divelab/Sys2Bench huggingface dataset:
Question: The sum of three numbers is 98. The ratio of the first to the second is 2/3, and the ratio of the second to the third is 5/8. The second number is
Options:
A)15
B)20
C)25
D)30
E)32
Rationale: Solution:
Let the three numbers be x, y and z.
Sum of the numbers is 98.
x + y + z = 98………………(i)
The ratio of the first to the second is 2/3.
x/y = 2/3.
x = 2/3 × y.
x = 2y/3.
The ratio of the second to the third is 5/8.
y/z = 5/8.
z/y = 8/5.
z = 8/5 × y.
z = 8y/5.
Put the value of x = 2y/3 and z = 8y/5 in (i).
2y/3 + y + 8y/5 = 98
49y/15 = 98.
49y = 98 × 15.
49y = 1470.
y = 1470/49.
y = 30 .
Therefore, the second number is 30.
ANSWER:D
Answer: D
Question: If there are 200 questions in a 3 hr examination. Among these questions are 100 type A problems, which requires twice as much as time be spent than the rest of the type B problems. How many minutes should be spent on type A problems?
Options:
A)72 min
B)62 min
C)70 min
D)74 min
E)120 min
Rationale: x=time for type B prolems
2x=time for type A problem
total time=3hrs=180min
100x+100*2x=180
x=180/300
x=0.6
time taken for type A problem=100*2*0.6=120min
ANSWER:E
Answer: E
Question: Two trains, each 160 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?
Options:
A)26 km/hr
B)17 km/hr
C)60 km/hr
D)77 km/hr
E)96 km/hr
Rationale: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(160 + 160)/8 = 3x => x = 40/3.
So, speed of the faster train = 80/3 = 80/3 * 18/5
= 96 km/hr.
Answer:E
Answer: E
Question: In a group of 6 boys&4 girls a Committee of 4 persons is to be formed. In how many different ways can it be done so that the committee has at least 1girl?
Options:
A)110
B)120
C)130
D)195
E)200
Rationale: The committee of 4 persons is to be so formed that it has at least 1 woman The different ways that we can choose to form such a committee are:
(i) lw. 3 m in t 6X5X4' x 6C3 = 4x — — 80 3X2X1
x 6c2 =42:: x 26:: = 90 (ii) 2w. 2 m in °C2 (iii) 3w. 1 m in 4C3 x 6C1 = 4 x 6 = 24 (iv) 4w in 6C4 = 1 Total no. of different ways in which a committee of 4 persons can be formed so that it has at least one woman. = 80 + 90 + 24 + 1 = 195
D
Answer: D
Question: In what time will a train 200 m long cross an electric pole, it its speed be 144 km/hr?
Options:
A)2.5 sec
B)1.9 sec
C)8.9 sec
D)6.9 sec
E)5 sec
Rationale: Speed = 144 * 5/18
= 40 m/sec
Time taken = 200/40
= 5 sec.
Answer: E
Answer: E
Question: The L.C.M of two numbers is 2310 and their H.C.F is 30. If one number is 231 the Other is
Options:
A)330
B)300
C)270
D)250
E)350
Rationale: The other number
= L.C.M * H.C.F/given number
= 2310*30/231 = 300
Answer is B.
Answer: B
Question: In an examination, a student scores 3 marks for every correct answer and loses 2 marks for every wrong answer. If he attempts all 100 questions and secures 300 marks, the number of questions he attempts correctly, is:
Options:
A)150
B)250
C)400
D)300
E)100
Rationale: Let the number of correct answers be x.
Number of incorrect answers = (100 â€“ x).
3x â€“ 2(100 â€“ x) = 300 or 5x = 500 or x = 100.
ANSWER:E
Answer: E
Question: An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m?
Options:
A)Rs. 3642.40
B)Rs. 3868.80
C)Rs. 4216.20
D)Rs. 4082.40
E)None of these
Rationale: Length of the first carpet = (1.44)(6) = 8.64 cm
Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)
= 51.84(1.4)(5/4) sq m = (12.96)(7) sq m
Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40
ANSWER:D
Answer: D
Question: Two persons start running simultaneously around a circular track of length 400 m from the same point at speeds of 20 km/hr and 30 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
Options:
A)28 sec
B)37 sec
C)21.6 sec
D)23 sec
E)27 sec
Rationale: Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 400 / (20 + 30)5/18 = 300* 18 / 50 * 5 = 21.6 seconds.
Answer : C
Answer: C
Question: 405 sweets were distributed equally among children in such a way that the number of sweets received by each child is 20% of the total number of children. How many sweets did each child receive?
Options:
A)7
B)9
C)18
D)45
E)None of these
Rationale: Let the total number of children be x.
Then, x × (20 % of x) = 405
⇔ 1⁄5 x2 = 405 ⇔ x2 = 2025 ⇔ x = 45
∴ Number of sweets received by each child
= 20% of 45 = 9
Answer B
Answer: B
Question: In the equation x^2+kx+1=0, x is a variable and k is a constant. If the quadratic equation has two distinct real roots, which of the following could be true?
I) k=0
II) k=−1
III) k=−3
Options:
A)I only
B)III only
C)I and II only
D)II and III only
E)I and III only
Rationale: Please format the question properly.
Per the question, x^2+kx+1=0 with k=constant.
For a quadratic equation (ax2+bx+c=0) to have 2 distinct roots ---> D=b2−4ac>0 ---> k^2−4>0 --->k<−2or k>2 . Only III falls in these ranges.
B is the correct answer.
Answer: B
Question: When 200 is divided by positive integer x, the remainder is 2. What is the remainder when 398 is divided by x?
Options:
A)2
B)3
C)4
D)6
E)8
Rationale: f200/x leaves a reminder 2 then (200-2) i.e. 198 is divisible by x
So (200+198)/x leaves a reminder rem(200/x)+rem(198/x)=> 2+0=2
Answer :A
Answer: A
Question: A certain company has records stored with a record storage firm in 15-inch by 12-inch by 10-inch boxes. The boxes occupy 1.08 million cubic inches of space. If the company pays $0.5 per box per month for the record storage, what is the total amount that the company pays each month for record storage?
Options:
A)a. 150
B)b. 300
C)c. 600
D)d. 1,200
E)e. 2,400
Rationale: Volume Per Box: 15x12x10 = 1,800
Total Volume: 1,080,000
Number of Boxes: Total Volume / Volume Per Box = 1,080,000 / 1,800 = 600
Price Per Month: Number of Boxes * Price Per Box = 600 * 0.5 = 300
Answer: B
Answer: B
Question: A group of students was interviewed for that if it was asked whether or not they speak Spanish and / or English. Among those who speak Spanish, 15 speak English well, while 45 of them do not speak English. If 70% of students do not speak Spanish, how many students were surveyed?
Options:
A)200
B)220
C)230
D)210
E)215
Rationale: Number of students who speak Spanish are 45 + 15 = 60
Of total students, the percentage of students who do not speak Spanish was 70% --> percentage of who do is 30%
60-------30%
x ------- 100%
x = 60*100/30 = 200 = number of all students
Answer is A
Answer: A
Question: Two carpenters, working in the same pace, can build 2 desks in two hours and a half. How many desks can 4 carpenters build in 2 hours?
Options:
A)2.4.
B)3.2.
C)4.2.
D)5.5.
E)6.4
Rationale: W = 2 desks
T = 2.5 hrs
Rate of 2 carpenters = 2×R
Rate = work done/ time
2xR = 2/2.5
R = 1/2.5 = 2/5 (this is the rate of each carpenter)
Work done by 4 carpenters in 2 hrs = 4 × rate of each carpenter x time = 4× 2/5 × 2 = 3.2 desks
B is the correct answer.
Answer: B
Question: Which of the following represents the profit from the investment of x dollars at n percent compound annual interest for 6 years?
Options:
A)5x (1+n/100)^5 - x
B)6x (1+n/100)^4 - x
C)x (1+n/100)^6 - x
D)2x (1+n/100)^7 - x
E)4x (1+n/100)^8 - x
Rationale: Amount after 6 years compounded yearly = x (1+n/100)^6
Thus profit = Final amount - original principle = x (1+n/100)^6 - x . Answer : C
Answer: C
Question: If 140/x is an integer and 108/x is an integer, which of the following must be true?
I. 9/x is an integer
II. 12/x is an integer
III. 36/x is an integer
Options:
A)I only
B)III only
C)I and II only
D)II and III only
E)I, II and III
Rationale: I think, here we should use the greatest common factor.
The greatest common factor for 144 and 108 is 36.
So 36/x is an integer.
For the rest of the answers, if x is 36 then 9/x and 12/x leads to fractions.
Ans is E.
Answer: E
Question: The current in a river is 6 mph. A boat can travel 20 mph in still water. How far up the river can the boat travel if the round trip is to take 10 hours?
Options:
A)69 miles
B)88 miles
C)96 miles
D)91 miles
E)112 miles
Rationale: Upstream Speed = 20-6=14 mph
Downstream Speed = 20+6 = 26 mph
D/14 + D/26 = 10 hours
Solving for D we get D=91
Answer: D
Answer: D
Question: How many minutes will it take for a car that is traveling at a constant rate of 9 miles per hour to travel a distance of 106 yards?	(1 mile = 1,160 yards)
Options:
A)2
B)5
C)4
D)3.61
E)4.3
Rationale: speed = 9 miles/hr = 4.4 yard/s = 29.33 yards/min
distance = 106 yards
time = distance/speed
=106/29.33
=3.61 minutes
ans - D
Answer: D
Question: A train passes a station platform in 30 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)200
B)220
C)240
D)150
E)260
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 30 = 15
x + 300 = 450
x = 150 m.
Answer: Option D
Answer: D
Question: Two tracks are parallel. The first track has 6 checkpoints and the second one has 10 checkpoints. In how many ways can the 6 checkpoints of first track be joined with the 10 checkpoints of the second to form a triangle?
Options:
A)120
B)150
C)200
D)270
E)420
Rationale: To make a triangle, you need 2 checkpoints from one track and 1 from the other. You cannot have all 3 from the same track since then the points will be in a line (assuming straight line of track)
You select 2 checkpoints from the first track and one from the second or two from the second track and one from the first.
6C2 * 10C1 + 10C2 * 6C1 = 150 + 270 = 420
Answer (E)
Answer: E
Question: Seller selling an apple for Rs.20, a Seller loses 1/6th of what it costs him. The CP of the apple is?
Options:
A)10
B)12
C)21
D)18
E)20
Rationale: SP=20Loss=CP21Loss=CP−SP=CP−20⇒CP21=CP−20⇒20 CP21=20⇒CP21=1⇒CP=21
C
Answer: C
Question: Sixty five percent of a number is 21 less than four fifth of that number. What is the number ?
Options:
A)240
B)140
C)230
D)130
E)125
Rationale: Let the number be x.
Then, 4*x/5 –(65% of x) = 21
4x/5 – 65x/100 = 21
5x = 2100
x = 140.
Answer B.
Answer: B
Question: 4.509/10.02 =
Options:
A) 0.45
B) 0.3505
C) 0.3509
D) 0.351
E) 0.3527
Rationale: 4.509 / 10.02
4509 / 1002 = 4.5
move the comma two places to the left as we have 2 decimal places from the divisor: 0.45. Answer: A
Answer: A
Question: An 80-liter solution of cool-drink is made from 10% jasmine water. If 8 liters of jasmine and 12 liters of water were added to the solution, what percent of the solution is jasmine?
Options:
A)12%
B)14%
C)16%
D)18%
E)20%
Rationale: The percent of jasmine in the resulting solution is: (amount of jasmine) / (total volume)
(0.1(80) + 8) / 100 = 16/100 = 16%
The answer is C.
Answer: C
Question: The ratio of two numbers is 2 : 3 and their H.C.F. is 6. Their L.C.M. is
Options:
A)48
B)22
C)36
D)27
E)67
Rationale: Explanation:
Let the numbers be 2x and 3x. Then, their H.C.F. = x. So, x = 6.
So, the numbers 12 and 18
L.C.M. of 12 and 18 = 36
Option C
Answer: C
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
Options:
A)30/83 hours
B)80/13 hours
C)30/19 hours
D)30/13 hours
E)31/13 hours
Rationale: Speed downstream = 20 + 6 = 26 kmph.
Time required to cover 60 km downstream = d/s = 60/26 = 30/13 hours.
Answer: D
Answer: D
Question: In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
Options:
A)200 %
B)75 %
C)150 %
D)50 %
E)70%
Rationale: Explanation:
Let C.P.= Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420.
New C.P. = 125% of Rs. 100 = Rs. 125
New S.P. = Rs. 420.
Profit = Rs. (420 - 125) = Rs. 295
Required percentage =(295/420*100)%=1475/21%=70%
Answer:E
Answer: E
Question: If the sum of the first n positive integers is x, then which of the following is the sum of the first 2n even positive integers?
Options:
A)2x + 2n^2
B)3x + 4n^2
C)4x + 2n
D)4x + n^2
E)4x + 2n^2
Rationale: n(n+1)/2 = x
or n^2 + n = 2x (1)
If the series has first 2n numbers, sum of n odd numbers = n^2.
So sum of n even numbers= Sum of first 2n numbers - n^2
In this case we have 2n even numbers so 2n odd numbers will be there, hence a total of 4n first numbers.
Sum of first 4n numbers = 4n(4n+1)/2 -----------(2)
Sum of first 2n odd numbers is (2n)^2 = 4n^2 ---------------- (3)
So sum of 2n even numbers is (2)-(3)
or 4n^2+2n
or 2n^2 + 2 (n^2+n)
or 2n^2 + 2(2x)
or 2n^2 + 4x
ANSWER:E
Answer: E
Question: Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Options:
A)7
B)8.2
C)2
D)10.8
E)11.2
Rationale: Answer: Option D
Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 160 = 300 m.
Required time = 300 * 9/250 = 54/5 = 10.8 sec
Answer: D
Question: A and B can do a piece of work in 6 2/3 days and 5 days respectively. They work together for 2 days and then A leaves. In how many days after that B will complete the work alone.
Options:
A)6 Â½ days
B)1 Â½ days
C)8 Â½ days
D)5 Â½ days
E)2 Â½ days
Rationale: Explanation:
3/20 * 2 + (2 + x)/5 = 1
x = 1 Â½ days
Answer:B
Answer: B
Question: If x ≠ 0 and x - (2- x^2)/x = y/x, then y =
Options:
A)− 2 − 3x^2
B)x^2 − 2
C)2x^2 − 2
D)x − 2 − x^2
E)x − 2 + x^2
Rationale: We're told that x ≠ 0 and x - (2- x^2)/x = y/x. We're asked for the value of y.
IF.... X = 3
3 - (2 - 3^2)/3 = y/3
9/3 - (-7/3) = y/3
Multiply everything by 3....
9 - (-7) = y
16 = y
So we're looking for an answer that equals 16 when x = 3...
Answer A) − 2 − 3x^2 This will be NEGATIVE, so no need to calculate it.
Answer B) x^2 − 2 = 7. NOT a match.
Answer C) 2x^2 − 2 = 16. This IS a match.
Answer D) x − 2 − x^2 This will be NEGATIVE, so no need to calculate it.
Answer E) x − 2 + x^2 = 10. NOT a match.
Final Answer:C
Answer: C
Question: If takes 25.5 minutes to download a file using Modem A. Modem B work at 17% of the speed of Modem A. How long does it take to download a file using a Modem B?
Options:
A)130 minutes
B)140 minutes
C)150 minutes
D)160 minutes
E)170 minutes
Rationale: Let Speed of modem A be k
So Speed of modem B is 17/100*k
Time taken by modem A = 25.5 minutes
Let time taken by modem B = x
k*25.5 = 17/100*k*x
0.17*x = 25.5
x = 25.5/0.17
= 150 minutes
ANSWER:C
Answer: C
Question: If the selling price of 5 books is same as the cost price of 10 books. Find the gain or loss percentage?
Options:
A)50%
B)100%
C)45%
D)55%
E)65%
Rationale: Let the C.P of each book be Re 1. Then,
S.P of 5 books= C.P of 10 books= Rs. 10
Now, C.P of 5 books= Rs.5, S.p of 5 books= Rs 10
Gain = Rs ( 10 -5 ) = Rs 5.
Gain% = ( 5/5× 100 ) % = 100%
Answer : B
Answer: B
Question: Two trains of equal length, running with the speeds of 50 and 40 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
Options:
A)5.55 sec
B)4.55 sec
C)5.95 sec
D)6.55 sec
E)9.55 sec
Rationale: RS = 50 -40 = 10 * 5/18 = 50/18
T = 50
D = 50 * 50/18 = 1250/9
RS = 50 + 40 = 90 * 5/18=25
T = 1250/9 * 1/25 = 5.55 sec
ANSWER:A
Answer: A
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 the son is:
Options:
A)22
B)28
C)32
D)48
E)92
Rationale: 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 is A.
Answer: A
Question: if b is a positive integer greater than 8, which of the following must be divisible by 4?
Options:
A) b(b-1)(b+2)(b+3)
B) b(b-1)(b+3)(b+4)
C) b(b-3)(b+2)(b+4)
D) b(b-3)(b+2)(b+3)
E) b(b+1)(b+3)(b+4)
Rationale: D.
For any integer b, D is the only answer choice which will always be divisible by 4.
A product of 4 consecutive integers will always be divisible by 4. Since, none of the answer choices are a product of 4 consecutive integers, we have to ensure at least one of the integers is always a multiple of 4. The best way to do that is to ensure the answer choice isb* [(b-1)OR(b+3)] * [(b-2)OR(b+2)] * [(b-3)OR(b+1)]. (answer D)
Answer: D
Question: The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
Options:
A)44%
B)46%
C)48%
D)50%
E)51%
Rationale: Let original length = x metres and original breadth = y metres.
Original area = (xy) m2.
New length = 120 x m = 6 x m.
100 5
New breadth = 120 y m = 6 y m.
100 5
New Area = 6 x x 6 y m2 = 36 xy m2.
5 5 25
The difference between the original area = xy and new-area 36/25 xy is
= (36/25)xy - xy
= xy(36/25 - 1)
= xy(11/25) or (11/25)xy
Increase % = 11 xy x 1 x 100 % = 44%.
25 xy
A
Answer: A
Question: 3,9,27,81,....
Options:
A)583
B)604
C)616
D)243
E)636
Rationale: 1*3=3
3*3=9
9*3=27
27*3=81
81*3=243
ANSWER:D
Answer: D
Question: A student scored an average of 80 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics?
Options:
A)21
B)27
C)26
D)80
E)28
Rationale: Given M + P + C = 80 * 3 = 240 --- (1)
M + P = 90 * 2 = 180 --- (2)
P + C = 70 * 2 = 140 --- (3)
Where M, P and C are marks obtained by the student in Mathematics, Physics and Chemistry.
P = (2) + (3) - (1) = 180 + 140 - 240 = 80.Answer: D
Answer: D
Question: A group of college friends plan to rent a house together for x dollars per month, which is to be shared equally among them. If five, rather than six people rent the house together, how many more dollars, in terms of x, will each person have to pay for rent per month?
Options:
A)x/15
B)x/30
C)x/6
D)x/5
E)5x/6
Rationale: If 6 people share the rent, each person would pay x/6.
If 5 people share the rent, each person will pay x/5.
The extra amount each person pays is x/5 - x/6 = 6x/30 - 5x/30 = x/30
The answer is B.
Answer: B
Question: If P represents the product of the first 13 positive integers, which of the following must be true?
I. P is an even number
II. P is a multiple of 6
III. P is a multiple of 24
Options:
A)I only
B)II only
C)III only
D)None of the above
E)All of the above
Rationale: The correct answer is E.
Answer: E
Question: The price of 5 kilograms of premium fertilizer is the same as the price of 8 kilograms of regular fertilizer. If the price of premium fertilizer is y cents per kilogram more than the price of regular fertilizer, what is the price, in cents, per kilogram of premium fertilizer?
Options:
A)y/30
B)5/6*y
C)6/5*y
D)5y
E)8y/3
Rationale: Usingpfor premium andrfor regular, I got two equations from the question stem:
5p = 8r and p = r+y
Substitute for p: 5(r+y) = 8r
Distribute: 5r + 5y = 8r
Subtract 5r from both sides: 5y = 3r
Plug back into the first equation: 5p = 8(5y/3)
Distribute: 5p = 40y/3
Divide both sides by 5: p = 8y/3
The answer is E.
Answer: E
Question: s(n) is a n-digit number formed by attaching the first n perfect squares, in order, into one integer. For example, s(1) = 1, s(2) = 14, s(3) = 149, s(4) = 14916, s(5) = 1491625, etc. How many digits Q are in s(99)?
Options:
A)Q=350
B)Q=353
C)Q=354
D)Q=356
E)357
Rationale: Focus on the points where the number of digits Q in squares change:
1, 2, 3 - Single digit squares. First 2 digit number is 10.
4 , 5,...9 - Two digit squares. To get 9, the last number with two digit square, think that first 3 digit number is 100 which is 10^2. so 9^2 must be the last 2 digit square.
10, 11, 12, ... 31 - Three digit squares. To get 31, think of 1000 - the first 4 digit number. It is not a perfect square but 900 is 30^2. 32^2 = 2^10 = 1024, the first 4 digit square.
32 - 99 - Four digit squares. To get 99, think of 10,000 - the first 5 digit number which is 100^2.
So number of digits in s(99) = 3*1 + 6*2 + 22*3 + 68*4 = 3 + 12 + 66 + 272 = 353.B
Answer: B
Question: If 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is?
Options:
A)20:15:16
B)20:15:68
C)20:15:12
D)20:15:11
E)20:15:19
Rationale: 6A = 8B = 10 C
A:B:C = 1/6:1/8:1/10
= 20:15:12
Answer: C
Answer: C
Question: A pizzeria in Castroville creates its own special blend of shredded cheese at a cost of $696.05 per kilogram. The blend includes Mozzarella, at $504.35 per kilogram, and Romano cheese, at $887.75 per kilogram. If the employees have already shredded 19 kilograms of Mozzarella cheese, how many kilograms of Romano cheese will they need to shred now?
Options:
A)19kg
B)13kg
C)10kg
D)23kg
E)15kg
Rationale: 504.35(19)+887.75x	=696.05(19 + x)
Solve the equation.
504.35(19) + 887.75x = 696.05(19 + x)
9,582.65 + 887.75x = 13,224.95 + 696.05x
9,582.65 + 191.7x = 13,224.95
191.7x = 3,642.3
x = 19	.
Answer is A.
Answer: A
Question: A sum of money becomes triple itself in 16 years. In how many years will it become 5 times at the same rate?
Options:
A)32
B)15
C)27
D)30
E)35
Rationale: Let sum be Rs.100. After 16 years it become 300. With in 16 years it increased Rs.200 i.e. after 8
years it is doubled. So after 32 years interest become Rs.400. Total Rs.500 i.e. 5 times more than the
sum. So 32 years is the answer.
ANSWER:A
Answer: A
Question: How many positive integers less than 50 are multiples of 6 but NOT multiples of 8?
Options:
A)4
B)6
C)8
D)10
E)12
Rationale: The LCM of 6 and 8 is 24.
If x <50 and x is divisible by 6 not by 8 --> x is NOT divisible by 24.
From 1--> 50, we have 2 numbers which is divisible by 24: 24, 48.
From 1-->50, we have (48-6)/6 +1 =8 numbers divisible by 6.
Therefore, our answer is 8-2 = 6 numbers.
B
Answer: B
Question: Find the area of the quadrilateral of one of its diagonals is 30 cm and its off sets 10 cm and 6 cm?
Options:
A)189 cm2
B)150 cm2
C)240 cm2
D)177 cm2
E)187 cm2
Rationale: 1/2 * 30(10 + 6)
= 240 cm2
Answer: C
Answer: C
Question: A heap of coconuts is divided into groups of 2, 3 and 5 and each time one coconut is left over. The least number of Coconuts in the heap is?
A. 31 B. 41 C. 51 D. 61
Options:
A)31
B)41
C)51
D)61
E)71
Rationale: LCM = 30
=> 30 + 1 = 3
ANSWER:A
Answer: A
Question: Which of the following is the sum of all the even numbers between 1 and 93, inclusive?
Options:
A)2550
B)2450
C)2600
D)2447
E)2652
Rationale: This question can be solved withbunching.
We're asked for the SUM of all of the EVEN integers from 1 to 99, so we really want the sum of 2, 4, 6, 8.....98.
If you take the next smallest and next biggest numbers, you have...
8+92 = 100
This pattern will continue on, so we're going to have a bunch of 100s, BUT we have to be careful to make sure that we don't miss a number if it'sin the middleand doesn't get paired up. Since we know that the sum of each pair is 100, we can 'jump ahead' to find the last few pairs...
44+56 = 100
46+54 = 100
48+52 = 100
There IS a middle number: 50; this number does NOT get paired up.
Since 48 is the 24th even integer, we know there are twenty-four 100s + one 50. 2400+50-3 = 2447
Final Answer:
D
Answer: D
Question: A cube is divided into 216 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that, the cube is painted with green on one set of opposite faces, red on another set of opposite faces, and blue on the third set of opposite faces. How many cubelets are painted with exactly one colour?
Options:
A)72
B)84
C)96
D)108
E)120
Rationale: Each side of the cube has 6 x 6 = 36 cubelets.
Only the interior cubelets are painted one colour.
On each side, 4 x 4 = 16 cubelets are painted one colour.
Since the cube has six sides, the number of cubes with one colour is 6*16 = 96
The answer is C.
Answer: C
Question: A man engaged a servant on the condition that he would pay him Rs.710 and a uniform after a year service. He served only for 8 months and got Rs.460 and a uniform. Find the price of the uniform?
Options:
A)Rs.40
B)Rs.30
C)Rs.25
D)Rs.20
E)Rs.45
Rationale: 8/12 = 2/3 * 710 = 473.33
460.00
---------------
13.33
1/3 uniform 13.33
1 --------------- ? => Rs.40
ANSWER:A
Answer: A