MU-NLPC/Calc-aqua_rat huggingface dataset:
If x^2=x-2, then x^3=?
Pick one.
A) 3x+2
B) 3x-2
C) 2x+1
D) -x-2
E) 3x+4

Solution: Given X^2 = X-2   X^3 = X*X^2 = x*(X-2)-- Substituted from above.   = X^2 - 2X = X-2-2X = -X-2.   Hence -x-2.
Answer: D
If 8 people can eat a gallon of ice cream in 10 days, how long would it take 5 people to eat a gallon of ice cream?
Select the correct option
A) 12 days B) 14 days C) 16 days D) 18 days E) 20 days

Solution: 8 * 10 = 5 * x   x = 16   Answer: 16 days
Answer: C
If -2<= x <= 2 and 3 <= y <= 4, which of the following represents the range of all possible values of y-x?  Choices.
A) 1 <= y-x <= 6
B) 1 <= y-x <= 5
C) 1 <= y-x <= 6
D) 5 <= y-x <= 10
E) 1 <= y-x <= 10

Solution: Maximum value of y-x= 4 - (-2)= 
4 - (-2) = 6
6   Minimum value of y-x= 3-2= 
3-2 = 1
1   1 <= y-x <= 6 mentions the correct range
Answer: A
A chair is bought for Rs.600/- and sold at a loss of 50% find its selling price	Choose the correct choice:
A) s.300/-
B) s.550/-
C) s.560/-
D) s.590/-
E) s.580/-

Solution: 100 % ------> 600 (100 * 6 = 600)   50 % ------> 540 (50 * 6 = 300)   Selling price = Rs.300/-   s.300/-)
Answer: A
16 children are to be divided into two groups A and B of 10 and 6 children. The average percent marks obtained by the children of group A is 75 and the average percent marks of all the 16 children is 76. What is the average percent marks of children of group B ?
Choose the correct choice.
A) 233/3	B) 733/3	C) 533/3	D) 293/3	E) 433/3

Solution: Explanation:   Required average = [(76 * 16) - (75 * 10)] / 6 = (1216 - 750)/6 = 466/3 = 233 /3.   233/3nswer: 233/3
Answer: A
Three table runners have a combined area of 204 square inches. By overlapping the runners to cover 80% of a table of area 175 square inches, the area that is covered by exactly two layers of runner is 24 square inches. What is the area of the table that is covered with three layers of runner?	Answers:  A) 18 square inches  B) 20 square inches  C) 24 square inches  D) 28 square inches  E) 30 square inches

Solution: Total = a + b + c - (sum of EXACTLY 2-group overlaps) - 2*(all three) + Neither   80%*175 = 204 - 24 - 2*(all three) + 0   2*(all three) = 204 - 24 - 140   all three = 20   Answer: 20 square inches
Answer: B
What is the sum of all the prime numbers greater than 50 but less than 70?  Select the correct option
A) 249	B) 248	C) 246	D) 240	E) 241

Solution: Required sum = (53 + 59 + 61 + 67 )= 
(53 + 59 + 61 + 67 ) = 240
240   Note: 1 is not a prime number   Answer 240
Answer: D
How many positive three-digit integers are divisible by both 5 and 7? Select the correct option
A) 10	B) 15	C) 18	D) 20	E) 26

Solution: A number to be divisible by both 5 and 7 should be divisible by the least common multiple of 5 and 7 so by 35.   Multiples of 35 between 100 and 999, inclusive is   (last-first)/multiple+1=(980-105)/35+1=25+1= 
25+1 = 26
26   Answer: 26.
Answer: E
From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is?
Choose the most appropriate option
A) 1/26
B) 1/27
C) 1/24
D) 1/21
E) 1/22

Solution: Let E1 be the event of drawing a red card.   Let E2 be the event of drawing a king .   P(E1 ∩ E2) = P(E1) . P(E2)   (1/26s E1 and E2 are independent)   = 1/2 * 1/13 = 1/26   1/26nswer: 1/26
Answer: A
Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 36?Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 4? Choose the most appropriate option
A) 5x = y - 6 B) 75x^2 = 3y^2 - 12 C) 25x^2 = (y + 2)(y - 2) D) 5x = y - 2 E) x^2 = (y^2 - 4)/25

Solution: 1) Take the original equation and try to manipulate it so that it becomes 4 of the 5 answers   2) Take each answer choice and see if you can manipulate it to make it into the original equation.   With Answer D, we have...   5X = Y - 6   If we square both sides, we end up with....   (5X)^2 = (Y-6)^2   (5X)(5X) = (Y-6)(Y-6)   25X^2 = Y^2 - 12Y + 36   This is NOT a match for the original equation, so it's the answer that is NOT equivalent.5x = y - 6
Answer: A
If m is an integer such that (-2)^2m=2^(6-m) then m=? Choices:  A) 1  B) 2  C) 3  D) 5  E) 6

Solution: (-2)^(2m) = 4^m   and   2^(6-m) = 4^((6-m)/2)   Therefore,   m = (6-m)/2   2m = 6 - m   m = 2   Answer 2
Answer: B
The least number of complete years in which a sum of money put out at 20% C.I. will be more than doubled is?	Pick one
A) 7  B) 4  C) 5  D) 3  E) 1

Solution: Explanation:   P(1 + 20/100)n > 2P or (6/5)n > 2   Now, (6/5 * 6/5 * 6/5 * 6/5) > 2. So, n = 4 years.   Answer:4
Answer: B
What Is The Smallest Positive Integer That Leaves A Remainder Of 1 When Divided By 2, Remainder Of 2 When Divided By 3, A Remainder Of 3 When Divided By 4, And A Remainder Of 9 When Divided By 10? Choices:
A) 58	B) 59	C) 60	D) 61	E) 62

Solution: remainder of 1 when divided by 2: (2-1=1)   remainder of 2 when divided by 3: (3-2=1)   remainder of 3 when divided by 4: (4-3=1)   remainder of 9 when divided by 10: (2-1=1)   so N+1 should be divisible by 2,3,4,10   (where N is desired number)   L.C.M. of 2,3,4,10 = 60 (= N+1)   N = 59   ANSWER:59
Answer: B
Of the four numbers, whose average is 100, the first is one-fourth of the sum of the last three. The first number is ? Select the correct option:	A) 28	B) 29	C) 80	D) 48	E) 10

Solution: Explanation:   Let the first number be x,   Then, sum of the four numbers = x + 4x = 5x.   so, 5x/4 = 100 or x = (100 * 4) / 5= 
(100 * 4) / 5 = 80
80   Answer: 80
Answer: C
If the mobile is bought by rs 490 and sold by rs 465.50.find loss%.
Choose the correct choice from the following choices:	A) 3%	B) 2%	C) 7%	D) 5%	E) 9%

Solution: sol. cp=rs490,sp= 465.50.   loss=rs(490-465.50)=rs 24.50.   loss%=[(24.50/490)*100= 
(24.50/490)*100 = 5
5%   Ans:5%
Answer: D
Suppose 6 monkeys take 6 minutes to eat 6 bananas. How many monkeys would it take to eat 18 bananas in 18 minutes?	Choose the correct choice from the following
A) 9
B) 10
C) 11
D) 6
E) 13

Solution: One monkey takes 6 min to eat 1 banana , so in 18 mins 1 monkey will eat 3 bananas , so for 18 bananas in 18 min we need  18/3= 
 18/3 = 6
6 monkeys   ANSWER:6
Answer: D
A certain manufacturer produces items for which the production costs consist of annual fixed costs totaling $130,000 and variables costs averaging $5 per item. If the manufacturer’s selling price per item is $15, how many items the manufacturer produce and sell to earn an annual profit of $150,000? Choose the correct choice from the following.
A) 2,858
B) 18,667
C) 28,000
D) 35,000
E) 40,000

Solution: Let the items manufactured or sold bex   130000+5x = 15x-150000   10x = 280000   x = 28000   Ans:28,000
Answer: C
The length of a rectangular plot is thrice its width. If the area of the rectangular plot is 768 sq meters, then what is the width (in meters) of the rectangular plot?
Answers.
A) 24 m  B) 16 m  C) 35 m  D) 54 m  E) 43 m

Solution: Area = L*W = 3W^2 = 768   W^2 = 256   W = 16   The answer is 16 m.
Answer: B
A bag with 100 kgs potatoes have 99% water. It is kept in the open under the sunlight. After sometime, little amount of water got evaporated and reduced to 98%. What is the weight now ?
Choose the correct choice:
A) 40 kg
B) 50 kg
C) 60 kg
D) 70 kg
E) 80 kg

Solution: let the reduced weight be x kg   (100-99)% of 100 kg = (100-98)% of x kg   1% of 100 = 2% of x   x = (1*100)/2= 
(1*100)/2 = 50
50 kg   ANSWER:50 kg
Answer: B
A company can manufacture 1000 phones in a day. One-fifth of the phones produced are defective and one-quarter of all phones produced are rejected by quality control technician. If one-tenth of the nondefective phones are rejected by mistake, and if all the phones not rejected are sold, then what percent of the phones sold by the company are defective?	Choose the correct choice from the following answers.
A) 4%	B) 16%	C) 24%	D) 2%	E) 8%

Solution: We have 20% defective and 80% non-defective; we have 25% rejected and 75% not rejected. We also know that 1/10 of the non-defective ones (8%) are rejected, so 72% sold. This means that we have 3% sold that are defective and 17% rejected that are defective. Overall, we have 3%/75% or 1 of every 25 that are sold (not rejected) and defective. Correct 4%nswer is 4%
Answer: A
A train leaves Delhi at 9 a.m. at a speed of 30 kmph. Another train leaves at 2 p.m. at a speed of 40 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet? Select
A) 540 km
B) 760 km
C) 900 km
D) 600 km
E) 340 km

Solution: 600 km   600 km = 30 * 5= 
30 * 5 = 150
150   RS= 40 – 30 = 10   T = 150/10= 
150/10 = 15
15   600 km= 40 * 15= 
40 * 15 = 600
600 km
Answer: D
The unit digit in the product (784 x 618 x 917 x 463) is: Choose the correct choice from the following: A) 4 B) 2 C) 9 D) 1 E) 8

Solution: Unit digit in the given product = Unit digit in (4 x 8 x 7 x 3) = (672) = 2   Answer 2) 2.
Answer: B
A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
Choose the correct choice from the following options:
A) 1 kmph  B) 4 kmph  C) 5 kmph  D) 7 kmph  E) 8 kmph

Solution: DS = 6   US = 4   S = ?   S = (6 - 4)/2= 
(6 - 4)/2 = 1
1 kmph   1 kmphnswer: 1 kmph
Answer: A
x is a positive integer of T less than 500. When x is divided by 7, the remainder is 1; when x is divided by 3, the remainder is 2. How many x are there?	Choices:
A) 21  B) 22  C) 23  D) 24  E) 25

Solution: Took me more than 2 mins to solve.   That's how I did it.   x is between 1-499 included.   Smallest number that can be written as 7n+1 (7*0+1) is 1   Largest number that can be written as 7n+1 is (7*71 +1) is 498   So there are total 72 numbers that can be written as 7n+1   Because x can also be written as 3m+2, we have to see how many numbers that can be written as 7n+1 also can be written as 3m+2   7*0+1 can not be written in the form 3m+2   7*1+1 can be written in the form 3m+2   7*2+1 can not be written in the form 3m+2   7*3+1 can not be written in the form 3m+2   7*4+1 can be written in the form 3m+2   Here we see a sequence that one out of every 4 numbers can be written as 3m+1   72/4= 24 numbers can be written as 3m+1   24 is the answer
Answer: D
Arya starts cycling along the boundaries of the squares. She starts from a point A and after 90 minutes she reached to point C diagonally opposite to A. If she is travelling with 28km/hr, then find the area of square field.  Choose the correct choice
A) 125	B) 225	C) 325	D) 441	E) None of these

Solution: Explanation :   D = 28*3/2= 
28*3/2 = 42
42 km. So side of square is 21km, so area – 441km^2   Answer – 441
Answer: D
A number when divided by a divisor leaves a remainder of 24.
When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?	Choices:
A) 34
B) 37
C) 38
D) 39
E) 41

Solution: Let the original number be 'a'   Let the divisor be 'd'   Let the quotient of the division of aa by dd be 'x'   Therefore, we can write the relation as a/d = x and the remainder is 24.   i.e., a=dx+24 When twice the original number is divided by d, 2a is divided by d.   We know that a=dx+24. Therefore, 2a = 2dx + 48   The problem states that (2dx+48)/d leaves a remainder of 11.   2dx2dx is perfectly divisible by d and will therefore, not leave a remainder.   The remainder of 11 was obtained by dividing 48 by d.   When 48 is divided by 37, the remainder that one will obtain is 11.   Hence, the divisor is 37.   37
Answer: B
How many different pairs of positive integers (a, b) satisfy the equation 1/a+1/b=34/51 ?	Choices: A) 6 B) 3 C) 2 D) 1 E) 0

Solution: a+b/ab=2/3   3=1*3 or 3*1   a+b in both case= 4   correct 0   ANSW0R:0
Answer: E
A bus covered a distance of 250 km, partly at an average speed of 40 kmph and partly at 60 kmph. If the total time taken is 5.2 hours, then the distance covered at 40 kmph is  Answers: A) 130 km B) 120km C) 100km D) 124km E) none of these

Solution: Let the partial distance covered at 40 kmph be X   Let the another partial distance covered at 60 kmph be (250 - x)   Thus, x/40 - (250 - x)/60 = 5.2   or, x/40 + (250 - x)/60 = 5.2   or, (3x + 500 - 2x)//120 = 5.2   or 500 + x = 624   x=124   ANSWER:124km
Answer: D
A cuboidal block 6cm x 9cm x 12cm is cut up into an exact number of equal cubes.The least possible number of equal cubes will be	Answers:
A) 6
B) 9
C) 24
D) 30
E) 26

Solution: Volume of block=(6x9x12)= 648cm3   Side of largest cube = H.24.F of 6,9,12 = 3cm   Volume of the cube=(3x3x3)=27cm3   Number of cubes=(648/27)= 
(648/27) = 24
24 ANSWER : 24
Answer: C
In a class there are 19 boys and 10 girls. In how many ways can a boy and a girl be selected? Options:
A) 288  B) 500  C) 277  D) 190  E) 255

Solution: We can select one boy from 19 boys in 19 ways.   We select one girl from 10 girls in 10 ways   We select a boy and girl in 19 * 10 ways i.e.,   = 190 ways.   Answer: 190
Answer: D
A sum of money triples itself in twelve years at simple interest. Find the rate of interest?  Choose the correct choice from the following choices:
A) 16 2/6 %	B) 16 6/3 %	C) 19 2/3 %	D) 16 3/3 %	E) 16 2/3 %

Solution: Let the pricipal be Rs. x, then amount = 3x(where R = rate of interest) => Interest = 3x - x = Rs. 2x   R = (100 * 2x)/(x * 12) = 50/3 % = 16 2/3 %   Answer: 16 2/3 %
Answer: E
What will Rs.1500 amount to in three years if it is invested in 20% p.a. compound interest, interest being compounded annually? Pick one:
A) 2400
B) 2592
C) 2678
D) 2540
E) 2440

Solution: Here P=1500, R=20% n=3 Find A   Substituting in the compound int. formula   A=P(1+R/100)^3, we get A=Rs.2,592   ANSWER:2592
Answer: B
Find the average of all prime numbers between 10 and 30.  Choose the correct choice:
A) 30
B) 33.6
C) 39.8
D) 18.6
E) None

Solution: Sol.   There are six prime numbers between 10 and 30.   They are 11, 13, 17, 19, 23, 29   âˆ´ Required average = [11+ 13+ 17+19+ 23+ 29 / 6] = 112/ 6 = 18.6   Answer 18.6
Answer: D
3 buffaloes eat as much as 4 cows or 2 oxen. At a farm, there are 15 buffaloes, 8 oxen, and 24 cows. The fodder for these cattle is available for 24 days. If 40 more cows and 15 more buffaloes are brought in, how many days will the fodder last?  Choices:	A) 10	B) 12	C) 15	D) 18	E) 21

Solution: 2 oxen = 3 buffaloes = 4 cows   Also: 15 buffaloes + 8 oxen + 24 cows   = 10 oxen + 8 oxen + 12 oxen = 30 oxen   There is enough fodder for 1 oxen for 30*24 days.   40 cows + 15 buffaloes = 20 oxen + 10 oxen = 30 oxen   The new total is equal to 60 oxen instead of 30 oxen.   30*24 / 60= 
30*24 / 60 = 12
12 days   The answer is 12.
Answer: B
If x is an integer, and 100 < x^2 <= 361, which of the following is the sum of all possible values of x?
Choose the correct choice from the following choices
A) 135  B) 124  C) 116  D) 105  E) None of the above

Solution: The range of x is from 9 .. to 19 and -9 to -19 so the sum is 0 hence ans None of the above, I guess, unless I am missing something!
Answer: E
Simplify: 0.72*0.43+0.12*0.34 Choose one
A) 0.3504 B) 0.4209 C) 0.4889 D) 0.6412 E) 0.4612

Solution: Given exp. = 0.72*0.43+(0.12*0.34) = 0.3096+0.0408= 
0.3096+0.0408 = 0.3504
0.3504   0.3504nswer is 0.3504
Answer: A
A can do a job in 18 days and B can do it in 30 days. A and B working together will finish thrice the amount of work in ------- days?	Choose the correct choice from the following answers:
A) 21 ½ days	B) 22 ½ days	C) 33 3/4 days	D) 12 ½ days	E) None of these

Solution: Explanation:   1/18 + 1/30 = 8/90 = 4/45   45/4 = 45/4 *3 = 33 3/4 days   Answer: 33 3/4 days
Answer: C
54, 61, 57, 9, 55, 4, 9.
Which of the following numbers is lower than the median but greater than the mean of the set of the numbers in the list?	Pick.
A) 19
B) 30
C) 47
D) 54
E) 56

Solution: Yes, it can be solved with observation even without approximation in 30 sec.   Just observe given numbers: 4,9, 9, 54, 55, 57,61,   Median is very easy to tell - its 55. Now we want a number lower than 54 and greater than mean. How many numbers are lower than 54? DE are already out.   Now, we have 19, 30 and 47 and we want a number among these which is greater than mean. logically whatever be the mean, if one value out of these 5 has to be greater than mean it has to be 47. (Notice, if 19 is more than mean then 47 is also. If 30 is more than mean, 47 is also. )   Hence 47 it is!
Answer: C
The ratio of the radius of two circles is 1: 3, and then the ratio of their areas is?  Choose the correct choice from the following choices:
A) 1: 8
B) 1: 1
C) 1: 9
D) 1: 4
E) 1: 3

Solution: r1: r2 = 1: 3   Πr12: Πr22   r12: r22 = 1: 9   Answer:1: 9
Answer: C
In one hour, a boat goes 21 km/hr along the stream and 11 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
Choose the correct choice from the following
A) 12 kmph	B) 13 kmph	C) 14 kmph	D) 15 kmph	E) 16 kmph

Solution: Explanation:   Let the speed downstream be a km/hr and the speed upstream be b km/hr, then   Speed in still water =1/2(a+b) km/hr   Rate of stream = 1/2(a−b) km/hr   Speed in still water = 1/2(21+11) kmph = 16 kmph.   Answer: Option 16 kmph
Answer: E
The length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field?
Select:
A) 32 m
B) 31 m
C) 30 m
D) 35 m
E) 38 m

Solution: 32 m/8 = 8 * 8 => 32 m = 8 * 8 * 8   x * 2x = 8 * 8 * 8   x = 16 => 2x = 32   32 mNSWER 32 m
Answer: A
1/2, 1/4, ....
In the sequence above each term after after the first one-half the previous term. If x is the tenth term of the sequence, then x satisfies which of the following inequalities?	Choose the most appropriate option:
A) 0.1 < x < 1
B) 0.01 < x < 0.1
C) 0.001 < x < 0.01
D) 0.0001 < x < 0.001
E) 0.00001 < x < 0.0001

Solution: In the Sequence notice that the sequence is just the 1/(2^n) ...   so for 1st term=1/2^1=1/2   2nd term=1/(2^2)1/4, 3rd term=1/(2^3)=1/8 and so on...   Thus the 10th term will be 1/(2^10)=1/1024   Roughly, 1/1024 can be   1/1000= 
  1/1000 = 1/1_000 = around 0.001
0.001 but since denominator is a bit more than 1000 therefore the actual value will be a bit less than 0.001.   thus the ans will lie btw. 0.1 and 1.(0.1 < x < 1)
Answer: A
If d is a positive integer greater than 1, what is the sum of the multiples of d from d to d^2, inclusive?	Choose the correct option
A) d(d + 1)(d-1)
B) d^2(d + 1)/2
C) d^2(d-1)
D) (x^3 + 2x)/2
E) x(x-1)^2

Solution: Ans :- B=d^2(d + 1)/2   I substituted 3 in all answer choices.   Option B and C were both satisfying the condition.   So i substituted 4 instead of 3 in all answer choices,   Only d^2(d + 1)/2 option satisfied.
Answer: B
At a certain zoo, the ratio of sea lions to penguins is 4 to 11. If there are 84 more penguins than sea lions at the zoo, how many sea lions are there? Choose the correct answer
A) 24  B) 36  C) 48  D) 72  E) 132

Solution: The ratio as mentioned = 4/11   also   sea lion + 84 = penguins   or,   4x+84=11x   x=84/7= 
84/7 = 12
12   number of sea lions= 12*4= 
12*4 = 48
48   ANSWER:48
Answer: C
Jane makes toy bears. When she works with an assistant, she makes 80 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent W? Choose the correct choice from the following options:
A) 20% B) 80% C) 100% D) 180% E) 200%

Solution: C.   Let's assume just Jane 40 bears per 40/hrs a week, so that is 1 bear/hr. With an assistant she makes 72 bears per 36 hours a week or 2 bears/hr ([40 bears * 1.8] / [40 hrs * .90]).   W=[(2 - 1)/1] * 100% = 100%(2 - 1)/1  * 100= 
(2 - 1)/1  * 100 = 100
100%
Answer: C
if length of rectangle is increased by 10%, and breadth is decreased by 10%.what will it effect on area of rectangle?
Choose the correct option:
A) it will have no effect B) 1% increase C) 1% decrease D) 2% increase E) 2% decrease

Solution: let initial length=l,and breadth=b   area=l*b   new length=l*110%=[l*110/100]=11l/10,new breadth=9b/10   new area=11l/10*9b/10=99/100lb   decrease in area=[lb-99/100lb]=lb/100=% decrease=[lb/100*1/lb*100]=1%   answer 1% decrease
Answer: C
if p/q=3/4
then3p+6q=? Select:
A) 25/4
B) 25/2
C) 20/4
D) 33/4
E) 25/3

Solution: 3p+6q=?   33/4ivided by q,   3(p/q)+6=x   3*(3/4)+6=33/4   ANSWER:33/4
Answer: D
If 9x-3y=12 and 3x-5y=7 then 6x-2y = ? Choose the correct answer: A) 9 B) 8 C) 7 D) 5 E) 3

Solution: Consider 9x - 3y = 12.........divide both sides by 3: 3x - y = 4............now multiply both sides by 2: 6x - 2y   = 8   Answer:8
Answer: B
Anand and Deepak started a business investing Rs. 6,000 and Rs. 8,000 respectively. Out of a total profit of Rs.4,600. Deepak's share is?  Select the correct option: A) s. 2600.31 B) s. 2628.57 C) s. 2450.32 D) s. 3400.41 E) s. 2400.32

Solution: Ratio of their shares = 6000 : 8000 = 3 : 4   Deepak's share = Rs. (4600 * 4/7) = Rs. 2628.57 ANSWER "s. 2628.57
Answer: B
The prime sum of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example , the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 +2 + 3 = 7. For which of the following integers is the prime sum greater than 34 ? Choose the correct choice from the following answers.
A) 440
B) 512
C) 550
D) 620
E) 750

Solution: Large numbers are made in two ways:   Either by taking small prime numbers and raising them to higher powers or taking large prime numbers in the first place.   31*2= 
31*2 = 62
62 (large prime number)   2^6= 64 (many small prime numbers)   To get a sum as large as 34 or more, you would need some large prime numbers. So options such as 512, 700 and 750 which have small prime numbers as factors should be ignored first. 440 also splits into 11, 4( which is 2*2), 2, 5 - relatively small prime numbers.   You are left with 620 which is 31*2*2*5 (sum greater than 34)   Answer (620)
Answer: D
A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? Choose one
A) 1.2 B) 1.9 C) 1.7 D) 1.5 E) 1.1

Solution: M = 4.5   S = x   1.5S = 4.5 + x   US = 4.5 + x   4.5 + x = (4.5 - x)2   4.5 + x = 9 -2x   3x = 4.5   x = 1.5   Answer: 1.5
Answer: D
The factorial expression 13!/2! is not divisible by which of the following integers?  Pick.
A) 3
B) 5
C) 6
D) 7
E) none of these

Solution: 13!/2! => 13 x 12 x 11 x 10 x 9 x8x7x6x5x4x3   (A) 3 Can divide 12 or 9   (B) 5 Can divide 10   (C) 6 Can divide 12   (D) 7 can divide 7, 21,42   Hence answer will be (none of these)
Answer: E
For how many different pairs of positive integers (a, b) can the fraction 2/15 be written as the sum 1/a + 1/b ? Pick one:
A) 4
B) 5
C) 8
D) 9
E) 10

Solution: (1/a)+(1/b)=215   I. 1/a+1/b=1/15+1/15(a,b)=(15,15)   II. 1/a+1/b=2∗2/15∗2=1/30+3/30(a,b)=10,30)and(30,10)   III.1/a+1/b=2∗3/15∗3=1/45+5/45(a,b)=(45,9)and(9,45)   IV.1/a+1/b=2∗4/15∗4=3/60+5/60(a,b)=(20,12)and(12,20)   Now, we know that the no of different pairs can only be of the form 2k+1. We already have 7 such combinations. Thus, the only value which will satisfy from the given options is 9.   Answer : 9
Answer: D
A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
Choose the most appropriate option:
A) 18 sec	B) 16 sec	C) 19 sec	D) 11 sec	E) 12 sec

Solution: :   Speed = 63 * 5/18 = 35/2 m/sec   Time taken = 280 * 2/35= 
280 * 2/35 = 16
16 sec   Answer: 16 sec
Answer: B
The maximum number of students among them 1340 pens and 1280 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils?	Pick one.
A) 25
B) 30
C) 20
D) 45
E) 90

Solution: number of pens = 1340   number of pencils = 1280   Required number of students = H.C.F. of 1340 and 1280 = 20   Answer is 20
Answer: C
How many gallons of milk that is 10 percent butter-fat must be added to 8 gallons of milk that is 35 percent butterfat to obtain milk that is 20 percent butterfat?	Choose the correct choice.
A) 6 B) 12 C) 14 D) 16 E) 28

Solution: Equate the fat:   0.1x + 0.35*8 = 0.2(x + 8) --> x = 12.   Answer: 12.
Answer: B
The positive integer f is divisible by 10. What is the remainder of dividing f(2+4)(1+f) by 5? Choices:	A) 0	B) 1	C) 2	D) 3	E) 4

Solution: When we multiply any of these options: 10*6*11 (f=10) or 20*6*21 (f=20) we end up with numbers ending in 0 which are exactly divisible by 5 leaving no remainder. Hence answer is 0.
Answer: A