mathewhe/aqua_rat huggingface dataset:
Question: A bag contains a total of 93 coins in the form of one rupee and 50 paise coins. If the total value of coins in the bag is Rs.56, find the number of 50 paise coins in the bag?
(A) 60
(B) 56
(C) 64
(D) 74
(E) 72
Rationale: Let the number of one rupee coins in the bag be x.
Number of 50 paise coins in the bag is 93 - x.
Total value of coins
[100x + 50(93 - x)]paise = 5600 paise
=> x = 74
ANSWER:D
Answer: (D) 74
Question: A train is moving at 6/7 of its usual speed. The train is 10 minutes too late. What is the usual time (in hours) for the train to complete the journey?
(A) 0.5
(B) 1
(C) 1.5
(D) 2
(E) 2.5
Rationale: new time = d / (6v/7) = 7/6 * usual time
10 minutes represents 1/6 of the usual time.
The usual time is 1 hour.
The answer is B.
Answer: (B) 1
Question: A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is
(A) 5
(B) 2
(C) 6
(D) 9
(E) 22
Rationale: Explanation:
Let the son's present age be x years. Then, man's present age = (x + 24) years.
(x + 24) + 2 = 2(x + 2)
x + 26 = 2x + 4
x = 22.
Answer: E
Answer: (E) 22
Question: A, B and C invested Rs.2400, Rs.7200 and Rs.9600 respectively, in a partnership business. Find the share of A in profit of Rs.9000 after a year?
(A) 1125
(B) 2400
(C) 7200
(D) 2500
(E) 2511
Rationale: Explanation:
2400:7200:9600
1:3:4
1/8 * 9000 = 1125
Answer: A
Answer: (A) 1125
Question: 4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?
(A) 4
(B) 16
(C) 8
(D) 1
(E) 0
Rationale: Explanation :
Let the required number of mats be x
More mat-weavers, more mats (direct proportion)
More days, more mats (direct proportion)
⇒ 4 × 4 × x = 8 × 8 × 4
⇒ x = 2 × 2 × 4 = 16. Answer : Option B
Answer: (B) 16
Question: Sandy bought 65 books for $1180 from one shop and 55 books for $860 from another shop. What is the average price that Sandy paid per book?
(A) $13
(B) $15
(C) $17
(D) $19
(E) $21
Rationale: average price per book = (1180 + 860) / (65 + 55) = 2040 / 120 = $17
The answer is C.
Answer: (C) $17
Question: A rectangular lawn 70 m × 30 m has two roads each 5 metres wide, running in the middle of it, one parallel to the length and the other parallel to the breadth. Find the cost of gravelling the road at the rate of 4 per square metre.
(A) 2,000
(B) 1,800
(C) 1,900
(D) 1,700
(E) None of these
Rationale: Total area of road
= Area of road which parallel to length + Area of road which parallel to breadth – overlapped road
= 70 × 5 + 30 × 5 – 5 × 5
= 350 + 150 – 25
= 500 – 25 = 475 m2
∴ Cost of gravelling the road
= 475 × 4 = 1900
Answer C
Answer: (C) 1,900
Question: Cream costs twice as much as skim milk. A certain brand of milk is 4/5 cream and 1/5 skim milk. What fraction of the cost of this brand is due to the cream?
(A) 3/4
(B) 4/5
(C) 5/6
(D) 7/8
(E) 8/9
Rationale: Let x be the cost of the skim milk in the mixture.
The cost of the cream is 4x*2 = 8x.
The total cost is x+8x = 9x and the fraction due to the cream is 8x / 9x = 8/9
The answer is E.
Answer: (E) 8/9
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 91000, then the share of B is?
(A) A)44500
(B) B)42000
(C) C)44098
(D) D)43007
(E) E)44098
Rationale: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 91000
Share of B = 6/13 (91000)
= Rs. 42000
Answer:B
Answer: (B) B)42000
Question: Find the average (arithmetic mean) of x and y if the average of x, y, and 50 is 20 more than the average of x, y, 50, and 70.
(A) 100
(B) 120
(C) 140
(D) 180
(E) 200
Rationale: consider "60 is 20 more than 40": 60 = 40 + 20
similarly
(x+y+50)/3 = (x+y+50+70)/4 + 20
(x+y+50)/3 = (x+y+120)/4 + 80/4
(x+y+50)/3 = (x+y+120+80)/4
(x+y+50)/3 = (x+y+200)/4
cross multiply
4(x+y+50) = 3(x+y+200)
4x+4y+200 = 3x+3y+600
4x-3x +4y-3y = 600 - 200
x + y = 400
so
(x+y)/2 = 400/2
(x+y)/2 = 200
thus the average of x and y is 200
E
Answer: (E) 200
Question: A spirit and water solution is sold in a market. The cost per liter of the solution is directly proportional to the part (fraction) of spirit (by volume) the solution has. A solution of 1 liter of spirit and 1 liter of water costs 30 cents. How many cents does a solution of 1 liter of spirit and 2 liters of water cost?
(A) 13
(B) 30
(C) 50
(D) 51
(E) 52
Rationale: Yes, ensure that you understand the relation thoroughly!
Cost per liter = K * Fraction of Spirit
30 cents is the cost of 2 liters of solution (1 part water, 1 part spirit). So cost per liter is 15 cents. Fraction of spirit is 1/2.
15 = K * (1/2)
K = 30
Cost per liter = 30 * (1/3) (1 part spirit, 2 parts water)
Cost for 3 liters = 30 * (1/3) * 3 = 50 cents
B. 30 cents
Answer: (B) 30
Question: A person covered one-fourth of the total distance at 26 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?
(A) 64/8kmph
(B) 64/3kmph
(C) 64/9kmph
(D) 64/6kmph
(E) 64/4kmph
Rationale: Let the total distance be x km
total time taken = (x/4)/16 + (3x/4)/24
= x/64 + x/32 = 3x/64
Average speed = x/(3x/64) = 64/3kmph
= 21 (1/3)kmph.
Answer: B
Answer: (B) 64/3kmph
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 60 m and they cross each other in 12 sec, then the speed of each train is?
(A) 30
(B) 35
(C) 18
(D) 12
(E) 38
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (60 + 60)/12 => x = 5
Speed of each train = 10 m/sec.
= 5 * 18/5 = 18 km/hr.
Answer: Option C
Answer: (C) 18
Question: A crew can row a certain course up the stream in 84 minutes; they can row the same course down stream in 15 minutes less than they can row it in still water. How long would they take to row down with the stream
(A) 45 or 23 minutes
(B) 63 or 12 minutes
(C) 69 minutes
(D) 19 minutes
(E) 25 minutes
Rationale: A method has been discussed here to nullify the calculations though.
All I can input here is,
speed of a crew in still water = 1/2 ( speed upstream + speed downstream)
approximating this for time,
t = 1/2(84+ (t-15))
giving t = 69
C
Answer: (C) 69 minutes
Question: The ratio between the length and the breadth of a rectangular park is 1 : 3. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 4 min, then the area of the park (in sq. m) is?
(A) 800 m
(B) 12000 m
(C) 36000 m
(D) 80000 m
(E) 30000 m
Rationale: Perimeter = Distance covered in 4 min. = (12000 x 4)/60 m = 800 m.
Let length = 1x metres and breadth = 3x metres.
Then, 2(1x + 3x) = 800 or x =100.
Length = 100 m and Breadth = 300 m.
Area = (100 x 300) m2 = 30000 m
E
Answer: (E) 30000 m
Question: A set of 11 positive integers has an average of 30. Which of the following is the greatest possible value for the median of this set?
(A) 25
(B) 30
(C) 36
(D) 54
(E) 46
Rationale: for the median to be max , we should take all the values below meadian to be the lowest and the remaining values to be the same..
here 1 is the lowest value(positive int) so the lowest 5 int will equal 5..
remaining 6= 30*11-5=325..
therefore each valueof these 6 int =325/6=54
ans D
Answer: (D) 54
Question: The present ages of three persons in proportions 3 : 7 : 5. Eight years ago, the sum of their ages was 51. Find their present ages (in years).
(A) 8, 20, 28
(B) 16, 28, 36
(C) 15,35,25
(D) 18, 24, 32
(E) None of these
Rationale: Explanation:
Let their present ages be 3x, 7x and 5x years respectively.
Then, (3x - 8) + (7x - 8) + (5x - 8) = 51
15x = 75
x = 5
Their present ages are 3x = 15 years, 7x = 35 years and 5x = 25 years respectively.
Answer: C
Answer: (C) 15,35,25
Question: The diagonal of a square is the height in an equilateral triangle. If the side of the square is x, what is the side of the equilateral triangle in terms of x?
(A) √(2/3) × x
(B) 2/√3 × x
(C) √3x
(D) √(8/3) × x
(E) 2√3 × x
Rationale: The diagonal of the square
x* sqrt(2)
If that's the altitude of the equilateral triangle, the formula for which is side * sqrt(3)/2
Side is 2 sqrt(2)* x/ sqrt(3)
Answer: (Option D)
Answer: (D) √(8/3) × x
Question: What approximate value should come in place of the question mark (?) in the following equation’?
3 3⁄5 of 157.85 + 39% of 1847 = ? – 447.30
(A) 1200
(B) 1500
(C) 1600
(D) 1800
(E) 2100
Rationale: ? ≈ 18⁄5 × 160 + 40⁄1000 × 1850 + 450
≈ 576 + 740 + 450 ≈ 1760 ≈ 1800
Answer D
Answer: (D) 1800
Question: Calculate the positive root of the polynomial (x - 1)(x - 2)(x - 3)(x - 4)- 63.
(A) 5+√37/2
(B) 4+√37/2
(C) 3+√37/2
(D) 2+√37/2
(E) 6+√37/2
Rationale: Note that
(x - 1)(x - 2)(x - 3)(x - 4) - 63 = [(x - 2)(x - 3)][(x -1)(x - 4)] - 63
= (x2-5x + 6)(x2 - 5x + 4) - 63
= [(x2 - 5x + 5 + 1)(x2 - 5x + 5 -1)] - 63
= [(x2 - 5x + 5)2 - 1] - 63
= (x2 -5x + 5)2 - 64
= (x2 - 5x + 5 + 8)(x2 -5x + 5 - 8)
= (x2 - 5x + 13)(x2- 5x - 3):
The polynomial x2 - 5x + 13 has no real roots, while the polynomial x2 -5x - 3 has roots
x=5+-√37/2.
since 5-√37/2<0,
the only positive root is 5+√37/2
correct answer A
Answer: (A) 5+√37/2
Question: If 1/(x+3)+1/(x-3)=1/(x+3), what is the value of x?
(A) 2
(B) 3
(C) -1
(D) -2
(E) -3
Rationale: If we solve the question, we get x=-3.
Option: E
Answer: (E) -3
Question: A octagon marked 1, 2, 3, 4, 5,6,7 and 8 on its eight sides. four colors, pink, yellow,green and blue are used to paint the eight sides of the octagon. If the adjacent faces are painted with the different colors, in how many ways can the octagon be painted?
(A) 6
(B) 4
(C) 27
(D) 12
(E) 8
Rationale: If the base of the Octagon is pink, then in order the adjacent faces to be painted with the different colors, the top must also be pink. 6 side faces can be painted in Yellow-Blue-Green Yellow-Blue-Green OR Blue-Green-Yellow Blue-Green-Yellow(2 options).
But we can have the base painted in either of the three colors, thus the total number of ways to paint the Octagon is 4*2=8.
Answer:E.
Answer: (E) 8
Question: When running a mile during a recent track meet, Nuria was initially credited with a final time of 5 minutes, 40 seconds. Shortly after her run, officials realized that the timing mechanism malfunctioned. The stopwatch did not begin timing her until 11/25 of a minute after she began to run. If the time was otherwise correct, how long did it actually take Nuria to run the mile?
(A) 5 minutes, 17.6 seconds
(B) 5 minutes, 21.8 seconds
(C) 5 minutes, 43.56 seconds
(D) 5 minutes, 44.44 seconds
(E) 6 minutes, 10.4 seconds
Rationale: One approach:
The watch starts to work after Nuria began his running. It means the time should be greater than credited 5 minutes, 40 seconds. The only number is 6 minutes, 10.4 seconds.
Another approach:
11/25 close to 30 second when added to the 5 minutes, 40 seconds, it means it passes 6 minute.
Answer: E
Answer: (E) 6 minutes, 10.4 seconds
Question: On a sum of money, the S.I. for 2 years is Rs. 660, while the C.I. is Rs. 696.30, the rate of interest being the same in both the cases. The rate of interest is?
(A) 22
(B) 99
(C) 27
(D) 11
(E) 37
Rationale: Difference in C.I. and S.I for 2 years = (696.30 - 660) = Rs. 36.30.
S.I for one year = Rs. 330.
S.I. on Rs. 330 for 1 year = Rs. 36.30
Rate = (100 * 36.30)/(330 * 1) = 11%.Answer: D
Answer: (D) 11
Question: In 1990 a total of 100 earthquakes occurred worldwide, some but not all of which occurred in Asia. If 20 of these earthquakes occurred in Asia, which of the following represents the ratio of the number of earthquakes that occurred in Asia to the number that did NOT occur in Asia?
(A) 1/7
(B) 1/6
(C) 1/2
(D) 1/4
(E) 1/3
Rationale: We're given a couple of facts to work with:
1) There were a total of 100 earthquakes
2) Of those earthquakes, 20 of them occurred in Asia
We're asked for the ratio of the number of earthquakes that occurred IN ASIA to the number of earthquakes that DID NOT occur in Asia.
Thus, there were 80 earthquakes that DID NOT occur in Asia....
The answer to the question is 20/80 ie. 1/4
Answer : D
Answer: (D) 1/4
Question: Danya prepared 4 different letters to 4 different addresses. For each letter, she prepared one envelope with its correct address. If the 4 letters are to be put into the four envelopes at random, what is the probability that only one letter will be put into the envelope with its correct address?
(A) 1/24
(B) 1/8
(C) 1/4
(D) 1/3
(E) 3/8
Rationale: Total Danya# of ways - 4! = 24.
Desired:
A-Mapped to the only correct address----------x 1 way only
B-Mapped to other two incorrect addresses - x 2 ways
C-Mapped to other two incorrect addresses - x 2 ways
D-Mapped to other two incorrect addresses - x 2 ways
Therefore, 1*2*2*2/24 = 1/3.?
Answer: (D) 1/3
Question: Excluding stoppages, the speed of a train is 67 kmph and including stoppages it is 51 kmph. Of how many minutes does the train stop per hour?
(A) 82
(B) 17
(C) 14
(D) 82
(E) 18
Rationale: Explanation:
T =16/67 * 60 = 14
Answer: Option C
Answer: (C) 14
Question: The mark up between weights of A and B is is 20 percent of the weight of A. The markup is what percent of the weight of B ?
(markup = weight of B - weight of A)
(A)  8%
(B)  10%
(C)  12 1/2%
(D)  15%
(E)  16 2/3%
Rationale: A = weight of A
B = weight of B
MP = 0.2 A
B = A + 0.2 A = 1.2 A
hence Markup = B-A = 0.2/1.2 B = 1/6 B. Hence MP is 16.67% of B
Answer E
Answer: (E)  16 2/3%
Question: In the sequence S, each term after the first is twice the previous term. If the first term of sequence S is 3, what is the sum of the 14th, 15th, 16th, 17th, 18th and 19th terms in sequence S?
(A) 3(2^16)
(B) 9(2^15)
(C) 21(2^14)
(D) 9(2^14)
(E) 189(2^13)
Rationale: The terms in the sequence can be shown as
a(n) = 2* a(n-1)
So, the sequence will look like: 3, 2*3, (2^2) *3,...
And the nth term will be given as 2^(n-1) *3
Therefore, a(14) = (2^13)*3, a(15) = (2^14) *3, a(16) = (2^15) *3, a(17) = (2^16) *3 , a(18) = (2^17) *3 and a(19) = (2^18) *3
So, a(14) + a(15) + a(16)+ a(17)+ a(18) = (2^13) *3 + (2^14) *3 + (2^15) *3+ (2^16) *3+ (2^17) *3+ (2^18) *3
= 3* (2^13) *(1+2+4+8+16+32) = 3* (2^13) *63
= 189 * (2^13)
Answer : E
Answer: (E) 189(2^13)
Question: What was the day of the week on 28th May,2006 ?
(A) Thursday
(B) Friday
(C) Saturday
(D) Sunday
(E) None of these
Rationale: Solution
28 May,2006 =(2005 years + Period from 1.1.2006 to 28.5.2006)
Odd days in 1600 years = 0
Odd days in 400 years = 0
5 years =(4 ordinary years + 1 leap year)=(4 x 1 + 1 x 2) odd days
=6 odd days
Jan. Feb. March April May
(31 + 28 + 31 + 30 + 28) = 148 days =(21 weeks + 1 day)
= 1 odd day
Total number of odd days = (0 + 0 + 6 + 1)=7 = 0 odd day.
Given day is Sunday. Answer D
Answer: (D) Sunday
Question: Jerry went to a shop and bought things worth Rs. 40, out of which 30 % went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) 19
(B) 19.7
(C) 21.3
(D) 31.5
(E) 34.7
Rationale: Total cost of the items he purchased = Rs.40
Given that out of this Rs.40, 30 % is given as tax
=> Total tax incurred = 30 % = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (40−30/100−x)6/100 = 30/100
⇒ 6(40 −0.3 −x) = 30
⇒ (40 − 0.3 − x) = 5
⇒ x = 40 − 0.3 − 5 = 34.7
E)
Answer: (E) 34.7
Question: Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 240 sandwiches were made, how many peanut butter sandwiches
were made?
(A) 15
(B) 30
(C) 38
(D) 42
(E) 96
Rationale: For deciding such task we should calculate all parts 5 + 7 + 8 = 20 parts
and we should calculate how many sandwiches holds 1 part:
240 / 20 =12 sandwiches in one part
For peanut butter we have 8 parts so:
8 * 12 = 96
Answer is E
Answer: (E) 96
Question: Two goods trains each 250 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 24 sec
(B) 88 sec
(C) 48 sec
(D) 18 sec
(E) 9 sec
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 250 + 250 = 500 m.
Required time = 500 * 6/125 = 48 sec.
Answer:A
Answer: (A) 24 sec
Question: If the perimeter of a rectangular park is 1000 m, its length when its breadth is 200 m is?
(A) 50
(B) 100
(C) 200
(D) 300
(E) 400
Rationale: 2(l + 200) = 1000 => l = 300 m Answer: D
Answer: (D) 300
Question: Two unbiased coins are tossed. What is probability of getting at most one tail ?
(A) 12
(B) 13
(C) 32
(D) 34
(E) None of these
Rationale: Explanation:
Total 4 cases = [HH, TT, TH, HT]
Favourable cases = [HH, TH, HT]
Please note we need atmost one tail, not atleast one tail.
So probability = 3/4
Answer: D
Answer: (D) 34
Question: Find the area of a parallelogram with base 20 cm and height 10 cm?
(A) 290 cm2
(B) 380 cm2
(C) 270 cm2
(D) 280 cm2
(E) 200 cm2
Rationale: Area of a parallelogram = base * height = 20 * 10
= 200 cm2
Answer:E
Answer: (E) 200 cm2
Question: A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 according to the following constraints. The first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?
(A) 144
(B) 152
(C) 160
(D) 168
(E) 176
Rationale: The first digit can be filled in 8 ways
For second digit , it can either be 0 or 1
Case 1 -
If second digit is 1 ,Third digit can take 10 values
number of codes = 8 * 1 * 10 = 80
Case 2 -
If second digit is 0,Third digit can take 9 values ( Third digit can't be zero)
number of codes = 8 * 1 * 9= 72
Total number of codes = 152
Answer B
Answer: (B) 152
Question: A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 27, what is the total amount?
(A) 178
(B) 105
(C) 176
(D) 159
(E) 162
Rationale: x:y:z = 100:45:30
20:9:6
9 --- 27
35 --- ? => 105
Answer: B
Answer: (B) 105
Question: A monkey ascends a greased pole 10 meters high. He ascends 2 meters in the first minute and then slips down 1 meter in the alternate minute. If this pattern continues until he climbs the pole , in how many minutes would he reach at the top of the pole ?
(A) 10th minute
(B) 21st minute
(C) 17th minute
(D) 22nd minute
(E) 13th minute
Rationale: The money is climbing 1meter in 2min. This pattern will go on till he reaches 10meters. I mean this will continue for first 8*2=16mins. he would have reached 8meters. After that he will climb 2meters and he will reach the pole. So total time taken = 16 + 1 = 17mins.
So, asnwer will be C
Answer: (C) 17th minute
Question: Which of the following equations has a solution in common with x^2 - 7x + 10 = 0 ?
(A) x^2 - 3x - 10 = 0
(B) 4x^2 + 9x + 2 = 0
(C) 4x^2 + 6x + 2 = 0
(D) x^2 + 10x + 25 = 0
(E) none of the above
Rationale: Given : x^2 - 7x + 10 = 0 => (x-2) (x-5) = 0 => 2 and 5 are the roots..
A. x^2 - 3x - 10 = 0 => (x+2) (x-5)
B. 4x^2 + 9x + 2 = 0 => (4x+1) (x+2)
C. 4x^2 + 6x + 2 = 0 => (2x+1) (2x+2)
D. x^2 + 10x + 25 = 0 => (x+5) (x+5)
None of the answer equations have exactly both the same roots as the question equation, but at least one of them does share one of the two roots.
So IMO "A" is correct answer... because it shares the one root (part of the solution), 5, from the (x-5) portion of its simplification.
Answer: (A) x^2 - 3x - 10 = 0
Question: Find the difference between the local value and face value of 5 in the numeral 475240 is
(A) 4990
(B) 4890
(C) 4995
(D) 4885
(E) 4775
Rationale: Explanation:
(Local value of 5) - (Face value of 5)
= (5000 - 5) = 4995
Answer: Option C
Answer: (C) 4995
Question: In a college, the ratio of the number of boys to girls is 8 : 5. If there are 100 girls, the total number of
students in the college is
(A) 420
(B) 520
(C) 620
(D) 260
(E) None of these
Rationale: Explanation:
Let the boy are 8x and Girls are 5x
=> 5x = 100
=> x = 20
Total students = 8x+5x = 13x = 13(20) = 260
Answer: D
Answer: (D) 260
Question: There are 4 identical pens and 7 identical books. In how many ways can a person select at least one object from this set?
(A) 11
(B) 12
(C) 39
(D) (2^4 - 1)(2^7 -1)
(E) 2^11 - 1
Rationale: 7 items can be chosen in 8 ways- 0,1,2..7 at a time
similarly 4 items can be chosen way will be 5- choosing 0, choosing 1.. choosing 4
total ways = 8*5=40..
But we are looking for AT LEAST 1, so subtract 1 way when both are 0..
ans 40-1=39.
ANSWER:C
Answer: (C) 39
Question: x, y, and z are three positive integers whose average is 10. If x≤y≤z and z-x=3, which of the following could be the median R of x, y, and z?
I. 9
II. 10
III. 11
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
Rationale: Average gives us an idea that 3 nos. are close to 10.
so 10, 10, 10 is an unacceptable option because (z-x =3), but it helps in getting other combinations.
Let us see options.
If 9 has to be median R.
1st term has to less than 9 or equal to 9. (also maintain z-x = 3)
9 9 12 --> satisfies all conditions so 9 can be a median value.
If 11 has to be a median
3rd term has to be 11 or more than 11. (also maintain z-x = 3)
8 11 11 -->satisfies all conditions so 9 can be a median value.
Now for 10 to be median.
z+ x = 20 and z-x = 3, we wont have integer values of z.
10 cannot be a median
E is the answer.
Answer: (E) I and III only
Question: An article is bought for Rs.765 and sold for Rs.1000, find the gain percent?
(A) 30.6%
(B) 30.5%
(C) 30.7%
(D) 30.8%
(E) 30.9%
Rationale: 765 ---- 235
100 ---- ? => 30.7%
Answer:C
Answer: (C) 30.7%
Question: If x/y = 2 and (a - x)/(3b - y) = 2, then the value of a/b is?
(A)  –3
(B)  -2
(C)  6
(D)  2
(E)  3
Rationale: x = 2y
a - 2y = 2(3b - y)
a - 2y = 6b - 2y
a = 6b
a/b = 6
Answer: C
Answer: (C)  6
Question: At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?
(A) 5%
(B) 3 1/2%
(C) 4%
(D) 5 1/2 %
(E) 6 1/2 %
Rationale: Explanation:
150 = (750*5*R)/100
R = 4%
ANSWER IS C
Answer: (C) 4%
Question: A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
A. 111.12 m
(A) 111.12 m
(B) 221.12 m
(C) 271.12 m
(D) 611.12 m
(E) 191.12 m
Rationale: Explanation:
A runs 1000 m while B runs 900 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/900 = 8000/9 = 888.88 m.
B can give C = 1000 - 888.88 = 111.12 m.
Answer:A
Answer: (A) 111.12 m
Question: A money lender lends Rs.2000 for six months at 20% p.a. rate. It the interest is reckoned quarterly than find the amount given after time limit.
(A) 2205
(B) 3387
(C) 2882
(D) 2997
(E) 1278
Rationale: A = 2000(21/20)2 = 2205
Answer: A
Answer: (A) 2205
Question: A number whose fifth part increased by 4 is equal to its fourth part diminished by 4 is ?
(A) 160
(B) 180
(C) 200
(D) 220
(E) None
Rationale: Answer
Let the number be N.
Then, (N/5) + 4 = (N/4) - 4
â‡’ (N/4) - (N/5) = 8
â‡’ (5N - 4N)/20 = 8
âˆ´ N = 160
Option: A
Answer: (A) 160
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes?
(A) 53
(B) 58
(C) 64
(D) 69
(E) 72
Rationale: Ans.(C)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways
Answer: (C) 64
Question: A bullet train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the bullet train is 54 km/hr, what is the length of the platform?
(A) 240 m
(B) 220 m
(C) 260 m
(D) 224 m
(E) 239 m
Rationale: A
240 M
Speed = 54 x 5/18 = 15 m/s
Length of the bullet train = (15 x 20)m = 300 m.
Let the length of the platform be x metres.
Then, (x + 300)/36 = 15
--> x + 300 = 540
x = 240m.
Answer: (A) 240 m
Question: The timing of a college is from 12 p.m to 5.00 p.m. Five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students. Find the duration of each lecture.
(A) 56 minutes
(B) 45 minutes
(C) 30 minutes
(D) 48 minutes
(E) 44 minutes
Rationale: Explanation:
Total time a student spends in college = 5 hours 00 minutes = 300 minutes
As there are 5 lectures, the number of breaks between lectures is 4. Total time of the break = 20 minutes
Hence, the duration of each lecture is = (300 â€“ 20)/5
= 56 minutes
ANSWER A
Answer: (A) 56 minutes