MU-NLPC/Calc-aqua_rat huggingface dataset:
MANO,INC recently conducted a survey and found that 100,000 of its customers live in rural areas. if the number of it customers who live in urban areas is 200 percents grater than the numbers of customers who live in rural areas, how many of MANO,INC customers live in urban areas ?
Choose the correct choice
A) 200,000 B) 216,000 C) 360,000 D) 300,000 E) 540.0

Solution: Let's say that we have a starting value of X...   100% of X = X   100% MORE than X = X + X = 2X   200% MORE than X = X + 2X = 3X   300% MORE than X = X + 3X = 4X   Etc.   Here, we're told that 100,000 customers live in rural areas and the number who live in urban areas is 200% GREATER than the number who live in rural areas. That means that the number who are in urban areas is 3 times the number in rural areas...   3(100,000) = 300,000   Final Answer:300,000
Answer: D
Which of the following inequalities is equivalent to −5 < x < 1?	Choose the correct choice from the following choices:
A) |x - 1| < 7  B) |x + 2| < 3  C) |x + 3| < 5  D) |x - 2| < 6  E) None of the above

Solution: We know that |x| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0   Given is, -5 < x < 1, let's say by adding y to this inequality we will get into the above format   -5+y < x+y < 1+y   Now, to move this into the mod format, we need to have (-5+y) + (1+y) = 0 => y = 2   Thus, -3< x+2 < 3 => |x+2| < 3.   Hence, answer is |x + 2| < 3
Answer: B
How many different arrangements of letters are possible if three letters are chosen from the letters A through H and the letters E and A must be among the letters selected?  Choices:
A) 30
B) 33
C) 36
D) 39
E) 42

Solution: Besides A and E, there are 6 letters and we can choose one of them.   6C1 = 6   Three letters can be arranged in 3! ways.   The number of arrangements is 6*3! = 36   The answer is 36.
Answer: C
Sachin is younger than Rahul by 4 years. If the ratio of their ages is 7:9, find the age of Sachin  Options:
A) 24.58 B) 24.5 C) 24.3 D) 24.9 E) 14

Solution: If Rahul age is x, then Sachin age is x-4,   so (x-4)/x = 7/9   => 9x-36 = 7x   => 2x = 36   => x = 18   So Sachin age is   18 - 4= 
  18 - 4 = 14
14   Answer: 14
Answer: E
In a barrel of juice there is 50 liters; in a barrel of beer there are 80 liters. If the price ratio between barrels of juice to a barrel of beer is 3:4, what is the price ratio between one liter of juice and one liter of beer?  Select the correct option.
A) 3:2.  B) 6:5.  C) 3:1.  D) 4:3.  E) 3:4

Solution: Price of 50 L juice= 3x   1L= 3x/50   Price of 80 L beer= 4x   1L= 4x/80   Ratio of 1 L price = 3x/50/4x/80= 6:5   6:5. is the answer
Answer: B
On a certain day, Peter's farm harvested 1253 oranges. If Peter distributes his oranges evenly across 9 different retail shops, how many oranges would remain with him.	Choose the correct choice from the following options:
A) 1 orange
B) 3 oranges
C) 5 oranges
D) 7 oranges
E) 9 oranges

Solution: This is equivalent to finding the first number that is divisible by 9 that occurs before 1253.   In order to divide the sum in 9 parts, the amount must be divisible by 9   Divisibility rule of 9: The sum of the digits must be divisible by 9   Sum of digits of 1253 = 11 and 9 is divisible by 9.   Hence, we need to add 7 to this number for it to be divisible by 9   Correct Option: 7 oranges
Answer: D
If the radius of a circle is decreased 50%, what happens to the area? Choose the correct choice from the following.
A) 10% decrease
B) 20% decrease
C) 75% decrease
D) 40% decrease
E) 50% decrease

Solution: Area of Square = Pi* radius^2   New Radius = 0.5 * old radius   so new area = (0.5)^2 old area => 0.25 of old area => 25% old area   Ans : 75% decrease
Answer: C
In 10 years, P will be as old as Q is now. Ten years ago, Q was twice as old as P was then. How old is P now?	Choose the correct choice from the following answers.
A) 15  B) 20  C) 25  D) 30  E) 35

Solution: Q = P+10   Q-10 = 2(P-10)   P = 2P-20   P = 20   The answer is 20.
Answer: B
Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?	Pick one.
A) 80/7 sec
B) 20/8 sec
C) 20/7 sec
D) 20/3 sec
E) 20/3 sec

Solution: They are moving in opposite directions, relative speed is equal to the sum of their speeds.   Relative speed = (54 + 72)*5/18   = 7*5= 
7*5 = 35
35 mps.   The time required= d/s   = 100/35   = 20/7 sec.   Answer: 20/7 sec
Answer: C
Printer P can print one lakh books in 8 hours. Printer Q can print the same number of books in 10 hours while Printer R can print the same in 12 hours. All the Printers started printing at 9 A.M. Printer P is stopped at 11 A.M. and the remaining 2printers complete work. Approximately at what time will the printing of 1 lac books be completed? Choose the correct choice from the following answers:
A) 12 am	B) 1 pm	C) 2 pm	D) 3 pm	E) 4 pm

Solution: Work done by P in 1 hour = 1/8   Work done by Q in 1 hour = 1/10   Work done by R in 1 hour = 1/12   Work done by P,Q and R in 1 hour = 1/8 + 1/10 + 1/12 = 37/120   Work done by Q and R in 1 hour = 1/10 + 1/12 = 22/120 = 11/60   From 9 am to 11 am, all the Printer were operating.   Ie, they all operated for 2 hours and work completed = 2 × (37/120) = 37/60   Pending work = 1- 37/60 = 23/60   Hours taken by Q an R to complete the pending work = (23/60) / (11/60) = 23/11   which is approximately equal to 2   Hence the work will be completed approximately 2 hours after 11 am ; ie around 1 pm   1 pm
Answer: B
In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?  Choose the correct choice from the following answers: A) 63 B) 72 C) 14 D) 62 E) 72

Solution: Required number of ways = (7C5 x 3C2) = (7C2 x 3C1) = = 63.   63NSWER 63 63
Answer: A
Find the amount on Rs.8000 in 9 months at 20% per annum, if the interest being compounded quarterly?	Choose the correct choice from the following answers:
A) 1323	B) 9261	C) 2788	D) 2999	E) 1722

Solution: A = 8000(21/20)3 = 9261   Answer:9261
Answer: B
If the function f(x) is defined for all real numbers x as the maximum value of 2x + 6 and 12 + 3x, then for which one of the following values of x will f(x) actually equal 2x + 4 ? Select
A) –4	B) –5	C) –6	D) –7	E) –9

Solution: Since f(x) defines maximum of 2x + 6 and 12 + 3x,   to find those x when 2x+6 has greater value,   2x + 6 > 12 + 3x   or x < -6   Only value that satisfy this is -7.   Answer is (–7),
Answer: D
The sum of two numbers is 18 and their difference is 12. Find their product. Select:
A) 104
B) 108
C) 45
D) 325
E) None

Solution: Sol.   Let the numbers be x and y.   Then, x + y = 18 and   x - y = 12   2x = 30 +> x = 15. So y = 3   xy = 15*3= 
15*3 = 45
45   Answer : 45
Answer: C
Anup start a bike at 6am. and rides it at 60kmph. Raghu started at 7pm with his car at 75kmph. When will Raghu overtake Anup?
Answers
A) 8:30am  B) 9:40am  C) 10:00am  D) 12:00pm  E) 11:00am

Solution: Suppose bike is overtaken by car xhrs after 6am   Distance covered by the bike in x hrs = distance covered by the car in x-1 hr   60x = 75(x-1)   15x = 75   x = 5 hrs   Required time = 6+5= 
6+5 = 11
11:00am   Answer is 11:00am
Answer: E
a,b and c are positive integers less than or equal to 9. If a,b and c are assembled into the six-digit number aabbcc, which of the following must be a factor of aabbcc? Choose the most appropriate option.
A) 9
B) 3
C) 7
D) 11
E) None of these

Solution: The sum of the digits in place 1,3 and 5 is a+b+c is equal to the sum of the digits in place 2,4 and 6 which is a+b+c. thus the number abcabc is divisible by 11. thus 11 must be a factor of abcabc.   Answer: 11
Answer: D
A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint to make a new paint color called Perfect Pink. How many pints of red paint would be needed to make 35 pints of Perfect Pink paint? Options:
A) 9
B) 16
C) 19
D) 25 1/3
E) 28 1/2

Solution: 3/4 pint is required to make 3/4 + 2/3 = 17/12 pint of perfect pink   so 17/12 pint requires 3/4 pint of red..   1 pint will require 3/4 * 12/17=9/17..   35 pints will require 9/17 * 35= 19 pints..   19
Answer: C
One out of every 600 light bulbs are defected. If 2 out of every 10 defected light bulbs have a broken glass and there are 20 broken glass light bulbs in the shipment, how many light bulbs total are there in the shipment?	Select:	A) 60,000	B) 5,000	C) 10,000	D) 50,000	E) 52,000

Solution: 20 broken glasses indicates that  10*10= 
 10*10 = 100
100 defected bulbs are present.   100 defected bulbs indicates that 100*600= 60,000 light bulbs are present.   60,000 is the answer
Answer: A
A train 450 metres long is moving at a speed of 25 kmph. It will cross a man coming from the opposite direction at a speed of 2 km per hour in :  Select the correct option.
A) 30 sec	B) 32 sec	C) 36 sec	D) 38 sec	E) 60 sec

Solution: Relative speed = (25+2) km/hr = 27 km/hr   = (27×5/18) m/sec = 15/2 m/sec.   Time taken by the train to pass the man =(450×2/15) sec=60 sec   ANSW60 secR :60 sec
Answer: E
If x is an even integer and y = 6x + 4, which of the following CANNOT be a divisor of y?	Choose the correct choice from the following answers.
A) 17
B) 20
C) 29
D) 41
E) 53

Solution: x takes even values as 2,4,6,8.,   y=6x+5   x is an even term so 6x must be an even term when it adds with 4 so it must be a even integer   20 didn't follows this condition ans is 20
Answer: B
John spends $320 buying his favorite dolls. If he buys only small Monkey dolls, which are $4 cheaper than the large Monkey dolls, he could buy 40 more dolls than if he were to buy only large Monkey dolls. How much does a large Monkey doll cost? Pick:
A) $7.2
B) $7.5
C) $8
D) $9
E) $10

Solution: A and B is not an integer. So we start with C   If large doll costs $8, then he can buy   320/8= 
  320/8 = 40
40 large dolls and   320/4= 
  320/4 = 80
80 small dolls.   Difference is 40, which is we wanted.   Answer $8.
Answer: C
At a monthly meeting, 3/5 of the attendees were males and 7/8 of the male attendees arrived on time. If 9/10 of the female attendees arrived on time, what fraction of the attendees at the monthly meeting did not arrive on time?  Choose the correct choice from the following
A) 23/200  B) 11/100  C) 7/50  D) 3/20  E) 4/25

Solution: Males who did not arrive on time are 1/8*3/5 = 3/40 of the attendees.   Females who did not arrive on time are 1/10*2/5 = 2/50 of the attendees.   The fraction of all attendees who did not arrive on time is 3/40 + 2/50 = 23/200   The answer is 23/200.
Answer: A
If a,b, and c are consecutive positive integers and a>b>c, what can be the value of (a^2-b^2)(b^2-c^2)?
Choose the correct choice
A) 35
B) 45
C) 55
D) 65
E) 75

Solution: (a^2-b^2)(b^2-c^2) = (a+b)*(a-b)*(b+c)*(b-c) = (a+b)*(-1)*(b+c)*(-1) = (a+b)*(b+c)   Therefore, the product should have factors with a difference of 2.   35 = 5*7, so this is a possible value for the original expression.   The answer is 35.
Answer: A
A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 75, the runs scored by C are?	Choose the correct choice
A) 11 B) 18 C) 45 D) 17 E) 12

Solution: A:B = 2:3   B:45 = 2:5   A:B:45 = 4:6:15   15/25 * 75= 
15/25 * 75 = 45
45   Answer:45
Answer: C
A fruit seller had some oranges. He sells 40% oranges and still has 360 oranges. How many oranges he had originally?
Pick one: A) 700 B) 710 C) 600 D) 730 E) 740

Solution: 60% of oranges = 360   100% of oranges =(360×100)/6=600   total oranges = 700   ANSWER : 600
Answer: C
The width of a rectangle is 10mtr and its area is 150 square meter. If length of the rectangle is increased, then its new area is 1(1/3) times of the original area. What is the new perimeter of the rectangle?  Pick one.
A) 45	B) 54	C) 67	D) 60	E) 69

Solution: Ans.(D)   Sol. Length of original rectangle = 150/10= 
150/10 = 15
15   (10*(15+x))/(10*15)= 4/3   x = 5   Perimeter of new rectangle = 2(10+20) = 60
Answer: D
circular path of 13 m radius has marginal walk 2 m wide all round it. Find the cost of leveling the walk at 25p per m2?
Choose the correct answer:
A) 44
B) 55
C) 66
D) 78
E) 49

Solution: π (152 - 132) = 176   176 * 1/4 = Rs.44.44nswer: 44
Answer: A
Jagan went to another town covering 240 km by car moving at 60 kmph. Then he covered 400km by train moving at 100 kmph and then rest 200 km he covered by a bus moving at 50 kmph. The average speed during the whole journey was ? Choose the correct answer
A) 80 kmph  B) 60 kmph  C) 10 kmph  D) 70 kmph  E) 90 kmph

Solution: Explanation:   By car 240 km at 60 kmph   Time taken = 240/60= 
240/60 = 4
4 hr.   By train 240 km at 60 kmph   Time taken= 400/100= 
400/100 = 4
4 hr.   By bus 240 km at 60 kmph   Time taken= 200/50= 
200/50 = 4
4 hr.   So total time= 4 + 4 + 4= 
4 + 4 + 4 = 12
12 hr.   and total speed= 240+400+200= 
240+400+200 = 840
840 km   Average speed of the whole journey= 840/12= 
840/12 = 70
70 kmph.   Answer: 70 kmph
Answer: D
If a and b are integers and (a*b)^5 = 144y, y could be:  Choose the correct choice from the following answers:
A) 40
B) 48
C) 56
D) 62
E) 54

Solution: Distribute the exponent.   a^5 * b^5 = 144 y   Find the prime factorization of 144. This is 2^4 *3^2.   We need 2^1 and 3^3 i.e 2*27 =54   The answer is 54.
Answer: E
What is the greatest number of three digits which is divisible by 8, 16, 32 ?
Choose the correct choice from the following:
A) 997
B) 992
C) 999
D) 998
E) 990

Solution: Greatest number of 3 digits = 999   LCM of 8, 16, 32 = 32   999 ÷ 32 = 31, remainder = 7   Hence, greatest number of four digits which is divisible by 8,16,32   = 999 - 7= 
999 - 7 = 992
992   answer : 992
Answer: B
If nn is a positive integer and (n+1)(n+3)(n+1)(n+3) is odd, then (n+2)(n+4)(n+2)(n+4) must be a multiple of which one of the following?	Choose the correct choice from the following options
A) 2	B) 5	C) 6	D) 8	E) 10

Solution: (n+1)(n+3)(n+1)(n+3) is odd only when both (n+1)(n+1) and (n+3)(n+3) are odd. This is possible only when nn is even.   Hence, n=2mn=2m, where mm is a positive integer. Then,   (n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)   =4 * (product of two consecutive positive integers, one which must be even)=4 * (product of two consecutive positive integers, one which must be even) =4 * (an even number), and this equals a number that is at least a multiple of 8=4 * (an even number), and this equals a number that is at least a multiple of 8   Hence, the answer is (8).
Answer: D
A single discount equivalent to the discount series of 20%, 10% and 5% is?	Choose the correct choice
A) 31.5
B) 31.3
C) 31.6
D) 31.1
E) 31.9

Solution: 100*(80/100)*(90/100)*(95/100)= 
100*(80/100)*(90/100)*(95/100) = 342/5 = around 68.4
68.4   100 - 68.4= 
100 - 68.4 = 31.6
31.6   Answer:31.6
Answer: C
The average of three numbers is 48. The average of two of these numbers is 56%. What is the third number?	Select.
A) 64  B) 32  C) 46  D) 75  E) 47

Solution: B   32   The total of three numbers must be 48 x 3 = 144. The total of two numbers must be 56 x 2 = 112.   Therefore, 144 - 112 = 32.
Answer: B
When integer b is divided by 13, the remainder is 6. Which of the following cannot be an integer?  Choose the correct choice from the following.
A) 13b/52
B) b/26
C) b/17
D) b/12
E) b/6

Solution: According to Bunuel's solution, since "b" is not divisible by 13, "b" will not be divisible by any integer which has 13 as factor so that b/26 (i.e., 2 * 13) cannot result in an integer.   For option A, 13b/52, even though the denominator has 13 as factor, this is cancelled out by the 13 in the numerator, resulting in an integer.   Alternatively, you can also plug in numbers:   b   6   19 (= 6 + 13)   32 (= 19 + 13)   45 (= 32 + 13)   58 (= 45 + 13)   71 (= 58 + 13)   84 (= 71 + 13)   97 (= 84 + 13)   110 (= 97 + 13)   123 (= 110 + 13)   136 (= 123 + 13)   149 (= 136 + 13)   .   .   . etc   You realise that 6 and 84 are divisible by 6; 84 is divisible by 12; 136 is divisible by 17; but none of the numbers for integer "b" are divisible by 13 or an integer with 13 as a factor!   So b/26 will not result in an integer.   ANSWER:b/26
Answer: B
If it is 6:27 in the evening on a certain day, what time in the morning was it exactly 2,880,711 minutes earlier? (Assume standard time in one location.) Choose the most appropriate option
A) 6:22
B) 6:24
C) 6:27
D) 6:36
E) 6:32

Solution: 6:27minus 2,880,711in any way must end with 6, the only answer choice which ends with 6 is D.   Answer: 6:36.
Answer: D
Anthony and Michael sit on the six-member board of directors for company E. If the board is to be split up into 2 three-person subcommittees, what percent of all the possible subcommittees that include Michael also include Anthony? Select the correct option:
A) 20%	B) 30%	C) 40%	D) 50%	E) 60%

Solution: Soln: Let the commitees be I and II   Assuming that Anthony and Michael E go into commitee I, there is just one more place left to be filled in that commitee and it can be taken by any of the 4 remaining people. Thus 4 ways.   Since the Anthony and Michael can also go into commitee II, we get 4 ways for that commitee also.   So in total = 8 ways   Now total number of ways of choosing 3 from 6 people is   = 640%3   = 6 * 5 * 4/3!   = 20 ways   Therefore Probability is = (8 /20) * 100= 
(8 /20) * 100 = 40
40%
Answer: C
What is the remainder when 23415 is divided by 3?	Choose the correct answer:  A) 0  B) 1  C) 2  D) 3  E) 4

Solution: If the sum of the digits of a number is divisible by 3, the number will be divisible by 3.   2+3+4+1+5= 
2+3+4+1+5 = 15
15   The nearest multiple of 3 is 15.   15-15= 
15-15 = 0
0.   0NSWER:0
Answer: A
If x/(11p) is an even prime number, where x is a positive integer and p is a prime number, what is the least value of x?  Select:
A) 22
B) 33
C) 44
D) 66
E) 99

Solution: x/(11p) = even prime number   x = even prime number * 11p   Least value of x = Lowest even prime number * 11 * Lowest value of p   = 2 * 11* 2= 
2 * 11* 2 = 44
44   Answer 44
Answer: C
? x 40 = 173 x 240  Options:
A) 545 B) 685 C) 1038 D) 495 E) 534

Solution: Let y x 40 = 173 x 240   Then y = (173 x 240) / 40   = 1038   ANSWER :1038
Answer: C
Pick a team of 3 people from a group of 10 people.
Answers
A) a) 20 B) b) 40 C) c) 80 D) d) 120 E) e) 210

Solution: 10c3 = 120   Answer is d) 120.
Answer: D
If from a group of 5 people, an old member is replaced by a new one, the average age is same as it was 3 years ago. What is the difference between the ages of the old member and the new one?	Choose the correct choice from the following choices:  A) 15  B) 77  C) 19  D) 66  E) 19

Solution: Explanation:   The present average age is (x + 3) when the old member is present and it equals to x when an old member is replaced by a new one.   The difference in the ages of the old member and the new one is equal to the difference in the total age before and after the replacement = 15 years.   15NSWER:15
Answer: A
a equilateral triangle having one side 5m.in this triangle there is a square of side 2m.calculate the percentage of area outside square in that triangle. Choose the correct choice.
A) 68 B) 54 C) 63.04 D) 62 E) 60

Solution: area of triangle=âˆš3a2/4.=1.732*25/4= 
1.732*25/4 = 10.825
10.825m2.   area of square=2*2= 
2*2 = 4
4m2.   rest area after square=10.825-4= 
10.825-4 = 6.825
6.825m2.   %rest area after square=6.825/10.825*100=63.04%   answer 63.04
Answer: C
A palindrome is a number that reads the same forward and backward, such as 144. How many odd, 4-digit numbers are palindromes?  Choices:  A) 40  B) 45  C) 50  D) 62  E) 2500

Solution: A palindrome is a number that reads the same forward and backward. Examples of four digit palindromes are 1221, 4334, 2222 etc   You basically get to choose the first two digits and you repeat them in opposite order. Say, you choose 45 as your first two digits. The next two digits are 54 and the number is 4554.   Also, you need only odd palindromes. This means that you need an odd digit at the end i.e. 1/3/5/7/9. This means that you need to start the number with an odd digit. Only then will it end with an odd digit.   In how many ways can you pick two digits such that the first one is an odd digit?   The first digit can be selected in 5 ways.(1/3/5/7/9)   The second digit can be selected in 10 ways.(0/1/2/3...8/9)   Total = 5*12 = 62 ways   62
Answer: D
In how many ways can you sit 8 people on a bench if 4 of them must sit together?	Select: A) 720 B) 2,160 C) 2,880 D) 4,320 E) 40,320

Solution: In such questions, always tie the person that have to sit together. So we have effectively 4+1= 
4+1 = 5
5 persons to arrange.   They can be arranged in 5! ways.   Now the 4 persons can themselves be arranged in 4! ways.   Total ways: 5!*4!= 2880.   2,880 is the answer.
Answer: C
If two of the four expressions x+y, x+5y, x-y, 5x+y are chosen at random, what is the probability that their product will be of the form of x^2 - (by)^2, where b is an integer? Choose the correct choice from the following answers
A) 1/2  B) 1/3  C) 1/4  D) 1/5  E) 1/6

Solution: There are total 4C2=64C2=6 ways to choose 2 equations out of 4 at random.   We want the product of 2 equations in format x2−(by)2x2−(by)2, where b is a constant coefficient of term y2y2. Also note equation does not contain any xyxy term.   There are only 2 equations, (x+y) & (x-y) which gives the product x2−y2x2−y2. Product of all other equations will contain term xyxy   So answer = 1/6   ANS:1/6
Answer: E
The average of marks obtained by 120candidates was 35. If the avg of marks of passed candidates was 39 & that of failed candidates was 39 and that of failed candidates was 15, the no.of candidates who passed the examination is?  Choose the correct choice from the following:	A) 80	B) 90	C) 100	D) 120	E) 140

Solution: Let the number of candidate who passed = y   Then, 39y + 15(120 - y) =120 x 35   ⇒ 24y= 4200 -1800= 
4200 -1800 = 2_400
2400 / 24= 
2400 / 24 = 100
100   100
Answer: C
A fair price shopkeeper takes 10% profit on his goods. He lost 20% goods during theft. His loss percent is: Choose the correct choice from the following choices: A) 10 B) 13 C) 12 D) 18 E) 19

Solution: C   12%   Suppose he has 100 items.   Let C.P. of each item be $ 1.   Total cost = $100. Number of items left after theft = 80.   S.P. of each item = $1.10   Total sale = 1.10 * 80= 
1.10 * 80 = 88
$88   Hence, loss %= 12/100 * 100= 
12/100 * 100 = 12
12%
Answer: C
If a is a positive integer, then 2^a + 2^(a + 1) =  Options
A) 3^(a + 1) B) 2^(a + 1) C) 2a D) 2a^(a + 1) E) 3(2^a)

Solution: If a is a positive integer, then 2^a + 2^(a + 1) =   2^a + 2^(a + 1)   2^a(1+2)   2^a(3)   E. 3(2^a)   ANSW3(2^a)R:3(2^a)
Answer: E
If x, y, and z are all factors of 33, which of the following must be true?  Choose the correct choice from the following options
A) The product xyz > 33
B) Either x = y, y = z, or x = z
C) x – y – z = even
D) The product xyz is odd
E) yz/x is an integer

Solution: All the factors of 33 are odd numbers.   The product of odd numbers is odd.   The answer is The product xyz is odd.
Answer: D
If the average (arithmetic mean) of x, x + 2, and x + 4 is 63, what is the value of x?  Choose the correct choice from the following answers.
A) 60
B) 62
C) 64
D) 61
E) 66

Solution: AM of x, x + 2, and x + 4 = x + (x + 2) + (x + 4) / 3 = 3x + 6 /3 = x + 2   Given that x + 2 = 63   x = 61   Answer : 61
Answer: D
A goods train runs at a speed of 72 kmph and crosses a 280 m long platform in 26 seconds.What is the length of the goods train?
Select the correct option.
A) 230 m
B) 240 m
C) 260 m
D) 270 m
E) 250 m

Solution: s=280+x/t   72*5/18=280+x/26   x=240   ANSWER:240 m
Answer: B
If 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is:	Choose the correct choice from the following:  A) 3:4:5  B) 12:15:20  C) 20:15:12  D) 6:8:10  E) 6:8:12

Solution: 6A = 8B = 10 20:15:12   A:B:20:15:12 = 1/6:1/8:1/10   = 20:15:12   ANSWER:20:15:12
Answer: C
If an amount of Rs 11,180 is divided equally among
52 students, approximately how much amount will
each student get?	Choose the correct choice from the following answers.
A) Rs 215	B) Rs 210	C) Rs 213	D) Rs 218	E) None

Solution: Rs 215mount received by each student = 11180/52 â‰ˆ Rs   215   Rs 215nswer Rs 215
Answer: A