mathewhe/aqua_rat huggingface dataset:
Question: A large delicatessen purchased X pounds of cheese for c dollars per pound. If d pounds of the cheese had to be discarded due to spoilage and the delicatessen sold the rest for s dollars per pound, which of the following represents the gross profit on the sale of the purchase? (gross profit equals sales revenue minus product cost)
(A) s(X-d) - cX
(B) s(p − d) − pc
(C) c(p − d) − ds
(D) d(s − c) − pc
(E) pc − ds
Rationale: Total cost price = c*X ............... (1)
Wastage = d pounds
Quantity sold = X-d
Selling price per pound = s
Total selling price = s(X-d) ........... (2)
Profit = (2) - (1)
= s(X-d) - cX
A
Answer: (A) s(X-d) - cX
Question: Find the average of the first 41 natural numbers?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 21
Rationale: Average of the first 'n' natural numbers = (n + 1)/2
We get (41 + 1)/2 = 21
ANSWER:E
Answer: (E) 21
Question: If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area?
(A) 120 cm2
(B) 130 cm2
(C) 312 cm2
(D) 315 cm2
(E) None of these
Rationale: The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle = 1/2 * 24 * 10 = 120 cm2
ANSWER:A
Answer: (A) 120 cm2
Question: A cricketer has a certain average for 10 innings. In the eleventh inning, he scored 108 runs, there by increasing his average by 6 runs. His new average is?
(A) 48 runs
(B) 72 runs
(C) 62 runs
(D) 54 runs
(E) 45 runs
Rationale: Let average for 10 innings be x. Then,
(10x + 108)/11
= x + 6
= 11x + 66
= 10x + 108
= x = 42.
New average = (x + 6)
= 48 runs.
Answer:A
Answer: (A) 48 runs
Question: It takes 6 beavers 10 hours to build a certain dam, working at a uniform rate. If five beavers start to build the same dam at noon, and one beaver per hour is added beginning at 6:00 PM, at what time will the dam be complete?
(A) 7:30 PM
(B) 8:00 PM
(C) 8:30 PM
(D) 9:00 PM
(E) 10:00 PM
Rationale: The rate of 1 beaver is 1/60.
The amount of work done by 5 beavers in 6 hours is 5/60 *6 = 30/60
In the next hour, 6 beavers do 6/60 for a total of 36/60.
In the next hour, 7 beavers do 7/60 for a total of 43/60.
In the next hour, 8 beavers do 8/60 for a total of 51/60.
In the next hour, 9 beavers do 9/60 for a total of 60/60.
The dam will be completed at 10:00 pm.
The answer is E.
Answer: (E) 10:00 PM
Question: M is 30% of Q. Q is 20% of P. N is 50% of P. Find M:N ratio
(A) 1:25
(B) 2:25
(C) 3:25
(D) 4:25
(E) 5:25
Rationale: Let p be 100
N = 50% of 100 (P=100) = 50
Q= 20% of 100 (P=100) = 20
M = 30% of 20 (Q=20) = 6
M:N = 6:50
M:N = 3:25
ANSWER:C
Answer: (C) 3:25
Question: Two buses A and B leave the same bus depot, A towards the North and B towads the East. The bus A travels at a speed of 5 km/hr more than that of the bus B. If after four hours the distance between the two buses is 100 km, find the speed of the bus A.
(A) 60 kmph
(B) 40 kmph
(C) 20 kmph
(D) 15 kmph
(E) 25 kmph
Rationale: Let the speed of the bus B be x km/hr. Then the speed of the bus A will be ( x +5) kmph
Distance traveled in 4 hours is 4x and 4(x + 5) for the two buses respectively
(4x)2 + {4 (x + 5) }2 = (100)2
16x2 + 16x2 + 160x + 400 = 1000
32x2 +160x –9600 = 0
x2 + 5x –300 = 0 (x-15) (x +20 ) = 0
x = 15
:. Speed of the bus A = 15 +5 = 20 kmph
ANSWER:C
Answer: (C) 20 kmph
Question: A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?
(A) 22
(B) 27
(C) 48
(D) 99
(E) 23
Rationale: D = 540 + 180 = 720
S = 54 * 5/18 = 15 mps
T = 720/15 = 48 sec
Answer: C
Answer: (C) 48
Question: Group A has 6 boys and 3 girls, group B has 2 boys and 2 girls and group C has 4 boys and 2 girls. One student is selected from each of the group. Find the probability that one girl and two boys are among the three selected?
(A) 3/45
(B) 1/18
(C) 29/10
(D) 7/18
(E) 7/27
Rationale: Group A has 6 boys and 3 girls; 9
Group B has 2 boys and 2 girls; 4
Group C has 4 boys and 2 girls. 6
Selected group should have one girl and two boys.
Girl from A, boy from B, boy from C: 3/9*2/4*4/6 = 1/9;
Boy from A, girl from B, boy from C: 2/4*2/4*4/6 = 1/6;
Boy from A, boy from B, girl from C: 6/9*2/4*2/6 = 1/9.
Sum = 1/9 + 1/6 + 1/9 = 7/18.
Answer: D.
Answer: (D) 7/18
Question: 587 x 999 = ?
(A) 586413
(B) 587523
(C) 614823
(D) 615173
(E) None of them
Rationale: =587 x 999 = 587 x (1000-1)
=587 x 1000 - 587 - 1
=587000 - 587
=586413
Answer is A
Answer: (A) 586413
Question: If you cut a 20ft piece of wood into two pieces making one piece 4ft longer than the other. What size is the smaller piece?
(A) 4ft
(B) 6ft
(C) 8ft
(D) 10ft
(E) 12ft
Rationale: Total length is 20ft, one piece is 4ft longer (x+4), leaving the other piece to figure out (x).
(x)+ (x+4)=20
x+x+4-4=20-4
2x=16
2x/2=16/2
x=8
The piece is C) 8ft.
Answer: (C) 8ft
Question: If a continuous cable 10 meters long was marked off at intervals of 1/3 meter and also 1/5 meter, and then if the cable were cut at each mark, how many different size length of cable would result?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: In this particular example length (10 meter) is just extraneous information.
The location of the marks for 1/3 meter would be 5/15, 10/15, 15/15, etc...
The location of the marks for 1/5 meter would be 3/15, 6/15, 9/15, 12/15, 15/15, etc...
The distances between marks are 3/15, 2/15, and 1/15.
The answer is C.
Answer: (C) 3
Question: Thirty percent of forty percent of fifty is sixty percent of what percent of two-hundred ?
(A) 0.5%
(B) 1%
(C) 5%
(D) 50%
(E) 500%
Rationale: x percent can be written as x/100
So, we get: (30/100)(40/100)(50) = (60/100)(x/100)(200)
Simplify all fractions to get: (3/10)(2/5)(50) = (3/5)(x/100)(200)
Expand: 300/50 = 600x/500
Simplify: 6 = 6x/5
Multiply both sides by 5 to get: 30 = 6x
Solve: x = 5
Answer: C
Answer: (C) 5%
Question: A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:2, and the ratio of soap to salt is four times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is halved by water evaporation. At that time, what is the ratio of water to salt in the solution?
(A) 1:1
(B) 2:3
(C) 3:2
(D) 9:4
(E) 36:8
Rationale: Water:soap = 3:2
Soap:Salt=12:2
=> For 12 soap, salt = 2
=> For 2 Soap, salt = (2/12)*2 = 1/3
So, water:soap:salt = 3:2:1/3 = 36:24:4
After open container, water:soap:salt = 18:24:4
So, water:salt = 18:4 = 36:8
E
Answer: (E) 36:8
Question: Of the science books in a certain supply room, 40 are on botany, 55 are on zoology, 90 are on physics, 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same area science?
(A) 187
(B) 256
(C) 282
(D) 304
(E) 331
Rationale: The worst case scenario is to remove all the books on botany, zoology, and geology.
Also we can remove 79 books each from physics and chemistry.
The total is 40 + 55 + 50 + 79 + 79 = 303.
The next book removed must either be physics or chemistry, ensuring 80 books in that subject.
The answer is D.
Answer: (D) 304
Question: 210 students were asked in a survey if they preferred Windows or Mac brand computers. 60 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 90 of the students had no preference. How many of the students in the survey preferred Windows to Mac brand computers?
(A) 25
(B) 40
(C) 50
(D) 60
(E) 75
Rationale: We are told that60 Students claimed that they preferred Mac to Windows, which means that 60 preferred Mac but NOT Windows, so # of students who preferred Mac (P(A) as you wrote), does not equal to 60, it equals to 60+20 (20 is # of students who equally preferred both brands). Also we are asked to find # of the students who preferred Windows to Mac, so if you denote x as those who prefer Windows then you should calculate x-20.
So, if we use your formula it should be: 210={Mac}+{Windows}-{Both}+{Neither}=(60+20)+x-20+90 --> x=60 (# of student who prefer Windows) --> # of the students who preferred Windows to Mac is x-20=40.
Answer: (B) 40
Question: In a circuit board factory, all circuit boards that pass a verification process are certified. Every board that fails the verification process is indeed faulty, but 1/8 of those that pass are also faulty.
Approximately how many faulty circuit boards exist in a group of 3,200 circuit boards where 64 fail inspection?
(A) 72
(B) 192
(C) 456
(D) 256
(E) 264
Rationale: Total of 3,200 boards. All that fail verification are indeed faulty. So the 64 are indeed faulty. 1/8 those that pass are also faulty.
From the 3,200 we know 64 fail. So 3,136 must pass. Of these 1/8 are faulty. 3,136 divided by 8 gives you 392.
What one must do now is to add to the 392 which were not detected the actually detected faulty ones, namely the 64.
Total faulty: 456.
Answer: C
Answer: (C) 456
Question: In what time will a railway train 96 m long moving at the rate of 45 kmph pass a telegraph post on its way?
(A) 3 sec
(B) 8 sec
(C) 5 sec
(D) 6 sec
(E) 7 sec
Rationale: T =96/45 * 18/5 = 8 sec
ANSWER:B
Answer: (B) 8 sec
Question: A watch was sold at a loss of 10%. If it was sold for Rs.168 more, there would have been a gain of 4%. What is the cost price?
(A) s:1000
(B) s:1067
(C) s:1200
(D) s:1028
(E) s:1027
Rationale: 90%
104%
--------
14% ---- 168
100% ---- ? =>
Rs:1200
Answer: C
Answer: (C) s:1200
Question: Sides of a rectangular park are in the ratio 4: 3 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is?
(A) s.132.3
(B) s.129
(C) s.125
(D) s.120
(E) s.121
Rationale: 4x * 3x = 3750 => x = 17.7
2(82.3 + 50) = 264.6 m
264.6 * 1/2 = Rs.132.3
Answer:A
Answer: (A) s.132.3
Question: A train 225 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
(A) 86
(B) 50
(C) 12
(D) 13
(E) 67
Rationale: Speed of the train relative to man = (225/10) m/sec = (45/2) m/sec. [(45/2) * (18/5)] km/hr = 81 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 81 ==> x = 86 km/hr.
Answer: Option A
Answer: (A) 86
Question: The average of 45 results is 12. The average of first 22 of them is 15 and that of last 22 is 20. Find the 23 result?
(A) 600
(B) 480
(C) 750
(D) 650
(E) 560
Rationale: 23th result = sum of 45results - sum of 44 results
12*45-15*22+20*22 = 540-330+440 = 650
Answer is D
Answer: (D) 650
Question: The total age of A and B is 10 years more than the total age of B and C. C is how many years younger than A?
(A) 12
(B) 10
(C) C is elder than A
(D) Data inadequate
(E) None
Rationale: Solution
[(A+B) - (B+C)]	= 10
â€¹=â€ºA - C
= 10.
Answer B
Answer: (B) 10
Question: On increasing the number of lines in a page by 80, they become 240. What is the % of increase in the no. of lines in the page?
(A) 20%
(B) 305
(C) 50%
(D) 55%
(E) 60%
Rationale: Explanation : Number of pages increased = 80
Now , the number of pages of book = 240
Number of pages of the books before increase = 240 – 80 = 160
% increase in the number of pages in the book = 80 160
x 100% = 50%
C
Answer: (C) 50%
Question: At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present ?
(A) 12 years
(B) 15 years
(C) 17 years
(D) 19 years
(E) 21 years
Rationale: Let the present ages of Arun and Deepak be 4x years and 3x years respectively.
4x + 6 = 26 4x = 20
x = 5.
Deepak's age = 3x = 15 years.
Answer: B
Answer: (B) 15 years
Question: The first photo shoot takes 3 minutes long and then the following shoots are taken at a rate of 20 seconds/shoot as the model is already at the scene. What is the maximum number of photo shoots taken under 10 minutes ?
(A) 13
(B) 14
(C) 15
(D) 20
(E) 22
Rationale: a must be an integer as it is the number shoots at a rate of 20sec/shoot
3*60 + 20a = 10*60
20a = 420
a = 21
The total number of shoots -->1 +21 = 22 and
23th shoot will be taken at 620 seconds which is above 10 minutes
ANSWER: E
Answer: (E) 22
Question: If after 500 grams of water were added to the 24%-solution of alcohol, the strength of the solution decreased by one-third, how much of the 24%-solution was used?
(A) 180 grams
(B) 220 grams
(C) 250 grams
(D) 350 grams
(E) 1000 grams
Rationale: I too think 1000 grams should be the answer.
My reasoning is
The h20 content in 200 gms of water is 1
h20 content in 24% solution is 0.76
Resulting new solution's concentration decreases by one third means. Now it becomes 16% solution which means h20 content is 0.84
Let amount of solution be X
Then the equation can be set up
500*1 + 0.76X = 0.84 (X+500)
0.08X = 80
8X = 8000
X = 1000 (ANS E)
Answer: (E) 1000 grams
Question: There is enough provisions for 100 girls in a hostel for 50 days. If there were 20 men less, how long will the provision last?
(A) 250
(B) 255
(C) 260
(D) 265
(E) 270
Rationale: We have, M1D1 = M2D2
100*50= 20* D2
D2 = 100*50/20 = 250 days.
ANSWER:A
Answer: (A) 250
Question: Which of the following fractions R, if written as a decimal, would have a 2 in the thousandths place ?
(A)  3/11
(B)  7/9
(C)  1/8
(D)  4/7
(E)  1/6
Rationale: (A) R=3/11 = 0.2727272727....
Answer: A
Answer: (A)  3/11
Question: A box contains 21 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is
(A) 4/19
(B) 7/19
(C) 12/19
(D) 21/95
(E) 31/88
Rationale: Solution
P( None is defective)
= 17C2 / 21C2
= 57/88.
P( at least one is defective)
= (1- 57/88)
= 31/88.
Answer E
Answer: (E) 31/88
Question: Sam’s car was fined when he gave Joe and Peter a ride, so they decided to help Sam pay the fine. Joe paid $8 more than 1/4 of the fine and Peter paid $8 less than 1/3 of the fine, leaving pay $15 less than 1/2 the fine to complete the payment. What fraction of the fine did Sam pay?
(A) $70
(B) $72
(C) $73
(D) $74
(E) $75
Rationale: Call the fine F. Joe paid (1/4)F + 4 and Peter paid (1/3)F – 4, leaving (1/2)F – 5 left. If we add those three up, they should add up to F.
F = [(1/4)F + 8] + [(1/3)F – 8] + [(1/2)F – 15]
F = (1/4)F + (1/3)F + (1/2)F – 15
Multiply all terms by 12 to clear the fractions.
12F = 3F + 4F + 6F – 180
12F = 13 F – 180
–F = – 180
F = 180
Well, if the fine cost $180, then Sam paid the part not covered by Joe or Peter. Half the fine is $90, and Sam paid $15 less than this: $75
Answer = E
Answer: (E) $75
Question: On a two-dimensional coordinate plane, the line s = x^2 - x^3 touches the x-axis in how many places?
(A)  0
(B)  1
(C)  2
(D)  3
(E)  4
Rationale: Apparently it's s = x^2 - x^3 instead of s = x^2 - s^3.
In this case: the x-intercept is the value(s) of x for s = 0.
0 = x^2 - x^3;
0 = x^2(1 - x);
x = 0 or x = 1.
Answer: C.
Answer: (C)  2
Question: What is R’s share of profit in a joit venture?
I.Q started business investing Rs. 80,000.
II.R joined him after 3 months.
III.P joined after 4 months with a capital of Rs. 1,20,000 and got Rs. 6000 as his share profit.
(A) All I, II and III
(B) I and III only
(C) II and III only
(D) Even with all I, II and III, the answer cannot be arrived at
(E) None of these
Rationale: Explanation:
From I, II and III, we get P : Q : R = (120000 x 8) : (80000 x 12) : (x x 9).
Since R’s investment is not given, the above ratio cannot be give.
Given data is inadequate.
Answer E
Answer: (E) None of these
Question: At a meeting, 5 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?
(A) 12
(B) 24
(C) 120
(D) 144
(E) 720
Rationale: The number of arrangements of n distinct objects in a row is given by n!
The number of arrangements of n distinct objects in a circle is given by (n−1)!
"The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:
R=n!-n=(n−1)!
(n−1)!=(5−1)!=24
Answer: B
Answer: (B) 24
Question: A certain kind of necklace is made from 9 silver, 6 red, and 3 black beads. What is the maximum number of these necklaces that can be made from 99 beads of each color ?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 15
Rationale: Atleast 9 silver breads are needed to make a necklace, so irrespective of the combinations of red and black beads, the number of necklaces that can be formed will be
99/9 =11
Answer:- D
Answer: (D) 11
Question: In the next Worldcup of cricket there will be 12 teams, divided equally in 2groups. Teams of eachgroup will play a match against each other. From each group 3 top teams will qualify for the next round. In this round each team will play against each others once. 4top teams of this round will qualify for the semifinal round, where they play the best of 3matches. The Minimum number of matches in the next World cup will be
(A) 34
(B) 45
(C) 53
(D) 55
(E) 59
Rationale: The number of matches in first round,
= 6C2 +6C2;
Number of matches in next round,
= 6C2;
Number of matches in semifinals,
= 4C2;
Total number of matches,
= 6C2 +6C2+6C2+4C2+2.
= 53.
C
Answer: (C) 53
Question: The least number which when increased by 7 each divisible by each one of 24, 32, 36 and 54 is :
(A) 857
(B) 859
(C) 869
(D) 4320
(E) None of these
Rationale: Solution
Required number = (L.C.M. of 24, 32, 36, 54) - 7 = 864 - 7 = 857. Answer A
Answer: (A) 857
Question: The average of first four prime numbers greater than 20 is?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: 23 + 29 + 31 + 37 = 120/4 = 30
ANSWER:C
Answer: (C) 30
Question: Bradley owns b video game cartridges. If Bradleyâ€™s total is one-fifth the total owned by Andrew and five times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?
(A) 16/3)b
(B) 17/4)b
(C) 13/4)b
(D) 31/5)b
(E) 7/12)b
Rationale: Step 1: Categorize the problem
This problem is testing basic algebra and equations, with an extra layer of complexity by having variables in the answer choices.
Step 2: Think like the test maker
What is the key detail or key details in the problem? The key detail to immediately recognize is that the problem gives you Andrew and Charlieâ€™s totals in relation to Bradleyâ€™s total rather than giving you Bradleyâ€™s total in relation to the other two; and then the problem asks you to solve the problem in terms of b. This means that you have to relate Andrew and Charlieâ€™s values in relation to Bradleyâ€™s total. The test maker is attempting to force you to structure the problem in the opposite way that most people are used to structuring information. By gaining this insight, it makes it easier to solve the problem.
Step 3: Solve the problem
b = Bradleyâ€™s total
5b = Andrewâ€™s total
(1/5)b = Charlieâ€™s total
Add each total
b + 5b+ (1/5)b = 6b + (1/5)b = (30/5)b + (1/5)b = (31/5)b
Therefore,choose D.
Answer: (D) 31/5)b
Question: Find the value of x from the below equation: x^2−7x+10=0
(A) 5
(B) 7
(C) 6
(D) 11
(E) 12
Rationale: Here we need to find out a and b such that a + b = -7 and ab = +10
a = -5 and b = -2 satisfies the above condition.
Hence
x^2−7x+10=(x−5)(x−2)
x2−7x+10=(x−5)(x−2)
x^2−7x+10
=0
⇒(x−5)(x−2)
=0
x2−7x+10=0⇒(x−5)(x−2)=0
Step 3: Equate each factor to 0 and solve the equations
(x−5)(x−2)
=0
⇒(x−5)
=0or (x−2)=0
⇒x= 5 or 2
A
Answer: (A) 5
Question: A train is 360 meter long is running at a speed of 52 km/hour. In what time will it pass a bridge of 140 meter length.
(A) 24.62 seconds
(B) 34.62 seconds
(C) 44.62 seconds
(D) 54.62 seconds
(E) None of these
Rationale: Explanation:
Speed = 52 Km/hr = 52*(5/18) m/sec
= 130/9 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
=500/130/9=34.62 seconds
Answer: B
Answer: (B) 34.62 seconds
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
(A) 120 metres
(B) 180 metres
(C) 324 metres
(D) 150 metres
(E) 160 metres
Rationale: Explanation:
Speed=	60 X5/18 m/sec	=50/3m/sec
Length of the train = (Speed x Time).
Length of the train =50/3 X 9 m =150m
ANSWER IS D
Answer: (D) 150 metres
Question: A hiker 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 at 5 miles per hour for 3 hours. How many miles in total did she walk?
(A) 53
(B) 44
(C) 58
(D) 60
(E) 62
Rationale: First day - 18 miles with 3 miles per hours then total - 6 hours for that day
Second day - 4 miles per hour and 5 hours - 20 miles
Third day - 5 miles per hour and 3 hours - 15 miles
Total 18+20+15 = 53
Answer: option A.
Answer: (A) 53
Question: In a game, a player can win by getting six consecutive tails in seven throws of a coin. What is the probability of winning if the player gets a tail on the first two throws?
(A) 1/2
(B) 1/4
(C) 1/8
(D) 1/16
(E) 1/32
Rationale: The only way to win is to get a tail on each of the next four throws.
P(four tails)=(1/2)^4=1/16
The answer is D.
Answer: (D) 1/16
Question: From a pack of cards, two cards are drawn one after the other, with replacement. What is the probability that the first card is a black card and the second card is a king?
(A) 1/26
(B) 1/13
(C) 3/52
(D) 3/26
(E) 15/26
Rationale: P(black card) = 1/2
P(king) = 1/13
P(black card then a king) = 1/2 * 1/13 = 1/26
The answer is A.
Answer: (A) 1/26
Question: A can give B 200 meters start and C 400 meters start in a kilometer race. How much start can B give C in a kilometer race?
(A) 111.12
(B) 250
(C) 111.64
(D) 111.11
(E) 101.12
Rationale: A runs 1000 m while B runs 800 m and C runs 600 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 600)/800 = 750 m.
B can give C = 1000 - 750= 250 m.
Answer:B
Answer: (B) 250
Question: 10^25 - 460 is divisible by all of the following except:
(A) A.11
(B) B.9
(C) C.5
(D) D.4
(E) E.3
Rationale: The last three digits ( 1000 - 460 ) 540
540 is divisible by 3,4,9,5
540 is not evenly divisible by 11 so the answer is A) 11
Answer: (A) A.11
Question: Lilly has 10 fish and Rosy has 8 fish. In total, how many fish do they have in all?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: 10+8=18
The answer is D.
Answer: (D) 18
Question: Thomas bought a table for Rs. 2000 and a chair for Rs. 1000. After one month of usage he sold table to David for Rs. 1800 and chair to Micheal for Rs. 900. What is the total percentage of loss incurred to Thomas?
(A) 20%
(B) 30%
(C) 10%
(D) 35%
(E) 45%
Rationale: Total amount spent by Thomas in buying table and chair= Rs.3000
Total money earned by Thomas by selling those=Rs (1800+900)=2700
Total loss incurred=Rs(3000-2700)= Rs.300
Total percentage of loss incurred to Thomas= (300/3000)*100=10%
Answer:C
Answer: (C) 10%
Question: N and M are each 3-digit integers. Each of the numbers 1, 2, 3, 7, 8 and 9 is a digit of either N or M. What is the smallest possible positive difference between N and M?
(A) 19
(B) 49
(C) 58
(D) 113
(E) 131
Rationale: You have 6 digits: 1, 2, 3, 7, 8, 9
Each digit needs to be used to make two 3 digit numbers. This means that we will use each of the digits only once and in only one of the numbers. The numbers need to be as close to each other as possible. The numbers cannot be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other.
The first digit (hundreds digit) of both numbers should be consecutive integers
Now let's think about the next digit (the tens digit). To minimize the difference between the numbers, the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . So let's not use 1 and 9 in the hundreds places and reserve them for the tens places . Now what are the options?
Try and make a pair with (2** and 3**). Make the 2** number as large as possible and make the 3** number as small as possible.
298 and 317(difference is 19) or
Try and make a pair with (7** and 8**). Make the 7** number as large as possible and make the 8** number as small as possible. We get 793 and 812 (difference is 19)
A
Answer: (A) 19