divelab/Sys2Bench huggingface dataset:
Question: At Chennai it rained as much on Tuesday as on all the others days of the week combined. If the average rainfall for the whole week was 3 cm. How much did it rain on Tuesday?
Options:
A)2.625 cm
B)3 cm
C)10.5 cm
D)15 cm
E)None of these
Rationale: Total rainfall = 3 x 7 = 21 cm
Hence, rainfall received on Tuesday = 21/2 (as it rained as much on Tuesday as on all the others days of the week combined)
= 10.5 cm.
ANSWER:C
Answer: C
Question: If the number is decreased by 5 and divided by 7 the result is 7. What would be the result if 6 is subtracted and divided by 8?
Options:
A)4
B)6
C)8
D)5
E)3
Rationale: Explanation:
Let the number be x. Then,
(x - 5)/7 = 7 => x - 5 = 49
x = 54
.: (x - 6)/8 = (54 - 6)/8 = 6
Answer: Option B
Answer: B
Question: Which of the following is closest to 1/7+1/77+1/777
Options:
A)1/5
B)1/4.5
C)1/6
D)1/9
E)1/6.4
Rationale: 1/7+1/77+1/777=0.1428571+0.0129870+0.001287=0.1571311=1/6.4
Answer E
Answer: E
Question: Jaime earned enough money by selling seashells at 20 cents each to buy several used paperback books at 55 cents each. If he spent all of the money he earned selling seashells to buy the books, what is the least number of seashells he could have sold ?
Options:
A)5
B)10
C)22
D)25
E)30
Rationale: Let's TEST Answer C: 22 seashells...
With 22 seashells, Jamie would have 22(20) =440 cents. This would allow him to buy 8 books for 440 cents total, so this is the correct answer.
C
Answer: C
Question: The total of company C's assets in 1994 was 500% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of company C's assets in in 1992 was N dollars, which one of the following represents company C's assets in 1994:
Options:
A)7N
B)8N
C)9N
D)12N
E)30N
Rationale: Let's use actual numbers. Starting in 1992, let's say company C had $100 in assets.
In 1993, the total assets were 400% GREATER, which means 1992 PLUS 400% of 1992:
$100 + 4x$100 = $100 + $400 =$500
In 1994, the total assets were 500% GREATER than they were in 1993, which means 1993 PLUS 300% of 1993:
$500 + 5x$500 = $500 + $2500 =$3000
This is 30 times the 1992 number, so the correct answer is30N.
Answer: E
Question: A sum of money lent out at S.I. amounts to Rs. 720 after 2 years and to Rs. 1020 after a further period of 5 years. The sum is?
Options:
A)776
B)267
C)269
D)600
E)298
Rationale: S.I for 5 years = (1020 - 720)
= Rs. 300.
S.I. for 2 years = 300/5 * 2
= Rs. 120.
Principal = (720 - 120)
= Rs.600.
Answer: D
Answer: D
Question: Which of the following values of x will satisfy the inequality x2 – x – 6 > 0 ?
Options:
A)x < – 2 or x > 3
B)–2 < x < 3
C)–3 < x < 2
D)x > – 2 or x < 3
E)None of these
Rationale: x2 – x – 6 > 0
or, x2 – 3x + 2x – 6 > 0
or, x(x – 3) + 2(x – 3) > 0
or, (x – 3)(x + 2) > 0
or, x = 3 or – 2
∴ x < – 2 or x > 3
Answer A
Answer: A
Question: Find the middle one when The sum of three consecutive even numbers is 36?
Options:
A)11
B)12
C)15
D)16
E)18
Rationale: 3 consecutive numbers can be a - 1, a, a + 1
So sum of numbers = 3a = 36.
Hence a = 12.
B
Answer: B
Question: The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?
Options:
A)16
B)17
C)18
D)19
E)20
Rationale: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 324/3 = 108 sq m
l b = 108 i.e., l * l/3 = 108
l2 = 324 => l = 18.
Answer: Option C
Answer: C
Question: What will be the compound interest on a sum of Rs. 20,000 after 3 years at the rate of 12% p.a.?
Options:
A)s:8098.56
B)s:10123.29
C)s:10123.20
D)s:10123.28
E)s:10123.12
Rationale: Amount
= [20000 * (1 + 12/100)3]
= 20000 * 28/25 * 28/25 * 28/25
= Rs. 28098.56
C.I. = (28098.56 - 20000)
= Rs: 8098.56
Answer: A
Answer: A
Question: Find large number from below question The difference of two numbers is 1200. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
Options:
A)1437
B)1250
C)1540
D)1600
E)1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1200 = 6x + 15
5x = 1185
x = 237
Large number = 237+1365 = 1437
A
Answer: A
Question: ----------------YES---------NO----UNSURE Subject M----500--------200-----100 Subject R----400--------100-----300 A total of 800 students were asked whether they found two subjects, M and R, interesting. Each answer was either yes or no or unsure, and the numbers of students who gave these answers are listed in the table above. If 190 students answered yes only for subject M, how many of the students did not answer yes for either subject?
Options:
A)100
B)210
C)300
D)400
E)500
Rationale: Since 190 students answered yes only for subject M, then the remaining 310 students who answered yes for subject M, also answered yes for subject R. So, 310 students answered yes for both subjects.
If 310 students answered yes for both subjects, then 400-310=90 students answered yes only for subject R.
So, we have that:
200 students answered yes only for subject M;
90 students answered yes only for subject R;
300 students answered yes for both subjects;
Therefore 800-(200+90+300)=210 students did not answer yes for either subject.
Answer: B.
Answer: B
Question: The Mathplanet school has increased its student body from 150 students to 240 from last year. How big is the increase in percent?
Options:
A)20
B)30
C)40
D)50
E)60
Rationale: We begin by subtracting the smaller number (the old value) from the greater number (the new value) to find the amount of change.
240−150=90
240−150=90
Then we find out how many percent this change corresponds to when compared to the original number of students
a=r⋅b
a=r⋅b
90=r⋅150
90=r⋅150
90150=r
90150=r
0.6=r=60%
Option E is correct.
Answer: E
Question: A person purchased a TV set for Rs. 12000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
Options:
A)16.68%
B)87.68%
C)70.68%
D)17.68%
E)18.68%
Rationale: The total CP = Rs. 12000 + Rs. 6250 = Rs. 18250 and SP
= Rs. 31150
Profit(%) = (31150 - 18250)/18250 * 100
= 70.68%
Answer:C
Answer: C
Question: One years ago,Promila was four times as old as her daughter Sakshi.Six years hence,Promila’s age will excepted her daughter’s age by 9 years.The ratio of the present ages of Promila and her daughter is
Options:
A)9 : 2
B)11 : 3
C)12 : 5
D)13 : 4
E)None of these
Rationale: Solution
Let the ages of Promila and Sakshi 1 year ago be 4x and x years respectively.
Then,[(4x +1)+6]-[(x + 4)+ 4]=64 ⇔ 4x = 48 ⇔ x =12.
∴ Required ratio =(4x +1 ) : (x + 1) : 13 : 4. Answer D
Answer: D
Question: We made a down payment of $80 and borrowed the balance on a new violin which cost $400. The balance with interest was paid in 23 monthly payments of $14 each and a final payment of $22. The amount of interest paid was what percent of the amount borrowed?
Options:
A)5.5%
B)6.5%
C)7.5%
D)8.5%
E)9.5%
Rationale: We borrowed $320.
To pay back this loan, we paid 23*$14 + $22=$344.
The interest was $344-$320=$24.
The percentage was $24/$320=0.075=7.5%.
The answer is C.
Answer: C
Question: Look at this series: 58, 52, 46, 40, 34, ... What number should come next?
Options:
A)23
B)33
C)28
D)35
E)28
Rationale: C
28
This is a simple subtraction series. Each number is 6 less than the previous number.
Answer: E
Question: Sandy purchased 20 dozen toys at the rate of $144 per dozen. Sandy sold each toy at the rate of $12.60. What was the percentage profit?
Options:
A)3%
B)5%
C)7%
D)9%
E)11%
Rationale: A dozen toys cost $144, so each toy cost $12.
selling price / cost price = 12.60 / 12 = 1.05
The percentage profit is 5%.
The answer is B.
Answer: B
Question: At a certain laboratory, chemical substance are identified by an unordered combination of three different colors. If no chemical may be assigned the same three colors as any other, what is the maximum number of substances that can be identified using ten colors?
Options:
A)21
B)35
C)105
D)120
E)210
Rationale: The prompt tells us that substance is identified by an UNORDERED combination of 3 colors and that no chemical may be assigned the same 3 colors as any other chemical.
As an example, a chemical with the colors A/B/C means that the following combinations CANNOT be used by any other chemical:
ABC
ACB
BAC
BCA
CAB
CBA
By extension, the first part of your calculation would be the number of possible substances that could be identified with 10 colors: 10c3 = 120 possible substances
D
Answer: D
Question: Find the simple interest on Rs.450 for 8 months at 5 paisa per month?
Options:
A)277
B)270
C)180
D)266
E)121
Rationale: I = (450*8*5)/100 = 180
Answer: C
Answer: C
Question: A solution of 66 litres contains milk and water in the ratio 7:x. If four litres of water is added to the solution, the ratio becomes 3:2, find the value of x?
Options:
A)8
B)5
C)3
D)4
E)6
Rationale: Total new quantity = original sol + water =66+4 =70
New ratio = 3:2, New quantity of milk =3/5*70 = 42 Lit,
New quantity of water = 2/5*70 = 28 Lit
Water present initially = (28-4) = 24 Lit
Ratio = 42/24 =7/4 There for x = 4
ANSWER:D
Answer: D
Question: The sum of the two digits of a number is 10. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number?
Options:
A)11
B)28
C)156
D)44
E)148
Rationale: Any two digit number can be written as (10P + Q), where P is the digit in the tens place and Q is the digit in the units place.
P + Q = 10 ----- (1)
(10Q + P) - (10P + Q) = 54
9(Q - P) = 54
(Q - P) = 6 ----- (2)
Solve (1) and (2) P = 2 and Q = 8
The required number is = 28
Answer: B
Answer: B
Question: On a map, 1.5 inches represent 24 miles. How many miles approximately is the distance if you measured 44 centimeters assuming that 1-inch is 2.54 centimeters?
Options:
A)174.2
B)277
C)288.1
D)296
E)282.4
Rationale: 1.5 inch = 2.54*1.5 cm.
So, 2.54*1.5 represents 24 miles.
So for 44 cm.:
44/(2.54*1.5) = x / 24 ---> x = 24*44/(3.81) = 277
Answer will be B.
Answer: B
Question: A bag contains 6 white and 4 black balls .2 balls are drawn at random. find the probability that they are of same colour.
Options:
A)71/9
B)7/15
C)7/18
D)4/17
E)2/17
Rationale: let S be the sample space
Then n(S)=no of ways of drawing 2 balls out of (6+4)=10c2=(10*9)/(2*1)=45
Let E=event of getting both balls of same colour
Then n(E)=no of ways(2 balls out of six) or(2 balls out of 4)
=(6c2+4c2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6=21
P(E)=n(E)/n(S)=21/45=7/15
Option B
Answer: B
Question: A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
Options:
A)5
B)8
C)9
D)2
E)3
Rationale: 30 --- 3 DS = 10
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (10 + 6)/2 = 8
Answer: B
Answer: B
Question: Find the value of m from (12)^3 x 6^4 ÷ 432 = m?
Options:
A)2346
B)3546
C)4566
D)3455
E)5184
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
E
Answer: E
Question: In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 80 questions and secures 130 marks, the no of questions he attempts correctly is :
Options:
A)A)35
B)B)38
C)C)90
D)D)88
E)E)42
Rationale: Let the number of correct answers be X.
Number of incorrect answers = (60 – X).
4x – (80 – x) = 130
=> 5x = 210
=> x = 42
Answer:E
Answer: E
Question: find the number, difference between number and its 3/5 is 60.
Options:
A)150
B)153
C)154
D)155
E)156
Rationale: Explanation:
Let the number = x,
Then, x-(3/5)x = 60,
=> (2/5)x = 60 => 2x = 60*5,
=> x = 150
Answer: Option A
Answer: A
Question: What is the decimal equivalent of (1/4)^1?
Options:
A)0.0016
B)0.0625
C)0.16
D)0.25
E)0.5
Rationale: (1/4)= 0.25
Answer : D
Answer: D
Question: Albert father was 48 years of age when she was born while her mother was 46 years old when her brother 2 years younger to her was born. What is the difference between the ages of her parents?
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: Mother's age when Albert's brother was born = 46years
Father's age when Albert's brother was born = 48+2 = 50years
Required difference = 50-46 = 4 years
Answer is B
Answer: B
Question: A man invested Rs. 14,400 in Rs. 100 shares of a company at 20% premium.If the company declares 4% dividend at the end of the year,then how much does he get ?
Options:
A)Rs. 500
B)Rs. 600
C)Rs. 650
D)Rs. 720
E)None
Rationale: Solution
Number of shares = (14400/120) = 120.
Face value = Rs. (100x120 ) = Rs. 12000.
Annual income = Rs.(4/100x12000) = Rs. 480.
Answer E
Answer: E
Question: The contents of a certain box consist of 20 apples and 30 oranges. How many oranges must be added to the box so that exactly 20% of the pieces of fruit in the box will be apples?
Options:
A)50
B)55
C)75
D)85
E)100
Rationale: apple = (apple + orange + x)*0.2
20 = (30 + 20 + x)*0.2
x = 50
Answer: A
Answer: A
Question: A certain sum amounts to Rs.1725 in 3 years and Rs.1875 in 5 years. Find the rate % per annum?
Options:
A)8%
B)5%
C)2%
D)3%
E)1%
Rationale: 3 --- 1725
5 --- 1875
--------------
2 --- 150
N = 1 I = 75 R = ?
P = 1725 - 225 = 1500
75 = (1500*1*R)/100
R = 5%
Answer: B
Answer: B
Question: A computer is programmed to multiply consecutive even integers 2*4*6*8*…*n until the product is divisible by 2013, What is the value of n?
Options:
A)22
B)38
C)62
D)122
E)672
Rationale: Same logic but with application of factorials.
2*4*6*8*...*n = 2(1*2*3*4*...n/2) = 2*(n/2)!
Now we have: 2*(n/2)!/2013=2*(n/2)!/(3×11×61)
For the expression 2*(n/2)! To be divisible by 2013 min value of n/2 should be 61.
So n/2=61 => n=122
Answer D.
Answer: D
Question: Find the sum lend at C.I. at 5 p.c per annum will amount to Rs.650 in 2 years?
Options:
A)221
B)287
C)400
D)589
E)171
Rationale: Explanation:
650 = P(21/20)2
P = 589.56
Answer:D
Answer: D
Question: A basket contains 8 blue, 8 red and 8 yellow marbles. If 8 marbles are extracted from the basket at random, what is the probability that a marble of each color is among the extracted?
Options:
A)2/21
B)3/25
C)1/6
D)9/28
E)64/253
Rationale: 24/24*16/23*8/22 = 64/253
the answer is (E)
Answer: E
Question: In May, the groundskeeper at Spring Lake Golf Club built a circular green with an area of 90π square feet. In August, the groundskeeper doubled the distance from the center of the green to the edge of the green. What is the total area of the renovated green?
Options:
A)360π
B)400π
C)450π
D)500π
E)600π
Rationale: Area = πR^2, so doubling the radius results in an area that is 4 times the original area.
4(90π) = 360π
The answer is A.
Answer: A
Question: Given that 0.0010010 x 10^q > 10^3, and q is an integer, which of the following is the smallest possible value of q?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: 0.0010010 x 10^q > 10^3, and q is an integer
This will be true only when LHS will be 1001
so the smallest possible value of q to make LHS > 10^3 is q=6
ANSWER:D
Answer: D
Question: The area of a triangle will be when a = 1m, b = 2m, c = 7m, a, b, c being lengths of respective sides?
Options:
A)3
B)6
C)5
D)9
E)1
Rationale: S = (1 + 2 + 7)/2= 5 Answer:C
Answer: C
Question: 0.6 of a number equals 0.09 of another number. The ratio of the number is:
Options:
A)2:3
B)1:15
C)20:3
D)3:20
E)None of these
Rationale: Explanation :
Let 0.6 of x be equal to 0.09 of y:
i.e. 0.6x = 0.09y
=> x/y = 0.09/0.6 = 3/20
Answer : D
Answer: D
Question: If Rs. 782 be divided into three parts, proportional to 1/2: 2/3: 3/4, then the first part is:
Options:
A)202
B)203
C)204
D)205
E)206
Rationale: (1/2+2/3+3/4)x=782
x=782*12/23=408
fist part is: (1/2)x=408/2=204
ANSWER:D
Answer: D
Question: The average marks of a class of 24 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students?
Options:
A)52.2
B)59.5
C)52.8
D)53.5
E)52.1
Rationale: Sum of the marks for the class of 24 students = 24 * 40 = 960
Sum of the marks for the class of 50 students = 50 * 60 = 3000
Sum of the marks for the class of 74 students =
960 + 3000 = 3960
Average marks of all the students = 3960/74
= 53.5
Answer:D
Answer: D
Question: If in a certain sequence of consecutive multiples of 50, the median is 725, and the greatest term is 950, how many terms that are smaller than 725 are there in the sequence?
Options:
A)6
B)5
C)8
D)12
E)13
Rationale: Since the median is 725 we know there must be a even number of integers because 50 is not a multiple of 725.
So the list around 725 must go. 600 650 700(725) 750 800 850 900 950
Since we know there are 5 numbers greater than 725 then there must be 5 numbers less then 725.
answer:B
Answer: B
Question: What will be the day of the week 15th August, 2010?
Options:
A)Tuesday
B)Saturday
C)Monday
D)Sunday
E)Friday
Rationale: 15th August, 2010 = (2009 years + Period 1.1.2010 to 15.8.2010)
Odd days in 1600 years = 0
Odd days in 400 years = 0
9 years = (2 leap years + 7 ordinary years) = (2 x 2 + 7 x 1) = 11 = 4 odd days.
Jan. Feb. Mar. Apr. May. Jun. Jul. Aug.
(31 + 28 + 31 + 30 + 31 + 30 + 31 + 15) = 227 days
227 days = (32 weeks + 3 days) 3 odd days.
Total number of odd days = (0 + 0 + 4 + 3) = 7 = 0 odd days.
Given day is Sunday
Answer is D.
Answer: D
Question: Find the area of the square, one of whose diagonals is 3.8 m long ?
Options:
A)7.22m^2
B)3.86m^2
C)8.96m^2
D)2.68m^2
E)7.89m^2
Rationale: Area of the square= 1/2(diagonal)^2
=(1/2*3.8*3.8)m^2
= 7.22m^2
Answer (A)
Answer: A
Question: If x is the sum of six consecutive integers, then x is divisible by which of the following: I. 6 II. 5
III. 7
Options:
A)I only
B)II only
C)III only
D)I,III only
E)II,III only
Rationale: We're told that X is the SUM of 6 CONSECUTIVE INTEGERS. We're asked what X is divisible by....
Let's TEST VALUES....
IF we use the 6 consecutive integers: 5, 6, 7,8,9 and 10, then the sum = 45.
45 is divisible by 5
45 is NOT divisible by 6
45 is NOT divisible by 7
There's only one answer that 'fits' with these facts. Answer : B
Answer: B
Question: Which number is the odd one out ?
9654 4832 5945 7642 7963 8216 3647
Options:
A)3647
B)9654
C)5945
D)7963
E)8216
Rationale: The product of first two digits in a number equals the last two digits, except in 3647. Hence, it is the odd one.
The answer is 3647.
ANSWER:A
Answer: A
Question: A train 490 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
A)25
B)26
C)27
D)28
E)29
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 490 * 2/35 = 28 sec
Answer: Option D
Answer: D
Question: In a race of length Lmetres, Johnson beats Lewis by M metres and Greene by N metres, By how many metres does Lewis beat Greene in the same race ? (M<N)
Options:
A)L(L-N) / L-M
B)(N-M)*L/(L-M)
C)L-N
D)M-N
E)M+
Rationale: the ans is quite simple N-M but since the ans is not given, the best way to 'find' the correct option is to plug in the numbers. For my work, i took the following numbers:
L = 100
M = 10
N =20.
So basically, L beat G by 10 meters. Now whatever options comes close to the figure 10 is the right ans..
looking the the opion C to E, one can make out that they are incorrect
Out of which, i choose B.
Answer: B
Question: Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 38 years. What is Deepak present age?
Options:
A)22
B)24
C)77
D)266
E)182
Rationale: Present age is 4x and 3x,
=> 4x + 6 = 38 => x = 8
So Deepak age is = 3(8) = 24
Answer: B
Answer: B
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 7 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
Options:
A)s.4529
B)s.4586
C)s.4597
D)s.6342
E)s.4528
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 7
=Rs.6342
Answer: D
Answer: D
Question: A man is 27 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is?
Options:
A)11
B)25
C)27
D)22
E)91
Rationale: Let the son's present age be x years.
Then, man's present age = (x + 27) years.
(x + 27) + 2 = 2(x + 2) x + 29 = 2x + 4 => x = 25.
Answer: B
Answer: B
Question: In how many different ways can the letters of the word â€˜EVERâ€™ be arranged?
Options:
A)12
B)280
C)300
D)310
E)360
Rationale: Number of ways = 4!/2! = 4X3X2X1/2X1 = 12
A
Answer: A
Question: The average of numbers 0.54204, 0.54203, 0.54202 and 0.54201 is ?
Options:
A)0.54202
B)0.54204
C)0.542022
D)0.542025
E)None
Rationale: Answer
Average = (0.54204 + 0.54203 + 0.54202 + 0.54201)/ 4
=2.1681/ 4
=0.542025
Correct Option: D
Answer: D
Question: Jill’s compact disc player randomly plays a song, so that no song is repeated before the entire album is played. If Bill plays a disc with 18 songs, what are the chances that the third song he hears will be his favorite?
Options:
A)1/18
B)1/12
C)1/11
D)3/14
E)1/3
Rationale: The player plays the songs on the album at random, so there are 18 songs that can be the third one played. Only 1 of these ways will result in Bill's favorite song being the third one played.
Total outcomes ==> 18
Total positive outcomes ==> 1
Correct answer is A) 1/18
Answer: A
Question: A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims 4 cups of tea are prepared, 2 in one way and 2 in other. Find the different possible ways of presenting these 4 cups to the expert.
Options:
A)25
B)24
C)30
D)34
E)None
Rationale: Solution:
Since, there are 2 cups of each kind, prepared with milk or tea leaves added first, are identical hence, total number of different people ways of presenting the cups to the expert is,
[4!/(2!x2!)]= 24
Answer: Option B
Answer: B
Question: A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After six months, C joined them with Rs.20,000. What will be A's share in the total profit of Rs.26,000 earned at the end of 2 years from the starting of the business?
Options:
A)Rs.7500
B)Rs.9000
C)Rs.9500
D)Rs.10,400
E)None
Rationale: Solution
A : B : C	=(20000×24):(15000×24):(20000×18)
=4 :3 :3
A's share	=Rs.(26000×4/10)
= Rs.10400.
Answer D
Answer: D
Question: What is the probability of rolling a nine with two, fair, six-sided dice?
Options:
A)1/6
B)1/9
C)2/13
D)1/12
E)5/36
Rationale: There are 4 ways to roll a nine: 3 and 6, 6 and 3, 4 and 5, 5 and 4 with two six-sided dice. There are 6 times 6 = 36 ways to roll two dice. The probability of rolling a 9 is thus 4/36 = 1/9. B
Answer: B
Question: Three race cars driven by James, Myles and Samantha start moving around a circular race track of length 1500m from the same point simultaneously in the same direction at speeds of 15 m/s, 25 m/s and 45 m/s respectively. When will they meet for the first time after they started moving?
Options:
A)540 seconds
B)240 seconds
C)200 seconds
D)300 seconds
E)150 seconds
Rationale: If they all meet after T seconds, it means they covered the distances 15T, 25T, and 45T respectively.
Since they all arrive to the same spot, it means that the differences taken pairwise between the distances must be positive integer multiples of the length of the track, which is 1500m. So, 10T, 20T, and 30T must all be multiples of 1500. 10T multiple of 1500 means T multiple of 150. The smallest T with this property is 150 and is on the list of answers.
Answer E.
Answer: E
Question: In Mike's opinion, his weight is greater than 65kg but leas than 72 kg. His brother does not agree with Mike and he thinks that Mike's weight is greater than 60kg but less than 70kg. His mother's view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of different probable weights of Mike?
Options:
A)54.3 kg
B)55.5 kg
C)66.5 kg
D)67.8 kg
E)69 kg
Rationale: Let Mike's weight be X kg.
According to Mike, 65 < X < 72.
According to Mike's brother, 60 < X < 70.
According to Mike's mother, X < 68.
The values satisfying all the above conditions are 66 and 67.
Required average = (66 + 67) / 2 = 66.5 kg
D
Answer: D
Question: If a + b + c = 13, then find the ab + bc + ca :
Options:
A)22
B)99
C)50
D)29
E)11
Rationale: Answer: C) 50
Answer: C