mathewhe/aqua_rat huggingface dataset:
Question: How long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length
(A) 33
(B) 44
(C) 55
(D) 77
(E) 22
Rationale: T = (660 + 165)/54 * 18/5
T = 55
Answer: C
Answer: (C) 55
Question: Find the C.I. on a sum of Rs.1600 for 9 months at 20% per annum, interest being compounded quarterly?
(A) 2266
(B) 7767
(C) 2522
(D) 1677
(E) 2671
Rationale: A = 1600(21/20)3 = 2522
Answer:C
Answer: (C) 2522
Question: The speed of a boat in upstream is 40 kmph and the speed of the boat downstream is 90 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 25 kmph
(B) 76 kmph
(C) 12 kmph
(D) 97 kmph
(E) 15 kmph
Rationale: Speed of the boat in still water
= (40+90)/2
= 65 kmph. Speed of the stream
= (90-40)/2
= 25 kmph.
Answer:A
Answer: (A) 25 kmph
Question: How many integers from 101 to 1000, inclusive, remains the value unchanged when the digits were reversed?
(A)  50
(B)  60
(C)  70
(D)  80
(E)  90
Rationale: question is asking for palindrome
first digit possibilities - 1 through 9 = 9
second digit possibilities - 0 though 9 = 10
third digit is same as first digit
=>total possible number meeting the given conditions = 9 *10 = 90
Answer is E.
Answer: (E)  90
Question: A pharmaceutical company received $5 million in royalties on the first $20 million in sales of and then $10 million in royalties on the next $108 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $20 million in sales to the next $108 million in sales?
(A) 8%
(B) 26%
(C) 45%
(D) 52%
(E) 56%
Rationale: (10/108)/(5/20) = 20/27 = 74% it means that 10/108 represents only 74%. Therefore a decrease of 26%.
Answer B
Answer: (B) 26%
Question: A driver goes on a trip of 70 kilometers, the first 35 kilometers at 48 kilometers per hour and the remaining distance at 24 kilometers per hour. What is the average speed of the entire trip in kilometers per hour?
(A) 30
(B) 32
(C) 35
(D) 36
(E) 40
Rationale: The time for the first part of the trip was 35/48 hours.
The time for the second part of the trip was 35/24 hours.
The total time fro the trip was 35/48 + 35/24 = 105/48 = 35/16 hours.
The average speed for the trip was 70 / (35/16) = 32 kph
The answer is B.
Answer: (B) 32
Question: How many 4 digit numbers can be formed using 0,1,2,3,4,5 and divisible by 4
(A) 190
(B) 200
(C) 210
(D) 220
(E) 230
Rationale: since a number cannot start with 0 so, 1st place of of 4 digit number can be filled in 5 ways i.e., 1,2,3,4,5.
second place of 4 digit number can be filled in 6 ways i.e., 0,1,2,3,4,5
since 4 digit numbers should be divisible by 4 so possibility of last 2 places are (04,12 20,24,32,40,52) i.e., 7 possibilities.
Therefore total number of 4 digut number divisible by 4 are- 5*6*7=210
ANSWER:C
Answer: (C) 210
Question: For what value of x between − 7 and 7, inclusive, is the value of x^2 − 10x + 16 the greatest?
(A) − 7
(B) − 2
(C) 0
(D) 2
(E) 7
Rationale: we can see from the statement that two terms containing x, x^2 will always be positive and -10x will be positive if x is -ive..
so the equation will have greatest value if x is -ive, and lower the value of x, greater is the equation.
so -7 will give the greatest value..
ans A
Answer: (A) − 7
Question: The average (arithmetic mean) of a normal distribution of a school's test scores is 65, and standard deviation of the distribution is 6.5. A student scoring a 73 on the exam is in what percentile of the school?
Choices
(A) 63rd percentile
(B) 68th percentile
(C) 84th percentile
(D) 96th percentile
(E) 98th percentile
Rationale: (78-65)/6.5 = 2 sigmas or 95.5th percentile for +-2 sigma but in our case we need only upper tail, so it's 100 - (100 - 95.5)/2 = 87th percentile
C
Answer: (C) 84th percentile
Question: Find the missing number in the sequence
8 ? 125 343 1331
(A) 9
(B) 2
(C) 4
(D) 6
(E) 7
Rationale: A
9
cube of prime numbers
2*2*2 => 8
3*3*3 => 27 ...Answer
5*5*5 => 125
7*7*7 => 343
11*11*11 =>1331
Answer: (A) 9
Question: If c is 30% of a and 25% of b, what percent of a is b?
(A)  2.5%
(B)  15%
(C)  120%
(D)  35%
(E)  250%
Rationale: Answer = C
30a/100 = 25b/100
b = 30a/25 = 120a/100 = 120%
Answer: (C)  120%
Question: If the speed of a man is 57 km per hour, then what is the distance traveled by him in 30 seconds ?
(A) 275m
(B) 360m
(C) 475 m
(D) 420 m
(E) 440 m
Rationale: The distance traveled in 30 sec = 57*(5/18) *30 =475m
ANSWER:C
Answer: (C) 475 m
Question: How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 7 m x 6 m x 22.5 cm?
(A) 6400
(B) 6410
(C) 5600
(D) 6500
(E) 6800
Rationale: Number of bricks = Volume of Wall/Volume of Bricks
=700x600x22.5/25x11.25x6= = 5600
answer :C
Answer: (C) 5600
Question: If w, x, and y are consecutive odd positive integers and w < x < y, which of the following could be equal to x - y - w ?
(A) -4
(B) -2
(C) -1
(D) 0
(E) -3
Rationale: Since W, X and Y are CONSECUTIVE ODD POSITIVE INTEGERS and W < X < Y, we can start with the easiest set of values that comes to mind:
W = 1
X = 3
Y = 5
The question asks for what COULD be the value of X - Y - W.
In this case, the value would be...
3 - 5 - 1 = -3
-3 IS among the answer choices, so we're done.
E
Answer: (E) -3
Question: The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs. 3. The ratio of the two selling prices is:
(A) 51:52
(B) 52:53
(C) 51:53
(D) 52:55
(E) 50:51
Rationale: Explanation:
Let C.P. of the article be Rs. x.
Then, required ratio = 104% of x / 106% of x
= 104/106 = 52/53 = 52:53
ANSWER IS B
Answer: (B) 52:53
Question: X and Y started a business by investing Rs.36000 and Rs.42000 respectively after 4 months Z joined in the business with an investment of Rs.48000, then find share of Z in the profit of Rs.14190 ?
(A) 3200
(B) 4000
(C) 3250
(D) 4128
(E) 3985
Rationale: Ratio of investment, as investments is for different time.
Investment x Number of units of time.
Ratio of investments X : Y : Z = 36000 : 42000 : 48000 => 6 : 7 : 8.
X = 6 x 12 Months = 72, Y = 7 x 12 = 84, Z = 8 X 8 = 64 => 18 : 21 : 16.
Ratio of investments => X : Y : Z = 18 : 21 : 16.
Investment Ratio = Profit sharing Ratio.
Z = 14190 Ã— 16/55 = Rs.4128.
Share of Z in the profit is Rs.4128.
Option D
Answer: (D) 4128
Question: An outlet pipe can empty 2/3 of a cistern in 12 minutes. In 4 minutes, what part of the cistern will be emptied?
(A) 1/3
(B) 2/5
(C) 2/7
(D) 2/9
(E) 3/10
Rationale: 4/12 * 2/3 = 2/9
The answer is D.
Answer: (D) 2/9
Question: Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 1209
(B) 1324
(C) 1245
(D) 1300
(E) 1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Large number = 270+1365 = 1635
E
Answer: (E) 1635
Question: A certain company consists of 4 managers and 8 non-managers. How many different teams of 3 employees can be formed in which at least one member of the team is a manager and at least one member of the team is not a manager? (Two groups are considered different if at least one group member is different)
(A) 84
(B) 108
(C) 160
(D) 270
(E) 990
Rationale: Total # of teams of 3 possible is 12C3=220
# of teams with only managers or only non-managers is: 4C3+8C3=4+56=60;
# of teams of 3 with at least one manager or at least one non-manager is: 220-60=160.
ANSWER:C
Answer: (C) 160
Question: 6) A marketing firm determined that , of 240 households surveyed, 80 used neither Brand A nor Brand B soap.60 used only Brand A soap and for every household that used both brands of soap, 3 used only brand B soap.how many of the 200 household surveyed used both brands of soap?
(A) a) 15
(B) b) 20
(C) c) 25
(D) d) 40
(E) e) 45
Rationale: 160 = At least one of Soap A or B
Both brands = x
Brand B = 3x
=> 60 + x + 3x = 160
=> 4x = 100
=> x = 25
Answer - C
Answer: (C) c) 25
Question: If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is :
(A) 52 km
(B) 62 km
(C) 55 km
(D) 50 km
(E) None
Rationale: Sol.
Let the actual distance travelled be x km. Then,
x/10 = (x+20)/14
⇔ 14x = 10x + 200
⇔ 4x = 200
⇔ x = 50 km.
Answer D
Answer: (D) 50 km
Question: A child must place 7 different toys in 4 different bins. If any of the toys can go in any of the bins, in how many ways can the child place the toys into the bins?
(A) 6^6
(B) 6^4
(C) 4^7
(D) 4^4
(E) 6^4-4^6
Rationale: there are 4 different bins and each of the toy can go to any of these bins..
so answer 7âˆ—7âˆ—7âˆ—7âˆ—7âˆ—7âˆ—7=4^7
ANSWER:C
Answer: (C) 4^7
Question: At the beginning of 2011, Company X created a list of n charities, and committed to donating 10% of its prots for the year to these charities, donating an equal amount to each charity. However, during the year, Company X removed a charities from this list, and donated 10% of its prot in equal amounts to each of the remaining charities on the list. If the Wesley Homeless Shelter was one of the charities on the list which received a donation from Company X, which of the following represents, in terms of n and a, the percent increase in the amount the Wesley Homeless Shelter received because the a charities were removed from the list?
(A) 100n/a
(B) 100a/(n-a)
(C) 100(n-a)/n
(D) 100n/(n-a)
(E) "100(n-a)" divided by "a"
Rationale: Sol:
Let profit be "P"
for n charities - each get p/n
when a charities are removed - each get p/(n-a)
increase will be (p/(n-a)) - (p/n) = pa/(n-a)*n
Increase % will be (pa/(n-a)*n) / (p/n) multiplied by 100.
result will be 100a/(n-a)
ANSWER:E
Answer: (E) "100(n-a)" divided by "a"
Question: After 4 games, team B had an average of 61.5 points per game. If it got only 47 points in game 5, how many more points does it need to score to get its total above 500?
(A) 85
(B) 74
(C) 67
(D) 53
(E) 207
Rationale: (4*61.5) + 47 +x >500
246+47+x > 500
293+x >500
=> x>207
Option E
Answer: (E) 207
Question: In an increasing sequence of 8 consecutive even integers, the sum of the first 4 integers is 268. What is the sum of all the integers in the sequence?
(A) 552
(B) 568
(C) 574
(D) 586
(E) 590
Rationale: In an increasing sequence of 8 consecutive even integers, the sum of the first 4 integers is 268. What is the sum of all the integers in the sequence?
x+x+2+x+4+x+6=268
x=64
64+66+68+70+72+74+76+78=568
ANSWER:B
Answer: (B) 568
Question: In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much
Look at this series: 1.2, 2.4, 3.6, 4.8, ... What number should come next?
(A) 4.7
(B) 3.6
(C) 4.9
(D) 6.0
(E) 4.4
Rationale: 6.0
In this simple addition series, each number increases by 1.2
Answer : D
Answer: (D) 6.0
Question: At a certain fruit stand, the price of each apple is 40 cents and the price of each orange is 60 cents. Mary selects a total of 20 apples and oranges from the fruit stand, and the average (arithmetic mean) price of the 20 pieces of fruit is 56 cents. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 52 cents?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Let number of Apples = A
number of oranges = B
A+B=20 --- 1
.56 =(.4A + .6 B)/20
=> 56 = 4A + 6B ----2
Solving 1 and 2, we get
A= 4
B= 16
Let the number of oranges put back = C
52*(20-c) = 40*4 + 60(16-C)
=> C= 10
Answer E
Answer: (E) 10
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) 3.37
(C) 3.35
(D) 3.76
(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: 39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
(A) 16
(B) 19
(C) 13
(D) 14
(E) 18
Rationale: Let the required number of days be X.
Less persons, More days (Indirect Proportion)
More working hours per day, Less days (Indirect Proportion)
Persons 30	:	39
Working hours/day	6	:	5 :: 12 : X
THEREFORE 30 x 6 x X = 39 x 5 x 12
X =(39 x 5 x 12)/(30 x 6)
X = 13.
ANSWER:C
Answer: (C) 13
Question: Jack and Jill work at a hospital with 5 other workers. For an internal review, 2 of the 7 workers will be randomly chosen to be interviewed. What is the probability that Jack and Jill will both be chosen?
(A)  1/3
(B)  1/4
(C)  1/21
(D)  3/8
(E)  2/3
Rationale: 1/7C2=1/21.
Answer: C.
Answer: (C)  1/21
Question: The ratio, by volume, of bleach to detergent to water in a certain solution is 4 : 40 : 100. The solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved. If the altered solution will contain 300 liters of water, how many liters of detergent will it contain?
(A) 80
(B) 70
(C) 60
(D) 40
(E) 50
Rationale: B:D:W = 4:40:100
Bnew / Dnew = (1/3)*(4/40) = (1/30)
Dnew / Wnew = (1/2)*(40/100) = (1/5)
Wnew = 300
Dnew = Wnew/5 = 300/5 = 60
So, answer will be
C
Answer: (C) 60
Question: After decreasing 24% in the price of an article costs Rs.1064. Find the actual cost of an article?
(A) 1667
(B) 6789
(C) 1200
(D) 6151
(E) 1400
Rationale: CP* (76/100)
= 1064
CP= 14 * 100 => CP
= 1400
Answer: E
Answer: (E) 1400
Question: The ratio between the sale price and the cost price of an article is 7:5. What is the ratio between the profit and the cost price of that article?
(A) 2 : 5
(B) 2 : 7
(C) 5 : 2
(D) 7 : 2
(E) None
Rationale: Solution
Let C.P. = Rs. 5x and	S.P. = Rs.7x.
Then, Gain = Rs. 2x.
∴ Required ratio	= 2x : 5x
‹=›2 : 5
Answer A
Answer: (A) 2 : 5
Question: Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
(A) 9
(B) 10
(C) 12
(D) 20
(E) 25
Rationale: Due to stoppages, it covers 9 km less.
Time taken to cover 9 km =(9/54 x 60) min	= 10 min
Answer:B
Answer: (B) 10
Question: What is the sum of all possible solutions to |x - 3|^2 + |x - 3| = 42 ?
(A) 4
(B) 3
(C) 5
(D) 6
(E) 2
Rationale: Denote |x - 3| as y: y^2 + y = 42 --> y = -7 or y = 6. Discard the first solution since y = |x - 3|, so it's an absolute value and thus cannot be negative.
y = |x - 3| = 6 --> x = 9 or x = -4. The sum = 5.
Answer: C.
Answer: (C) 5
Question: Two trains travelling in the same direction at 40 and 22 kmph completely pass off another in 1 minute. If the length of the first train is 125 m, what is the length of the second train?
(A) 118 m
(B) 128 m
(C) 231 m
(D) 175 m
(E) 142 m
Rationale: D
175 m
RS = 40 – 22 = 18 * 5/18 = 5 mps
T = 60 sec
D = 5 * 60 = 300 m
(-) 125
--------
175 m
Answer: (D) 175 m
Question: When y is divided by 288, the remainder is 44. What is the remainder when the same y is divided by 24?
(A) 20
(B) 21
(C) 23
(D) 25
(E) 26
Rationale: y = 288*a + 44 = (24*12)*a + 24 + 20
The answer is A.
Answer: (A) 20
Question: Tough and Tricky questions: Combinations.
The product of the digits of the four-digit number h is 30. No two digits of h are identical. How many different numbers are possible values of h?
(A) 24
(B) 30
(C) 36
(D) 42
(E) 54
Rationale: Answer = A= 24
Let number =abcd
Given that a*b*c*d = 30
a,b,c,d can be 1,2,3,5
Number of ways = 4*3*2 = 24
Answer: (A) 24
Question: A train sets off at 9:00 am at the speed of 70 km/h. Another train starts at 10:30 am in the same direction at the rate of 84 km/h. At what time will the second train catch the first train?
(A) 4:30
(B) 5:00
(C) 5:30
(D) 6:00
(E) 6:30
Rationale: In one hour and thirty minutes the first train travels 105 km.
The second train catches the first train at a rate of 84 km/h - 70 km/h = 14 km/h.
The second train will catch the first train in 105/14 = 7.5 hours, so at 6:00 pm.
The answer is D.
Answer: (D) 6:00
Question: Train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. The length of train P is three-fourths the length of train Q. What is the ratio of the speed of train P to that of train Q?
(A) 15:8
(B) 12:0
(C) 13:9
(D) 14:2
(E) 13:0
Rationale: Given that train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds.
Let the length of train P be LP and that of train Q be LQ
given that LP = 3/4 LQ
As the train P and Q crosses the pole in 30 seconds and 75 seconds respectively,
=> Speed of train P = VP = LP/30
Speed of train Q = VQ = LQ/75
LP = 3/4 LQ
=> VP = 3/4 LQ/(30) = LQ/40
Ratio of their speeds = VP : VQ
= LQ/40 : LQ/75 => 1/40 : 1/75 = 15 : 8
Answer:A
Answer: (A) 15:8
Question: A salesmanâ€™s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1000 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 700 more than that by the previous schema, his sales were worth?
(A) s. 8,000
(B) s. 9,000
(C) s. 20,000
(D) s.10,000
(E) s. 50,000
Rationale: [1000 + (X-4000) * (2.5/100)] - X * (5/100) = 700
X = 8000
ANSWER A
Answer: (A) s. 8,000
Question: Water boils at 212°F or 100°C and ice melts at 32°F or 0°C . If the temperature of a pot of water is 50°C, what is the temperature of the pot of water in °F?
(A) 101°F
(B) 108°F
(C) 116°F
(D) 122°F
(E) 127°F
Rationale: Let F and C denote the temperature in Fahrenheit and Celsius respectively.
(F - 32) /(212 - 32) = (C - 0)/(100 - 0)
F = 9C/5 + 32
F = 9(50)/5 + 32 = 122°F
The answer is D.
Answer: (D) 122°F
Question: When x + p is divided by p + 1, the quotient is n and there is no remainder. Which of the following must be the value of x?
(A) n(p +1)
(B) n(p − 1)
(C) p(n + 1)
(D) p(n - 1) + n
(E) n(p + 1) (p − 1)
Rationale: Given in question (x+p)/p+1= n
=> x+p= n(p+1)
=>x= np+n-p
or x= np-p+n
Now we are good to check the options
x= p(n-1) + n
Answer D
Answer: (D) p(n - 1) + n
Question: A train speeds past a pole in 15 sec and a platform 120 m long in 25 sec, its length is?
(A) 100
(B) 150
(C) 160
(D) 170
(E) 180
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 120)/25 = x/15 => x = 180 m.
Answer: Option E
Answer: (E) 180
Question: Zinc and copper are melted together in the ratio 9 : 11. What is the weight of melted mixture, if 35.1 kg of zinc has been consumed in it?
(A) 78 kg
(B) 60 kg
(C) 64 kg
(D) 70 kg
(E) None
Rationale: Sol.
For 9 kg Zinc, mixture melted = (9+11) kg.
For 35.1 kg Zinc, mixture, melted = [20/9 x 35.1] kg
= 78 kg.
Answer A
Answer: (A) 78 kg
Question: An accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate
when the clock shows 2 o'clock in the afternoon?
(A) 180 degrees
(B) 190 degrees
(C) 200 degrees
(D) 280 degrees
(E) None
Rationale: Angle traced by the hour hand in 6 hours = ( 360/12 * 11/3 )degrees
=180 degrees
A
Answer: (A) 180 degrees
Question: A work could be completed in 100days by x workers. However, due to the absence of 10workers, it was completed in 110days. The original no.of workers was:
(A) 100
(B) 120
(C) 110
(D) 130
(E) 140
Rationale: sax Letlheo g alnumberofworkers hex
x workers can do the wor - 100 days
(x — 10) workers can do the work in 110 days
4 100x 1u1x— 10)
1100 Q x 110
C
Answer: (C) 110
Question: There are 300 giraffes at a large zoo. The number of giraffes is 3 times the number of all the other animals combined. How many more giraffes are there than non giraffes animals at the zoo?
(A) 400
(B) 360
(C) 300
(D) 290
(E) 200
Rationale: Answer is D.
Total giraffes= 300 = 3 * Other Animals (X)
or X = 10.
So, Difference in giraffes and X = 300-10 = 290.
Answer: (D) 290
Question: Find the ratio in which rice at Rs.7.20 a kg be mixed with rice at Rs.5.80 a kg to produce a mixture worth Rs.6.30 a kg?
(A) 5 : 9
(B) 2 : 3
(C) 3 : 4
(D) 4 : 5
(E) None of these
Rationale: Solution
Required ratio = 50 : 90 = 5 : 9
Answer A
Answer: (A) 5 : 9
Question: A customers identification code consists of a vowel followed by a 3-digit number greater than 200. Exactly 2 of the 3 digits in the code should be identical. How many different codes is it possible to form?
(A) 211
(B) 216
(C) 1075
(D) 1080
(E) 2160
Rationale: A customers identification code will be of the type -,-,-,-
first digit can be selected from any of the 5 vowels in 5C1 ways
now for the remaining three digit lets consider the following two cases
case 1: when the number is greater than 200 but less than 300
number will be of the type 2,_,_. now suppose repeating number is same as first digit number i.e. 2. and the third number is one of the remaining 9 numbers (we are rejecting 2 here, because it will result in 222, which is not acceptable as per the given condition). thus these two number can arrange themselves in two blank spaces in 2! ways. hence total number of numbers in which repeating digit is same as the first digit = 1.9.2! =18
now, suppose that repeating number is different than first digit. thus possible case in this case are 8 as listed below:
211
233
244
255
266
277
288
299
here again we have rejected 200( because number must be greater than 200) and 222 ( exactly two repeating digits are allowed)
thus total possible cases are 18 + 8 =26
case 2: number ranging from 300 to 999
here for first digit we have 7 cases (3,4,5,6,7,8,9)
now if the repeating number is same as the first number then we will have 18 cases ( same reasoning as mentioned in the previous case)
if the repeating number is different than first digit number then we will have 9 cases ( because here number ending with two zeros are allowed)
hence total number of ways = 7(18+9) = 189
thus different number of codes = 5(189+26) = 1075
hence C
Answer: (C) 1075
Question: A bowl of fruit contains 12 apples and 23 oranges. How many oranges must be removed so that 60% of the pieces of fruit in the bowl will be apples?
(A)  3
(B)  6
(C)  15
(D)  17
(E)  20
Rationale: Number of apples = 14
number of oranges = 23
let number of oranges that must be removed so that 60% of pieces of fruit in bowl will be apples = x
Total number of fruits after x oranges are removed = 12+(23-x) = 35-x
12/(35-x) = 6/10
=>20 = 35-x
=>x= 15
Answer C
Answer: (C)  15
Question: The sum of a number and its reciprocal is one-fifth of 26. What is the sum of that number and its square.
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Explanation:
Let the number be x. Then,
x + 1/x = 26/5
=> (x2 + 1)/x = 26/5
=> 5x2 - 26x + 5 = -0
=> (x - 5)(5x - 1) = 0
=> x = 5 or 1/5
Answer: Option C
Answer: (C) 5
Question: X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?
(A) 3 days.
(B) 4 days.
(C) 9 days.
(D) 8 days.
(E) 10 days.
Rationale: Work done by X in 4 days =1/20	x 4=	1/5.
Remaining work =1 -	1/5=	4/5.
(X + Y)'s 1 day's work =1/20+1/12=8/60=2/15.
Now,	2/15	work is done by X and Y in 1 day.
So,	4/5 work will be done by X and Y in	15/2	x 4/5= 6 days.
Hence, total time taken = (6 + 4) days = 10 days.
Answer: Option E
Answer: (E) 10 days.
Question: The average marks scored by Ganesh in English, Science, Mathematics and History is less than 20 from that scored by him in English, History, Geography and Mathematics. What is the difference of marks in Science and Geography scored by him?
(A) 80
(B) 50
(C) 60
(D) Data inadequate
(E) None of these
Rationale: E+H+G+M/4âˆ’E+S+M+H/4=20
â‡’ G - S = 80
Answer A
Answer: (A) 80
Question: At the opening of a trading day at a certain stock exchange, the price per share of stock K was $10. If the price per share of stock K was $15 at the closing of the day, what was the percent increase in the price per share of stock K for that day?
(A) 1.4%
(B) 50%
(C) 11.1%
(D) 12.5%
(E) 23.6%
Rationale: Opening = 10
Closing = 15
Rise in price = 5
So, percent increase = 5/10 * 100 = 50%
Answer : B
Answer: (B) 50%
Question: If the cost price of 50 articles is equal to the selling price of 40 articles, then the gain or loss percent is?
(A) 27%
(B) 65%
(C) 285%
(D) 245%
(E) 25%
Rationale: Given that, cost price of 50 article is equal to selling price of 40 articles.
Let cost price of one article = Rs. 1
Selling price of 40 articles = Rs. 50
But Cost price of 40 articles = Rs. 40
Therefore, the trader made profit.\Percentage of profit = 10/40 * 100 = 25%.Answer:E
Answer: (E) 25%