mathewhe/aqua_rat huggingface dataset:
Question: Some of the people in Town B are left-handed, some are tall, some are both, and some are neither. In Town Y, three times as many people are left-handed > as are left-handed in Town B, three times as many people are tall as are tall in Town B, three times as many people are both as are both in Town B, but no one is neither. If the total number of people in Town B is four times greater than the total number of people in Town Y, which of the following could be the number of people in Town B who are neither left-handed nor tall?
(A)  23
(B)  39
(C)  72
(D)  143
(E)  199
Rationale: Yes, correct answer is indeed D.
{B}={Left} + {Tall} - {Both} + {Neither};
{Y} = 3*{Left} + 3*{Tall} - 3*{Both};
Since the total number of people in Town B is four times greater than the total number of people in Town Y, then:
{Left} + {Tall} - {Both} + {Neither}=4*(3*{Left} + 3*{Tall} - 3*{Both});
{Neither}=11*({Left} + {Tall} - {Both}), which means that # of people in Town B who are neither left-handed nor tall must be a multiple of 11.
Only answer choice D, is a multiple of 11: 143=11*13.
Answer: D.
Answer: (D)  143
Question: January 1, 2007 was Monday. What day of the week lies on Jan. 5, 2008?
(A) Monday
(B) Tuesday
(C) Wednesday
(D) Saturday
(E) Sunday
Rationale: The year 2007 is an ordinary year. So, it has 1 odd day.
day of the year 2007 was Monday
day of the year 2008 will be 5 days beyond Monday
Hence, It will be Saturday. answer : D
Answer: (D) Saturday
Question: Beth received 1/5 of the votes cast in a certain election. What fraction of the other votes cast would she have needed in order to have received 1/2 of the votes cast?
(A) 1/5
(B) 2/7
(C) 3/8
(D) 7/20
(E) 1/2
Rationale: Let the total votes be 10. Beth received 2 votes, other votes 10-2=8. In order to have received 1/2 of the votes she needed 5 votes so 3 more, which is 3/8 of the other votes.
Answer: C.
Answer: (C) 3/8
Question: One pipe can fill a tank four times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:
(A) 180 min
(B) 160 min
(C) 280 min
(D) 18 min
(E) 190 min
Rationale: Let the slower pipe alone can fill the tank in x minutes
Then the faster pipe can fill the tank in x/4 minutes
Part filled by the slower pipe in 1 minute = 1/x
Part filled by the faster pipe in 1 minute = 4/x
Part filled by both the pipes in 1 minute = (1/x)+(4/x)
Answer is A
It is given that both the pipes together can fill the tank in 36 minutes
⇒ Part filled by both the pipes in 1 minute = 1/36
(1/x)+(4/x)=1/36
5/x=1/36
x=5×36=180
i.e.,the slower pipe alone fill the tank in 180 minutes
Answer: (A) 180 min
Question: the present average age of a couple and their daughter is 35 years. Fifteen years from now, the age of the mother will be equal to the sum of present ages of the father and the daughter. Find the present age of mother?
(A) 38
(B) 49
(C) 55
(D) 45
(E) 50
Rationale: D
45
(f + m + d)/3 = 35
=> f + m + d = 105 --- (1)
m + 15 = f + d
Substituting f + d as m + 15 in (1), we get
2m + 15 = 105
2m = 90 => m = 45 years.
Answer: (D) 45
Question: A firm has 4 senior partners and 6 junior partners. How many different groups Q of 3 partners can be formed in which at least one member of the group is a senior partner. (2 groups are considered different if at least one group member is different)
(A) 48
(B) 100
(C) 120
(D) 288
(E) 600
Rationale: What seems to work as well, though its tougher to come up with this solution:
(10*9*8) * 2/3 + (10*9*4)*1/3 = 600. Divided by all possible permutations (=3!) yields 100.
Explanation: For the first spot you have 10 possible canditates, for the 2nd 9. For the 3rd spot you need to differentiate if a senior partner has been picked for one of the first 2 spots or not. If yes, then you can pick one of the 8 remaining guys, so 10*9*8. If no senior partner has been picked yet, you need 10*9*4.
Now you need to weight the 2 cases with the corresponding probabilities: probability of no senior partner being picked in the first 2 draws = 6/10*5/9=1/3, so you weight 10*9*4 with 1/3. For the complementary case (senior partner was picked in the first 2 draws) you just take the complementary prob (1-1/3)= 2/3 and weight 10*9*8 with it.
Now you just need to divide the answer (600) by the number of different positions (=3!) and get Q=600/6=100.B
Answer: (B) 100
Question: A software programmer does 20% of the work in 70% of the time, and 80% of the work in the remaining 20% of the time. If the code he writes is X lines long and he was given one month (30 days) to accomplish the task, then, assuming that the programmer works at a constant rate in each of the two stages, How many lines of code were written in the last two weeks, in terms of X?
(A) 13x /15
(B) 15x/15
(C) 7x/15
(D) 2x/30
(E) 13x/30
Rationale: Take X=30 lines
70% of 30 = 24 lines
20% of 30 = 6 lines
W - R - T
6 lines - r1 - 24 (first 70% of the 30 days)
24 lines - r2 - 6 ( last 20% of the 20 days)
r1 = 1/4r2 = 4
Now Work in last 14 days = 6 days programmer worked at r2 + 8days programmer worked at r1
=> 6 * 4 + 8 * 1/4 = 24 + 2 = 26
Insert, X=30 in all options => B is the answer.
Answer: (B) 15x/15
Question: If 7^(x - y) = 343 and 7^(x + y) = 16807, what is the value of x?
(A) 3
(B) 4
(C) 2
(D) 1
(E) 7
Rationale: 7^(x - y) = 343 = 7^3
=> x - y = 3 ---------------------------(Equation 1)
7^(x + y) = 16807 = 7^5
=> x + y = 5 ---------------------------(Equation 2)
(Equation 1)+ (Equation 2) => 2x = 3 + 5 = 8
=> x = 8/2 = 4
Answer is B
Answer: (B) 4
Question: The average marks obtained by 100 candidates in an examination is 50. Find how many candidates have passed in the examination, if the average marks of candidates who passed is 70 and that of failed candidates is 20.
(A) 33
(B) 77
(C) 60
(D) 29
(E) 11
Rationale: Explanation:
Let the number of students who passed the examination be X
Number of students failed = (100 - X)
Total marks of students who have passed = 70X
Total marks of 100 students = 100 * 50 = 5000
Total marks of students who have failed = 20(100 – X)
20(100 – X) + 70X = 5000
2000 – 20 X + 70X = 5000
50 X = 3000
X = 60
ANSWER: C
Answer: (C) 60
Question: David has d books, which is 2 times as many as Jeff and 1/2 as many as Paula. How many books do the three of them have altogether, in terms of d?
(A)  5/6*d
(B)  7/3*d
(C)  10/3*d
(D)  7/2*d
(E)  9/2*d
Rationale: Although we could plug in a real value for d, the problem can be just as easily solved by setting up equations. However, let’s start by defining some variables. Since we are given that David has d books, we can use variable d to represent how many books David has.
number of books David has = d
number of books Jeff has = j
number of books Paula has = p
We are given that David has 3 times as many books as Jeff. We can now express this in an equation.
d = 2j
d/2 = j
We are also given that David has ½ as many books as Paula. We can also express this in an equation.
d = (1/2)p
2d = p
Notice that we immediately solved forj in terms of d and p in terms of d. Getting j and p in terms of d is useful when setting up our final expression. We need to determine, in terms of d, the sum of the number of books for David, Jeff, and Paula. Thus, we have:
=d + d/2 + 2d
=7d/2
The answer is D
Answer: (D)  7/2*d
Question: The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
(A) 0
(B) 1
(C) 10
(D) 19
(E) 21
Rationale: Explanation:
Average of 20 numbers = 0.
Sum of 20 numbers (0 x 20) = 0.
It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is (-a)
ANSWER IS D
Answer: (D) 19
Question: At a certain supplier, a machine of type A costs $20,000 and a machine of type B costs $55,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?
(A) $10,000
(B) $11,200
(C) $12,000
(D) $19,800
(E) $13,200
Rationale: 1 machine of type B will cost: 20% down payment of 55,000 = 11,000plusremaining sum (55,000-11,000=44,000) with 40% of finance charges 44,000*1.4=61,600 --> 11,000+61,600=72,600;
2 machine of type A will cost: 20% down payment of 2*20,000 = 8,000plusremaining sum (40,000-8,000=32,000) with 40% of finance charges 32,000*1.4=44,800 --> 8,000+44,800=52,800;
Difference = 72,600 - 52,800 = 19,800.
Answer: D.
Answer: (D) $19,800
Question: A watch was sold at a loss of 10%. If it was sold for Rs.182 more, there would have been a gain of 4%. What is the cost price?
(A) s:1000
(B) s:1067
(C) s:1278
(D) s:1300
(E) s:1027
Rationale: 90%
104%
--------
14% ---- 182
100% ---- ? =>
Rs:1300
Answer: D
Answer: (D) s:1300
Question: If the complement of a certain angle is three times the measure of that certain angle, then what is the measure of that certain angle?
(A) 45
(B) 30
(C) 22.5
(D) 18
(E) 15
Rationale: The original angle is x, so the complement is 3x, and together, these add up to 90 degrees.
x + 3x = 90
4x = 90
x = 22.5
Answer = (C)
Answer: (C) 22.5
Question: The length of a rectangular garden is three times its width. If the area of the rectangular garden is 432 square meters, then what is the width of the rectangular garden?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: Let x be the width of the garden.
3x^2 = 432
x^2 = 144
x = 12
The answer is E.
Answer: (E) 12
Question: If the number 517*324 is completely divisible by 7, then the smallest whole number in the place of * will be:
(A) 3
(B) 1
(C) 2
(D) 4
(E) 6
Rationale: Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 7.
x = 6.
E
Answer: (E) 6
Question: Vijay went to a shop and bought things worth Rs. 25, out of which 30 Paise 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
(D) 21.1
(E) 23
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
B)
Answer: (B) 19.7
Question: In a certain population, there are 4 times as many people aged twenty-one or under as there are people over twenty-one. The ratio of those twenty-one or under to the total population is
(A)  4 to 5
(B)  1 to 3
(C)  1 to 4
(D)  2 to 3
(E)  3 to 4
Rationale: Consider the ratio of the under population of 21 to over the 21 as 4:1
therefore 4x:1X
Now the ratio of the under to the whole population becomes 4x/4x+1x
= 4/5
Answer is A
Answer: (A)  4 to 5
Question: In how many ways can 8 Indians , 4 Americans and 4 Englishmen be selected in a row so that all persons of the same nationality sit together?
(A) 3!8!4!4!
(B) 2!4!4!
(C) 8!
(D) 4!4!4!
(E) 4!4!
Rationale: Treat each nationality as one. So there are 3 persons can be arranged in 3! ways
8 Indians can be arranged in 8! ways
4Englishman can be arranged in 4!ways
4American can be arranged in 4! ways
Required number of ways = 3!8!4!4!
Answer is A
Answer: (A) 3!8!4!4!
Question: Sonika bought a V.C.R. at the list price of 18,400. If the rate of sales tax was 8%, find the amount she had to pay for purchasing the V.C.R.
(A) 19,872
(B) 19,780
(C) 19,680
(D) 19,380
(E) None of these
Rationale: Sol. List price of V.C.R. =18,400
Rate of sales tax = 8%
∴ Sales tax = 8% of 18,400
= 8⁄100 × 18400 = 1472
So, total amount which Sonika had to pay for purchasing the V.C.R. = 18,400 + 1472
= 19,872. Answer A
Answer: (A) 19,872
Question: A word is defined as a sequence of four dots arranged in a row. Each dot is colored either red, yellow, or blue. How many distinct words can be formed?
(A) 36
(B) 48
(C) 64
(D) 81
(E) 120
Rationale: 3^4 = 81
The answer is D.
Answer: (D) 81
Question: The area of a triangle is with base 4m and height 6m?
(A) 11 m2
(B) 10 m2
(C) 18 m2
(D) 19 m2
(E) 12 m2
Rationale: 1/2 * 4 * 6
= 12 m2
Answer: E
Answer: (E) 12 m2
Question: A can do a piece of work in 21 days and B in 28 days. Together they started the work and B left after 4 days. In how many days can A alone do the remaining work?
(A) 33
(B) 276
(C) 27
(D) 14
(E) 66
Rationale: Let A worked for x days.
x/21 + 4/28 = 1 => x/21 = 6/7 => x = 18
A worked for 18 days. So, A can complete the remaining work in 18 - 4 = 14 days.
Answer: D
Answer: (D) 14
Question: House owner decides to repaint the house. He want to make a particular wall in the hall, decorative and decides to put 7 coloured horizontal stripes in it. The seven colours he chose is Violet, Indigo, Blue, Green, Yellow, Orange, Red. As Blue, Violet and Indigo are very similiar shades he decides not to put them next to each other. How many different patterns do he have to choose from?
(A) 6! - (5!×3!)
(B) 7! - (5!×2!)
(C) 6! - (2!×4!)
(D) 7! - (5!×3!)
(E) 7! - (6!×3!)
Rationale: The answer is not direct. Problem require us to find the number of different arrangements of 7 coloured stripes. The constraints we have is that B, V and I should not come next to each other. We can find the answer by substracting the number of arrangments in which B, V and I come together from the total arrangements of 7 stripes. Arrangements in which B, V and I come together: we can consider B, V and I as a single object, but remembering that there can be 3! different such objects. For each BVI object we can arrange BVI, R, O, Y, G in 5! Ways. There four in total there is 5! × 3! Ways of arranging 7 stripes with B, V, I together. And total arrangement of 7 stripes is 7!. Therefore the answer we need is D. (7! -( 5!×3!))
Answer: (D) 7! - (5!×3!)
Question: Four equal circles are described about the four corners of a square so that each touches two of the others. If a side of the square is 14 cm, then the area enclosed between the circumferences of the circles is :
(A) 24 cm2
(B) 42 cm2
(C) 154 cm2
(D) 196 cm2
(E) None of these
Rationale: The shaded area gives the required region.
Area of the shaded region = Area of the square – area of four quadrants of the circles
= (14)2 - 4 × 1⁄4π(7)2
= 196 - 22⁄7 × 49 = 196 - 154 = 42 cm2
Answer B
Answer: (B) 42 cm2
Question: A number is to be multiplied by the fraction 4/5.But amit, by mistake multiplied it by 5/4 and obtained the number 81 more than the correct value.what was the original number?
(A) 200
(B) 240
(C) 180
(D) 120
(E) 100
Rationale: let the no. be x.
x*5/4 - x*4/5 =81. solving this we get 180
ANSWER:C
Answer: (C) 180
Question: The ratio of the adjacent angles of a parallelogram is 6 : 9. Also, the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12. What is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral?
(A) 168°
(B) 228°
(C) 156°
(D) 224°
(E) None of these
Rationale: The measures of the adjacent angles of a parallelogram add up to be 180°
Given
So, 6x + 9x = 180°
Or, 15x = 180°
Or, x = 12°
Hence the angles of the parallelogram are 72° and 108°
Further it is given
We know sum of all the four angles of a quadrilateral is 360°
So, 5y + 6y + 7y + 12 y = 360°
Or, 5y + 6y + 7y + 12 y = 360°
Or, 30y = 360°
Or, y = 12°
Hence the angles of the quadrilateral are 60° , 72, 84° and 144°
Will be 72° + 84° = 156°
Answer : C
Answer: (C) 156°
Question: What is x if x + 2y = 10 and y = 3?
(A) 2
(B) 4
(C) 5
(D) 8
(E) 9
Rationale: Substitute y by 3 in x + 2y = 10
x + 2(3) = 10
x + 6 = 10
If we substitute x by 4 in x + 6 = 10, we have 4 + 6 = 10. Hence
x = 4
correct answer B
Answer: (B) 4
Question: If the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 7 (B + G) is ?
(A) more than 7
(B) Less than 3
(C) More than 3
(D) Less than 1/3
(E) none of these
Rationale: Let number of boys = x
Let number of girls = y
Therefore x/y = B and y/x = G
7(B + G) = 7[(x/y) + (y/x)] = 7[(x2 + y2)/xy] > 7
ANSWER:A
Answer: (A) more than 7
Question: 10% of the inhabitants of village having died of cholera, a panic set in during which 25% of the remaining inhabitants left the village. The population is then reduced to 4050. Find the number of original inhabitants.
(A) 5000
(B) 6000
(C) 4000
(D) 8000
(E) 9000
Rationale: Let the total number of orginal inhabitants be x.
((75/100))*(90/100)*x)=4050 ==> (27/40)*x=4050
==> x=((4050*40)/27)=6000.
Answer B.
Answer: (B) 6000
Question: The cost of a Washing machine was $400 in 1985. In 2014, the cost had increased to $800. What was the percent increase in the cost of Washing machine?
(A) 10
(B) 40
(C) 60
(D) 200
(E) 100
Rationale: Increase = 800 - 400 = 400
% increase = 400*100/400 = 100%
Answer: option E
Answer: (E) 100
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 3%. What is the cost price?
(A) 1000
(B) 2876
(C) 1077
(D) 2778
(E) 2711
Rationale: 90%
103%
--------
13% ---- 140
100% ---- ? => Rs.1077
Answer: C
Answer: (C) 1077
Question: At a party, there were seven times as many females as males and twice times as many adults as children. Which of the following could NOT be the number of people at the party?
(A) 384
(B) 258
(C) 215
(D) 120
(E) 72
Rationale: Five times as many females as males --> F = 7M.
Three times as many adults as children --> (F + M) = 2C.
The number of people at the party = F + M + C = 2C + C = 3C.
The number of people at the party must be a multiple of 3. The only answer choice which is NOT a multiple of 3 is C.
Answer: C.
Answer: (C) 215
Question: Ratio of the earnings of A and B is 4:7. If the earnings of A increases by 50% and those of B decreased by 25%, the new ratio of their earnings becomes 8:7. What are A's earnings?
(A) 26,000
(B) 83,20
(C) 23,320
(D) Data inadequate
(E) 39,309
Rationale: Answer: Option D
Explanation:
Let the original earnings of A and B be Rs. 4x and Rs. 7x.
New earnings of A = 150% 0f Rs. 4x = (150/100 * 4x) = Rs. 6x
New earnings of B = 75% of Rs. 7x = (75/100 * 7x) = Rs. 21x/4
6x:21x/4 = 8:7
This does not give x. So, the given data is inadequate.
Answer:D
Answer: (D) Data inadequate
Question: Village P’s population is 1150 greater than Village Q's population. If Village Q’s population were reduced by 200 people, then Village P’s population would be 4 times as large as Village Q's population. What is Village Q's current population?
(A) 600
(B) 625
(C) 650
(D) 675
(E) 700
Rationale: P = Q+1150.
P=4(Q-200).
4(Q-200)=Q+1150.
3Q=1950.
Q=650.
The answer is C.
Answer: (C) 650
Question: 22 + 23 + 24 + ... 61 + 62 + 63 = ?
(A) 1361
(B) 1362
(C) 1363
(D) 1364
(E) 1785
Rationale: Sum = 22 + 23 + 24 + ... 61 + 62 + 63
Sum of n consecutive positive integers starting from 1 is given as n(n+1)/2
Sum of first 63 positive integers = 63*64/2
Sum of first 21 positive integers = 21*22/2
Sum = 22 + 23 + 24 + ... 61 + 62 + 63 = 63*64/2 - 21*22/2 = 1376
Answer : E
Answer: (E) 1785
Question: Present ages of Sameer and Anand are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Anand's present age in years?
(A) 18
(B) 76
(C) 24
(D) 20
(E) 12
Rationale: Let the present ages of Sameer and Anand be 5x and 4x years respectively.
Then, (5x + 3)/(4x + 3) = 11/9
9(5x + 3) = 11(4x + 3) => x = 6
Anand's present age = 4x = 24 years.Answer:C
Answer: (C) 24
Question: A and B invests Rs.6000 and Rs.12000 in a business. After 6 months, A withdraws half of his capital and B withdraws two-third of his capital. In what ratio should they share the profits at the end of the year?
(A) 27:32
(B) 25:32
(C) 32:27
(D) 27:29
(E) 27:31
Rationale: A : B
(6000*6)+(3000*6) : (12000*6)+(4000*6)
54000 : 96000
27 : 32
Answer: A
Answer: (A) 27:32
Question: On 5th Mar, 2012 Monday falls. What day of the week was it on 5th Mar, 2011?
(A) Saturday
(B) Sunday
(C) Monday
(D) Tuesday
(E) Wednesday
Rationale: Explanation:
5th Mar 2012 – 5th Mar 2011 = 52 weeks 1 day. So Mar 5th 2011 is behind one day = Sunday
Answer: B
Answer: (B) Sunday
Question: A man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 20%, he is only able to save Rs. 200 per month. What is his monthly salary?
(A) 5000
(B) 2999
(C) 2878
(D) 2990
(E) 2771
Rationale: Income = Rs. 100
Expenditure = Rs. 80
Savings = Rs. 20
Present Expenditure 80*(20/100) = Rs. 96
Present Savings = 100 – 96 =Rs. 4
100 ------ 4
? --------- 200 => 5000
Answer: A
Answer: (A) 5000
Question: A dessert recipe calls for 50% melted chocolate and 50% raspberry puree to make a particular sauce. A chef accidentally makes 15 cups of the sauce with 30% melted chocolate and 70% raspberry puree instead. How many cups of the sauce does he need to remove and replace with pure melted chocolate to make the sauce the proper 50% of each?
(A) 1.5
(B) 2.14
(C) 3
(D) 4.5
(E) 5
Rationale: Yes, we assume that the mix is homogeneous. Otherwise, we will not be able to solve the question.
You have 15 cups of sauce with 30% chocolate. You also have unlimited amount of pure chocolate sauce. Now you need to mix these two in such a way that you get total 15 cups of sauce with 50% chocolate.
Using scale method:
w1/w2 = (100 - 50)/(50 - 30) = 5/2
w1 - Amount of 30% chocolate sauce
w2 - Amount of pure chocolate sauce
So for every 5/2 cups of 30% chocolate sauce, we need 2 cup of pure chocolate sauce. This will give us 7 cups of 50% chocolate sauce. But we need 15 cups of 50% chocolate sauce.
So we need to mix 5*15/7 = 12.5 cups of 40% chocolate sauce with 1*15/7 = 2.14 cups of pure chocolate sauce.
Answer (B)
Answer: (B) 2.14
Question: A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:
(A) 45m
(B) 50m
(C) 54m
(D) 72m
(E) 70m
Rationale: Explanation:
2 kmph =	(	2 x5/18)m/sec =	5/9m/sec.
4 kmph =(4x5/18)m/sec =10/9m/sec.
Let the length of the train be x metres and its speed by y m/sec.
Then,	(x/y-5/9)=9and(x/y -	10/9)=10.
9y - 5 = x and 10(9y - 10) = 9x
=> 9y - x = 5 and 90y - 9x = 100.
On solving, we get: x = 50.
Therefore Length of the train is 50 m.
ANSWER IS B
Answer: (B) 50m
Question: A number of the form 213ab, where a and b are digits, has a reminder less than 10 when divided by 100. The sum of all the digits in the above number is equal to 13. Find the digit b.
(A) 9
(B) 10
(C) 7
(D) 12
(E) 13
Rationale: 213ab may be written as
213ab = 21300 + 10a + b
When 213ab is divide by 100, the reminder is 10a + b. The only way for the remainder to be less that 10 is that a = 0. Hence the sum of the digits is
2 + 1 + 3 + 0 + b = 13
Solve for b
b = 7
correct answer C
Answer: (C) 7
Question: If the sales tax reduced from 3 1/2 % to 3 1/3%, then what difference does it make to a person who purchases an article with market price of Rs. 8400 ?
(A) Rs 10
(B) Rs 12
(C) Rs 14
(D) Rs 16
(E) Rs 18
Rationale: Required difference = [3 ½ % of Rs.8400] – [3 1/3 % of Rs.8400]
= [(7/20-(10/3)]% of Rs.8400 =1/6 % of Rs.8400
= Rs. [(1/6)8(1/100)*8400] = Rs. 14.
ANSWER C 14
Answer: (C) Rs 14
Question: For all integers x>1. <x>=2x+(2x-1)+(2x-2)+......2+1. What is the value of <4>*<2>?
(A)  60
(B)  116
(C)  360
(D)  263
(E)  478
Rationale: Since <x>=2x+(2x-1)+(2x-2)+......2+1=1+2+..+(2x-2)+(2x-1)+2x then<x> is basically the sum of all integers from 1 to 2x, inclusive.
Hence <4> is the sum of all integers from 1 to 2*4=8 and <2> is the sum of all integers from 1 to 2*2=4 --> <4>=36 and <2>=10 --> <3>*<2>=36*10=360.
Answer: C.
Answer: (C)  360
Question: If a function f is defined by f(x)= -1/x for all non zero numbers x. If f(a) = -1/2 and f(ab) = 1/12 then b= ?
(A) -1/6
(B) 1/6
(C) 6
(D) -6
(E) 3
Rationale: f(a) = -1/2 = -1/a, and thus a = 2
f(ab) = 1/12, and thus ab = -12
2b = -12
b = -6
The answer is D.
Answer: (D) -6
Question: The majority owner of a business received 25% of the profit, with each of 4 partners receiving 25% of the remaining profit. If the majority owner and two of the owners combined to receive $50,000, how much profit did the business make?
(A) $80,000
(B) $100,000
(C) $120,000
(D) $150,000
(E) $200,000
Rationale: Let P be the total profit.
P/4 + 1/2*(3P/4) = P/4 + 3P/8 = 5P/8 = 50000
P = $80,000
The answer is A.
Answer: (A) $80,000