MU-NLPC/Calc-aqua_rat huggingface dataset:
In a box of 16 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?	Select:  A) 1/6  B) 2/9  C) 6/20  D) 13/20  E) 3/4

Solution: Method- 1   There are 9 fine pieces of pen and 3 defective in a lot of 16 pens   i.e. Probability of first pen NOT being defective = (13/16)   i.e. Probability of Second pen NOT being defective = (12/15) [15 pen remaining with 12 defective remaining considering that first was defective]   Probability of Both pen being NON-defective = (12/15)*(13/16) = 13/20   Answer: option 13/20
Answer: D
Find the average of first 4 multiples of 5?	Choose one
A) 10  B) 15  C) 12.5  D) 13  E) 21

Solution: average = (5+10+15+20)/4= 
(5+10+15+20)/4 = 25/2 = around 12.5
12.5   Answer is 12.5
Answer: C
If 36/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) I, II, and III C) I and II only D) I only E) III only

Solution: The largest possible value of x is 36 (the greatest common factor of 36 and 108), and if x=36 then   III only
Answer: E
The ratio of the length and the width of a rectangle is 4 : 3 and the area of the rectangle is 4332 sq cm. What is the ratio of the width and the area of the rectangle?
Choose the correct choice from the following answers.
A) 1:72  B) 1:76  C) 1:80  D) 1:84  E) 1:88

Solution: Let the length and the width be 4x and 3x respectively.   Area = (4x)(3x) = 4332   12x^2 = 4332   x^2 = 361   x = 19   The ratio of the width and the area is 3x : 12x^2 = 1 : 4x = 1 : 76   The answer is 1:76.
Answer: B
What is the sum of all remainders obtained when the first 110 natural numbers are divided by 9?	Choices:
A) 397 B) 401 C) 403 D) 405 E) 399

Solution: A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, 8, and 0.   1 divided by 9 gives the remainder of 1;   2 divided by 9 gives the remainder of 2;   ...   8 divided by 9 gives the remainder of 8;   9 divided by 9 gives the remainder of 0.   We'll have 11 such blocks, since  99/9= 
 99/9 = 11
11. The last will be:   91 divided by 9 gives the remainder of 1;   92 divided by 9 gives the remainder of 2;   ...   98 divided by 9 gives the remainder of 8;   99 divided by 9 gives the remainder of 0.   The last number, 100, gives the remainder of 1 when divided by 9, thus the sum of all remainders will be:   11(1+2+3+4+5+6+7+8+0)+1=403.   Answer: 403.
Answer: C
A is twice as good a workman as B and they took 7 days together to do the work B alone can do it in.  Pick one:	A) 17 days	B) 21 days	C) 29 days	D) 25 days	E) 27 days

Solution: WC = 2:1   2x + x = 1/7   x = 1/21 => 21 days   ANSWER:21 days
Answer: B
At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/10 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten? Choose the correct choice from the following choices: A) 20 greater B) 17 fewer C) 28 fewer D) 36 fewer E) 44 fewer

Solution: Soln>> from the given ratio of 16:1 u can derive that ter are 480 students   KG= 1/10 * 480= 
1/10 * 480 = 48
48   5th and 6th graders= 1/3 * 384= 
1/3 * 384 = 128
128 (1/3 of remainder)   1st and 2nd grade= 1/4 * 480= 
1/4 * 480 = 120
120 ( 1/4 of all students)   equal number of students in 3rd and 4th=> 480 - 344= 
480 - 344 = 136
136 and   136/2= 
  136/2 = 68
68 each since equal number   (344 is the sum of remaining students)   thus 48-68=20>>> therfore answer is 20 greater   20 greater
Answer: A
A train 455 m long, running with a speed of 63 km/hr will pass a tree in? Choose the correct choice from the following options
A) 22 sec  B) 16 sec  C) 17 sec  D) 39 sec  E) 12 sec

Solution: Speed = 63 * 5/18 = 35/2 m/sec   Time taken = 455 * 2/35 = 39 sec   Answer:39 sec
Answer: D
The ratio of the radius of two circles is 4: 3, and then the ratio of their areas is?	Choices:
A) 1: 8  B) 1: 6  C) 1: 9  D) 16: 9  E) 1: 2

Solution: r1: r2 = 4: 3   Πr12: Πr22   r12: r22 = 16: 9   Answer:16: 9
Answer: D
{1,2,3,4,5,5,6,6}how many four digited numbers can be formed without repiting the numbers?  Choose the correct choice from the following choices.
A) 180
B) 360
C) 460
D) 500
E) 520

Solution: n*(n-1)*(n-2)...   hence four digits with out repetition total 6 digits=n   6*5*4*3= 
6*5*4*3 = 360
360   ANSWER:360
Answer: B
If k > 0, which of the following could be true?
I. k^3 > k^2
II. k^2 = k
III. k^2 > k^3 Select:
A) I only
B) III
C) IIIII
D) All of the above
E) None of the above

Solution: 1. k^3 > k^2 Well this is true for all k > +1 (but not for values 0 < k < 1)   2. k^2 = k This is true for only one positive number, 1   3. k^2 > k^3 Again this is true only for values of k such that 0 < k < 1   So the answer is All of the above, since there exists at least one value of k which satisfies the equation/ in equation(s)
Answer: D
A box has exactly 100 balls, and each ball is either red, blue, or white. If the box has 12 more blue balls than white balls, and twice as many red balls as blue balls, how many white balls does The box has ? Choose the correct choice from the following answers
A) 8 B) 10 C) 12 D) 14 E) 16

Solution: x = the number of red balls   y = the number of blue balls   z = the number of white balls   From the first sentence we have   Equation #1: x + y + z = 100   ...the box has 12 more blue balls than white balls...   Equation #2: y = 12 + z   ...thrice as many red balls as blue balls...   Equation #3: x = 2y   Solve equation #2 for z: z = y - 12   Now, we can replace both x and z with y in Equation #1   2y + y + (y - 12) = 100   4y - 12 = 100   4y = 112   y = 28   There are 28 blue balls. This is 15 more than the number of white balls, so z = 16. That's the answer. Just as a check, x = 56, and   56 + 28 + 16= 
  56 + 28 + 16 = 100
100.   Answer= 16,(16)
Answer: E
Three competing juice makers conducted a blind taste test with mall shoppers. The shoppers could choose to taste any number of the three brands of juices but had to select at least one juice that they liked. If 100 shoppers liked brand J, 200 shoppers liked brand K, 700 shoppers liked brand L, 300 shoppers liked exactly 2 juices, and 100 shoppers liked all three juices, how many shoppers took the taste test?  Choose the most appropriate option:  A) 1,300  B) 1,000  C) 900  D) 700  E) 500

Solution: Given: Atleast 1 juice was liked by the participants. --> Neither = 0   Assume, I -->No overlap between the sets   II --> Overlap between 2 sets   III --> Overlap between 3 sets   I + 2*(II) + 3*(III) = 100 + 200 + 700   I + 2*(300) + 3*(100) = 1000   I = 100   Total number of shoppers who took the taste test = I + II + III = 100 + 300 + 100= 
100 + 300 + 100 = 500
500   Answer: 500
Answer: E
If m is an integer greater than 6, which of the following must be divisible by 3?  Choose the correct choice from the following answers
A) m (m+2) (m-1)	B) m (m+1) (m-4)	C) m (m+3) (m-5)	D) m (m+4) (m-2)	E) m (m+5) (m-6)

Solution: anything in the form of (m-1) (m) (m+1) is divisible by 3. in other word, a product of any 3 consecutive intevers is divisible by 3.   m (m+1) (m-4) = m (m+1) ((m-1)-3) is equivalant to (m-1) (m) (m+1)   m (m+2) (m-1) is equivalant to (m+1) missing.   m (m+3) (m-5) is equivalant to (m-1) missing and m repeating.   m (m+4) (m-2) is equivalant to odd/even consqcutive integers   m (m+5) (m-6) is equivalant to (m+1) missing and m repeating.   Answer : m (m+1) (m-4)
Answer: B
A man can swim in still water at 6 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
Choose the correct choice from the following answers:	A) 3	B) 7.5	C) 2.25	D) 2	E) 4

Solution: M = 6   S = x   2S = 6 + x   US = 6 - x   6 + x = (6 - x)2   6 + x = 12 -2x   3x = 6   x = 2   ANSWER:2
Answer: D
Mr. Kutty has only hens and sheep. If the total number of their heads is 38 and the total number of legs is 100 then what is the ratio between the numbers of hens and sheep?	Answers:
A) 2 : 1  B) 1 : 2  C) 6 : 13  D) 13 : 6  E) None of these

Solution: Let the total number of hens and sheep be x and y respectively.   i.e., x + y = 38 and 2x + 4y = 100   ∴ Ratio = 13 : 6   Answer 13 : 6
Answer: D
If |4x+6| = 50, what is the sum of all the possible values of x?	Choose one:
A) 2
B) -2
C) 4
D) -3
E) 6

Solution: There will be two cases   4x+6= 50 or 4x+6 = -50   => x =11 or x= -14   sum of both the values will be -14 +11 = -3   Answer is -3
Answer: D
A total of $20,000 was invested in two certificates of deposit at simple annual interest rates of 6 percent and 8 percent, respectively. If the total interest on the two certificates was $1,440 at the end of one year, what fractional part of the $20.000 was invested at the higher rate?	Choose the most appropriate option:
A) 3/8	B) 2/5	C) 1/2	D) 3/5	E) 3/4

Solution: Let "$x" be invested with the higher rate of 8%   Thus, "20000-x" must have been invested with lower rate of 6%   Simple Interest = Principal* Rate* Time   For the Amount invested at 8%   Principal = x   Rate = 0.08   Time = 1   Simple Interest = x* 0.08* 1= 0.08x   For the Amount invested at 6%   Principal = 20000-x   Rate = 0.06   Time = 1   Simple Interest = (20000-x)* 0.06* 1= 1200-0.06x   Total Interest = $1440   0.08x+1200-0.06x=1440   0.02x=240   x = 240/0.02= 
240/0.02 = 12_000
12000   Fraction of x per total amount= 12000/20000 = 12/20 = 3/5   Ans: "3/5"
Answer: D
If ab = 3(a + 1) + b and a and b are integers, a could be any of the following values EXCEPT:  Select:	A) 2	B) 3	C) 6	D) 4	E) 7

Solution: ab = 3(a + 1) + b   ab - b = 3(a + 1)   b = 3(a + 1)/(a-1)   b won't be an integer only if a = 6 (from the options).   Answer: 6
Answer: C
If logX/(a2 + ab + b2) = log Y/(b2 + bc + c2) = logZ/(c2 + ca + a2), then Xa - b.Yb - c. Zc - a =? Choose the correct option:  A) 0  B) -1  C) 1  D) 2  E) 3

Solution: Each ratio = k = log X = k(a2 + ab + b2)   => (a - b)logX = k(a3 - b3)   Similarly, Yb - c = ek(b3 - c3), Zc - a= ek(c3 - a3)   Therefore, Xa - b.Yb - c.Zc - a = e0 = 1.   ANSWER:1
Answer: C
If a, b, c are integers and ab>0, bc >0, ac<0, then which of the following is false?
I.	a=0, b>0, c>0
II.	a>0, b=0, c>0
III.	a>0, b>0, c=0 Choices:
A) I only B) II only C) III only D) I, II and III E) None of the above

Solution: We could solve this easily.   I is false. If a=0 then ab=0, ac=0. But since ac<0, it is false.   II is false. If b=0 then ab=0, bc=0. But since bc>0, it is false.   III is false. If c=0 then ac=0, bc=0. But since ac<0, it is false.   So, the answer is I, II and III
Answer: D
when n divided by 3, the remainder is 2.
when n divided by 4, the remainder is 1
what is the the remainder when divided by 15	Choose the correct choice.
A) 1  B) 3  C) 4  D) 5  E) 2

Solution: case1   N=5,8,11,14,17,20   case 2   M=5,9,13,17,21   Therefore n=17   Remainder of 17/15 will be 2   2
Answer: E
A man cycling along the road noticed that every 3 minutes a bus overtakes him and every 9 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?
Choices: A) 5 minutes B) 6 minutes C) 8 minutes D) 9/2 minutes E) 10 minutes

Solution: Let's say the distance between the buses is d. We want to determine Interval=\frac{d}{b}, where b is the speed of bus.   Let the speed of cyclist be c.   Every 9 minutes a bus overtakes cyclist: \frac{d}{b-c}=9, d=9b-9c;   Every 3 minutes cyclist meets an oncoming bus: \frac{d}{b+c}=3, d=3b+3c;   d=9b-9c=3b+3c, --> b=2c, --> d=9b-9b/2=9b/2.   Interval=\frac{d}{b}=\frac{9/2b}{b}=9/2   Answer: 9/2 minutes (9/2 minutes).
Answer: D
A, B and C have Rs.400 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?
Choose the correct choice from the following answers:
A) Rs.250  B) Rs.90  C) Rs.50  D) Rs.150  E) Rs.70

Solution: A+B+C = 400   A+C = 200   B+C = 350   --------------   A+B+2C = 550   A+B+C = 400   ----------------   C = 150   ANSWER:Rs.150
Answer: D
How many quarters are equal to 5 dollars?
Options
A) 1
B) 8
C) 12
D) 20
E) 7

Solution: 5*4= 
5*4 = 20
20 quarters   Answer : 20
Answer: D
Carmen made a sculpture from small pieces of wood. The sculpture is 2 feet 10 inches tall.Carmen places her sculpture on a base that is 6 inches tall. How tall are the sculpture andbase together?	Choose one.
A) 3.1 feet  B) 3.2 feet  C) 3.3 feet  D) 3.4 feet  E) 3.5 feet

Solution: we know 1 feet =12 inch then   2 feet =24 inch     24+10= 
  24+10 = 34
34 then     34+6= 
  34+6 = 40
40   40/12=3.3 feet   ANSWER:3.3 feet
Answer: C
The number 90 can be written as the sum of the squares of 4 different positive integers. What is the sum of these 4 integers?
Choose the correct choice from the following options.
A) 17  B) 16  C) 15  D) 14  E) 13

Solution: 4^2 + 3^2 + 8^2 + 1^2 = 90 --> 1 + 3 + 8 + 4 = 16.   16
Answer: B
In a simultaneous throw of two dice , what is the probability of getting to total of 10 or 11?
Choose the correct choice from the following answers
A) 5/36	B) 5/7	C) 7/4	D) 9/8	E) 36/5

Solution: n(S)36   n(E)=5   P(E)=5/36   5/36ns: 5/36
Answer: A
Can you deduce the pattern and find the next number in the series?
1, 8, 27, 64, 125, ?  Pick one:
A) 276  B) 208  C) 278  D) 279  E) 216

Solution: Solution:   216   216xplanation:   1=1*1*1   8=2*2*2   27=3*3*3   64=4*4*4   125=5*5*5   Thus the next number will be    6*6*6= 
 6*6*6 = 216
216   Answer 216
Answer: E
Two trains are traveling on parallel tracks in the same direction. The faster train travels at 130 miles per hour, while the slower train travels at 100 miles per hour. At 2 o’clock the faster train is 30 miles behind the slower one. How far apart are the two trains at 5 o'clock? Choices
A) 60 miles	B) 80 miles	C) 90 miles	D) 120 miles	E) 400 miles

Solution: Answer = A. 60 miles   Relational speed = 130 - 100= 
130 - 100 = 30
30 miles per hour   In 3 hours, difference= 30 * 3= 
30 * 3 = 90
90 miles   Fast train trailing 30 miles, so effective difference= 90 - 30= 
90 - 30 = 60
60 miles
Answer: A
How long does a train 100 m long travelling at 60 kmph takes to cross a bridge of 120 m in length?	Choose the correct answer
A) 15.8 sec  B) 13.2 sec  C) 12.4 sec  D) 16.8 sec  E) 11.8 sec

Solution: 13.2 sec   13.2 sec   D = 100 + 120= 
100 + 120 = 220
220 m   S= 60 * 5/18 = 50/3   T = 220 * 3/50= 
220 * 3/50 = 66/5 = around 13.2
13.2 sec   Answer is 13.2 sec
Answer: B
A coin is weighted so that the probability of heads on any flip is 0.1, while the probability of tails is 0.9. If the coin is flipped 5 times independently, which of the following represents the probability that tails will appear no more than twice?	Select:
A) (0.1)^5 + 5(0.1)^4(0.9) + 10(0.1)^3(0.9)^2
B) (0.1)^5 + 4(0.1)^4(0.9) + 6(0.1)^3(0.9)^2
C) (0.6)^5 + 3(0.6)^4(0.4) + 2(0.6)^3(0.4)^2
D) (0.6)^5 + 2(0.6)^4(0.4) + (0.6)^3(0.4)^2
E) (0.6)^5 + (0.6)^4(0.4) + (0.6)^3(0.4)^2

Solution: Probability of Head, P(H) = 0.1   Probability of Tail, P(T) = 0.9   Tail will appear NO more than twice   i.e. favourable cases   2 Tails and 3 Heads, Probability = 5C2*(0.1)^3*(0.9)^2   1 Tail and 4 Heads, Probability = 5C1*(0.1)^4*(0.9)^2   0 Tail and 5 Heads, Probability = (0.1)^5   Required Probability = Sum of all Favourable cases = (0.1)^5 + 5(0.1)^4(0.9) + 10(0.1)^3(0.9)^2   (0.1)^5 + 5(0.1)^4(0.9) + 10(0.1)^3(0.9)^2nswer: option (0.1)^5 + 5(0.1)^4(0.9) + 10(0.1)^3(0.9)^2
Answer: A
What is the positive difference between the sum of the squares of the first 8 positive integers and the sum of the prime numbers between the first square and fourth square?  Answers.
A) 161 B) 162 C) 163 D) 164 E) 165

Solution: Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.   the sum of the squares of the first 4 positive integers = 1^2 + 2^2 + 3^2 +...+8^2= 204   the sum of the prime numbers between the first square(=1) and fourth square(=16) = 2+3+5+7+11+13= 
2+3+5+7+11+13 = 41
41.   So the difference between 41 and 204 is 163.   So the answer is (163).
Answer: C
If (c - a)/(c - b) = 1, then (5b + 5a)/(c - a) = Choose the most appropriate option
A) 10  B) 1  C) 1.5  D) 2  E) 2.5

Solution: Let's say c=2, b=1, a=1 so that our 1st expression holds true. Now, ibsert those numbers in the second expression and we'll get10   10nswer 10 (hopefully )))
Answer: A
A man's speed with the current is 15 km/hr and the speed of the current is 2.8 km/hr. The man's speed against the current is?  Choose the correct choice from the following answers
A) 9.4  B) 20  C) 50  D) 30  E) 40

Solution: Man's speed with the current = 15 km/hr   => speed of the man + speed of the current = 15 km/hr   speed of the current is 2.8 km/hr   Hence, speed of the man = 15 - 2.8= 
15 - 2.8 = 12.2
12.2 km/hr   man's speed against the current= speed of the man - speed of the current   = 12.2 - 2.8= 
12.2 - 2.8 = 9.4
9.4 km/hr   9.4nswer is 9.4.
Answer: A
Akash's club with a total membership of 30 has formed 3 committees, M, S and R which have 8,12, and 5 members respectively. If no member of committee M is on either of the other 2 committees, what is the greatest possible number of members in the club who are on none of the committees. Choose the correct choice from the following choices
A) 5 B) 7 C) 8 D) 10 E) 12

Solution: Akash's club with a total membership of 30 has formed 3 committees Given no member of committee M is on either of the other 2 committees -- hence (M n R) and (M n S) and (M n R n S) is zero.   Hence only M is 8. Now we need to consider only S, (S n R) and R.   (M U R U S) = M + R + S - (M n R) - (M n S) - (R n S) + (M n R n S) + Neither.   30 = 8 + (12 - x) + (5 - x) + 0 + 0 + x + 0 + Neither.   22 = (12-x) + (5-x) + x + Neither.   Now the max value of x could be 5 and the min value of x could be 0.   When x is 5 (max), Neither is 10.   When x is 0 (min), Neither is 5. We need maximum no of people who do not belong to any group. Hence max value of neither is 10.   Answer 10 (10).
Answer: D
Calculate the ratio between x and y if 15% of x equal to 50% of y?
Choices.
A) 3 : 5 B) 3 : 7 C) 3 : 8 D) 3 : 10 E) 3 : 9

Solution: Explanation:   15 x = 50 y   x: y = 15: 50 = 3 : 10   Answer:3 : 10
Answer: D
The wages earned by Robin is 30% more than that earned by Erica. The wages earned by Charles is 70% more than that earned by Erica. How much percent is the wages earned by Charles more than that earned by Robin? Answers:
A) 18.75%  B) 23%  C) 30%  D) 31%  E) 100%

Solution: Let wage of Erica = 10   Wage of Robin = 1.3*10= 
1.3*10 = 13
13   Wage of Charles= 1.7 *10= 
1.7 *10 = 17
17   Percentage by which wage earned by Charles is more than that earned by Robin= (17-13)/13 * 100%   = 4/13 * 100%   =31%   Answer 31%
Answer: D
Two trains of length 140 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?	Options
A) 100/7 sec B) 108/7 sec C) 57/7 sec D) 120/7 sec E) 50/7 sec

Solution: Relative speed = (54 + 72)* 5/18 = 7 * 5= 
7 * 5 = 35
35 mps.   The time required= d/s = (140 + 100 + 300)/35   = 540/35 = 108/7 sec.   ANSWER:108/7 sec
Answer: B
Out of 8 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
Choose one:
A) A)5/7
B) B)5/4
C) C)5/14
D) D)5/6
E) E)9/14

Solution: P(at least one graduate) = 1 - P(no graduates)   = 1 - ⁶C₃/¹⁰C₃   = 1 - (6 * 5 * 4)/(6 * 7 * 8)   = 9/14   Answer:9/14
Answer: E
A has to pay Rs. 220 to B after 1 year.B asks A to pay Rs. 110 in cash and defer the payment of Rs. 110 for 2 years. A agrees to it. If the rate of interest be 10% per annum, in this mode of payment :  Choose the correct choice from the following options.
A) There is no gain or loss to any one
B) A gains Rs. 7.34
C) A loses Rs. 7.34
D) A gains Rs. 11
E) None of these

Solution: A has to pay = P.W. of Rs. 220 due 1 year hence = Rs.[ 220 x100/100+( 10x1)]= Rs. 200.   A actually pays = Rs. 110 + P.W. of Rs. 110 due 2 years hence   [110 + 110x 100/100+( 10x2 ) ] = Rs. 192.66.   ∴ A gains = Rs. (200- 192.66)= Rs. 7.34.   Answer A gains Rs. 7.34
Answer: B
A team has to design a flag. The team has four yellow strips of cloth and five green strips of cloth that they must use as is to make the flag. How many different flags can the team design with the materials at hand?
Answers.
A) 24  B) 120  C) 126  D) 140  E) 156

Solution: The # of permutations of total 4+5= 
4+5 = 9
9 strips where 4 are identical yellow and 5 are identical green is 9!/(4!*5!)=126 (note that they must use all the materials at hand, also I guess that the strips must be either only vertical or only horizontal).   Answer: 126.
Answer: C
Five years ago, the average age of A, B, C and D was 40 yr. with E joining them now, the average of all the five is 49 yr. How old is E?  Pick
A) 25 yr B) 40 yr C) 45yr D) 65 yr E) NOne

Solution: Solution:   Total present age of A, B, C and D,   = (40*4)+(4*5)= 
(40*4)+(4*5) = 180
180 yr;   Total age present age of A, B, C, D and E,= 49*5= 
49*5 = 245
245 yr.   So, age of E= 65 yr.   Answer: Option 65 yr
Answer: D
How many times in a day, the hands of a clock are straight?	Choose one:
A) 44 B) 40 C) 30 D) 25 E) 20

Solution: 12 hrs ==> 22 times   24 hrs ==> 44 times   44NSWER 44
Answer: A
What is the tens digit of 6^22?	Choose the most appropriate option:
A) 1 B) 3 C) 5 D) 7 E) 9

Solution: The tens digit of 6 in integer power starting from 2 (6^1 has no tens digit) repeats in a pattern of 5: {3, 1, 9, 7, 5}:   The tens digit of 6^2=36 is 3.   The tens digit of 6^3=216 is 1.   The tens digit of 6^4=...96 is 9.   The tens digit of 6^5=...76 is 7.   The tens digit of 6^6=...56 is 5.   The tens digit of 6^7=...36 is 3 again.   etc...   22 has the form 5n+2, so the tens digit of 6^22 is 3.   The answer is 3.
Answer: B
If julie rows 32 km upstream and 72 km down steam taking 4 hours each, then the speed of the stream Choose the correct choice from the following choices.
A) 1.5kmph	B) 0.5kmph	C) 0.4kmph	D) 1.6kmph	E) 2.5kmph

Solution: Speed upstream = 32/4= 
32/4 = 8
8 kmph   Speed down stream= 72/8= 
72/8 = 9
9 kmph   Speed of stream= ½ (9-8) = 0.5kmph   ANSWER:0.5kmph
Answer: B
A boy is standing in one corner of a square ground of side 90m.He can throw a stone upto maximum 70m. Find the area in which that boy can throw that stone in that ground?  Select
A) 2850 B) 3150 C) 3250 D) 3450 E) 3850

Solution: Area covered by stone = Pi*r^2/4 ( here we divide by 4 because the boy is standing in the corner of the ground and only 1/4 part of the ground , the stone can reach)   where r= 70 m = length of throw   So area = (22/7)*70*70/4= 
(22/7)*70*70/4 = 3_850
3850 sq m   answer :3850
Answer: E
A man spends 10% of his income in house rent, 20% of the rest on his children’s education, 25% of the rest miscellaneous causes. If he now posses Rs. 1944 then his income is?	Choose the correct choice from the following choices
A) Rs.3600  B) Rs.4000  C) Rs.4500  D) Rs.3000  E) Rs.5000

Solution: X * (90/100) * (80/100) * (75/100) = 1944   X * 0.9 * 0.8 * 0.75   X = 1944/0.54= 
1944/0.54 = 3_600
3600   Rs.3600NSWER:Rs.3600
Answer: A
If r is the smallest positive integer that is not prime and not a factor of 50!, what is the sum of the factors of r?
Choose the correct choice from the following options: A) 51 B) 162 C) 72 D) 54 E) 50!+2

Solution: In fact 51=3*17 IS a factor of 50!.   The smallest positive integer that is NOT prime and NOT a factor of 50! is 106=2*53. The sum of the factors of 106 is 162.   Answer: 162.
Answer: B