rationale: Just checking options (In case you have difficulty then choose values of r=2 and t=1)
x = even
y= Odd
A. xy = Even*Odd = EvenINCORRECT
B. 5xy = Odd*Even*Odd = EvenINCORRECT
C. 6(x^2)y = 6*(Even^2)*Odd = EvenINCORRECT
D. 5x + 6y = 5*Even + 6*Odd = Even+Even = EvenINCORRECT
E. 6x + 5y = 6*Even + 5*Odd = Even+Odd = OddCORRECT
Answer: option E
Answer: (E) 6x + 5y
Question: The average marks of 10 students in a class is 100. But a student mark is wrongly noted as 50 instead of 10 then find the correct average marks?
(A) A)78
(B) B)82
(C) C)96
(D) D)91
(E) E)85
Rationale: correct avg marks = 100+(10-50)/10
avg = 100-4 = 96
Answer is C
Answer: (C) C)96
Question: The difference between the ages of two persons is 10 years. Fifteen years ago, the elder one was twice as old as the younger one. The present age of the elder person is
(A) 25 years
(B) 30 years
(C) 35 years
(D) 40 years
(E) None
Rationale: Sol.
Let their ages of x years and (x + 10) years respectively.
Then, (x + 10) - 15 = 2(x - 15)
⇔ x - 5 = 2x - 30
⇔ x = 25.
∴ Present age of the elder person = (x + 10)
= 35 years.
Answer C
Answer: (C) 35 years