MU-NLPC/Calc-aqua_rat huggingface dataset:
For 2consecutive yrs, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the 2nd yr is Rs. 42000 & my expenses in the first yr in Rs.21000, my total savings for the two-year is
Select.
A) Rs. 5000  B) Rs. 6000  C) Rs. 7000  D) Rs. 8000  E) Rs. 10000

Solution: Sol. Income in first year = * x 42000 = Rs. 24000   Expenses in second year = \ x 21000 = Rs. 35000 Total savings = Total income - Total expenses = (42000 + 24000)- (21000 + 35000)   = 66000 - S6000 = Rs. 10000   Rs. 10000
Answer: E
6x − 18 = 6y
5y + 5x = 15
Which of the following is the number of solutions to the system of equations shown above? Options:  A) More than three  B) Exactly three  C) Exactly two  D) Exactly one  E) None

Solution: 6x − 12 = 6y   => 6x - 6y = 18   => x- y =3 -- 1   5y + 5x = 15   =>x + y = 3 -- 2   From equation 1 and 2 , we get   2x = 6   => x=3   y=0   Therefore , the given system will have Exactly one solution   Exactly one
Answer: D
A and B can do a work in 8 days, B and C can do the same work in 12 days. A,B and C together can finish it in 6 days. A and C together will do it in how many days? Choose the correct choice: A) 7 B) 6 C) 5 D) 8 E) 9

Solution: Let the total units of work be 48.   Units of work completed by A and B in one day = 6.   Units of work completed by B and C in one day = 4   Units of work completed by A, B, and C in one day = 8.   From the above information we get the work completed by A and C in one day is 6 units.   Therefore, the number of days taken by A and C to complete the whole work = 48/6= 
48/6 = 8
8 days.   ANSWER:8
Answer: D
Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is?  Choose the correct answer: A) 125 B) 150 C) 200 D) 250 E) 300

Solution: 3x * 2x = 3750 => x = 25   2(75 + 50) = 250 m   250 * 1/2 = Rs.125   125NSWER 125
Answer: A
A jar contains only three types of objects: red, blue, and silver paper clips. The probability of selecting a red paper clip is 1/10, and the probability of selecting a blue paper clip is 1/2. What is the probability of selecting a silver paper clip?
Select the correct option:
A) 5/13	B) 1/2	C) 4/10	D) 3/4	E) 11/12

Solution: Prob of Red = 1/10   Prob of Blue = 1/2   Prob of Silver = ?   P(Silver) = 1 - P(Red) - P(Blue) ==> 1-1/10-1/2 = 4/10   Ans: 4/10
Answer: C
The sector of a circle has radius of 42 cm and central angle 135o. Find its perimeter? Pick:
A) 91.5 cm
B) 92.2 cm
C) 28.9 cm
D) 29.2 cm
E) 183 cm

Solution: Perimeter of the sector = length of the arc + 2(radius)   = (135/360 * 2 * 22/7 * 42) + 2(42)   = 99+ 84= 
99+ 84 = 183
183 cm   Answer:183 cm
Answer: E
A jar has 250 marbles. 46 are blue, 56 are red, 75 are green, 25 are yellow, and the remainder, purple.
What percent of the marbles are purple?	Choose the correct choice from the following answers
A) 76%	B) 24%	C) 30%	D) 16%	E) 27%

Solution: Total number of blue, red, green, and yellow marbles: 46 + 56 + 75 + 25 = 190   Percentage of marbles other than purple: 190/250 = 76%   Percenage of purple marbles: 1-.76= 
1-.76 = 0.24
.24=24%   Answer is 24%
Answer: B
All of the citizens of a country have a three-character or four-character national identification code that is created using the 26 letters of the alphabet and the 10 digits from 0 to 9. What is the maximum number of citizens who can be designated with these codes?
Pick:  A) 36^7  B) 37(36^3)  C) 35(36^4)  D) 35(36^3)  E) 37(36^4)

Solution: The number of possible 3-digit codes is 36^3.   The number of possible 4-digit codes is 36^4.   The total sum is 36^3 + 36^4 = 36^3(1+36) = 37(36^3)   The answer is 37(36^3).
Answer: B
Find the simple interest on Rs. 64,000 at 16 2/3% per annum for 9 months.	Choose the most appropriate option.
A) s.8500
B) s.8000
C) s.7500
D) s.7000
E) s.6500

Solution: P = Rs.64000,R = 50/3% p.a and T = 9/12 years = 3/4years.   S.I. = (P*R*T)/100 = Rs.(64,000*(50/3)*(3/4)*(1/100))   = Rs.8000   Answer is s.8000.
Answer: B
A man two flats for $675958 each. On one he gains 15% while on the other he loses 15%. How much does he gain or lose in the whole transaction?  Select
A) 2%	B) 2.25%	C) 3.12%	D) 4.65%	E) 5.12%

Solution: In such a case there is always a loss   Loss% = (15/10)^2 = 9/4= 
9/4 = 9/4 = around 2.25
2.25%   Answer is 2.25%
Answer: B
The nth term in a certain sequence is defined for positive integer n as 1+(−1)(n(n+1)/2)^2. What is the total of the first 64 terms of this sequence?	Choose the correct choice from the following answers:
A) −164
B) 0
C) 16
D) 32
E) 64

Solution: sequence goes like this 0 , 1, 0 , 1, 0 ...... 1(64th term)   sum of 64 terms = 32   ANSWER:32
Answer: D
For which of the following functions is f(w) = f(−w) for all values of w ?	Pick one
A) f(x) = x^3 + 3  B) f(x) = −x  C) f(x) = 2x + 3  D) f(w) = −w^2 + 2  E) f(x) = 5x − 4

Solution: f(w) = f(−w)   The above is a property of an even function .   f(w) = f^(n)   f(w) = f(−w) will hold when n is an even integer .   The only case when w is even is option f(w) = −w^2 + 2   Answer f(w) = −w^2 + 2
Answer: D
Given that a is the average (arithmetic mean) of the first eight positive multiples of six and b is the median of the first twelve positive multiples of six, what is the ratio of a to b?
Choose the correct choice.
A) 3:4	B) 10:13	C) 5:6	D) 9:13	E) 4:3

Solution: The first nine positive multiples of six are {6, 12, 18, 24,30, 36, 42, 48}   The first twelve positive multiples of six are {6, 12, 18, 24, 30,36,42, 48, 54, 60, 66, 72}   Both sets are evenly spaced, thus their median=mean:   a=(24+30)/2= 
(24+30)/2 = 27
27 and b=(36+42)/2= 
(36+42)/2 = 39
39 --> a/b=27/39=9/13.   Answer: 9:13.
Answer: D
Grace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jackets for her business trip. If an outfit consists of one of each item of clothing except shirts, of which she will wear 2, how many different outfits C can does Grace have available during her trip? Select:
A) 2,520	B) 1,260	C) 620	D) 360	E) 120

Solution: The idea is to multiply the number of possibilities for each item of clothing with the different items. For the shirts you essentially choose 2 out of 8 so you should use the combination forumla (don't know how to use math symbols here).   This gives you C=5 x 3 x 28 x 3 = 1'260. Hence, solution 1,260 is correct.
Answer: B
Line D passes through point (-2,5), and the product of its x-intercept and y-intercept is positive. Which of the following points could be on line D?
Choose the correct option
A) (5,10) B) (-3,2) C) (-1,7) D) (-1,2) E) (-3,1)

Solution: The slope of the line is -ve, the only point that makes the slope -ve is D.   (5 - 2)/(-2 + 1) = 3/-1   Answer - (-1,2)
Answer: D
Find the average (arithmetic mean) of x and y if the average of x, y, and 5 is 20 more than the average of x, y, 5, and 15.  Pick one:
A) 110	B) 120	C) 130	D) 140	E) 150

Solution: consider the statement 50 is 20 more than 30: 50 = 30+20   similarly   the average of x, y, and 5 = (the average of x, y, 5, and 15) + 20   (x+y+5)/3 = (x+y+5+15)/4 + 20   (x+y+5)/3 = (x+y+20)/4 + 20   (x+y+5)/3 = (x+y+20)/4 + 80/4   (x+y+5)/3 = (x+y+20+80)/4   (x+y+5)/3 = (x+y+100)/4   cross multiply   4(x+y+5) = 3(x+y+100)   4x+4y+20 = 3x+3y+300   4x-3x +4y-3y = 300 - 20   x + y = 280   so   (x+y)/2 = 280/2   (x+y)/2 = 140   i.e the average of x and y is 140   140
Answer: D
The number 97215*6 is completely divisible by 11. What is the smallest whole number in place of * ?
Select: A) 3 B) 4 C) 1 D) 2 E) 11

Solution: From the above given "Divisibility by 11 rule", it is clear that   if 97215*6 is divisible by 11, then (9 + 2 + 5 + 6) - (7 + 1 + *) is divisible by 11   => 22 - (8 + *) is divisible by 11   => (14 - *) is divisible by 11   The smallest whole number which can be substituted in the place of * to satisfy the   above equation is 3 such that   14 - 3= 
  14 - 3 = 11
11 and 11 is divisible by 11.   3nswer is 3
Answer: A
A gambler has won 40% of his 30 poker games for the week so far. If, all of a sudden, his luck changes and he begins winning 70% of the time, how many more games must he play to end up winning 60% of all his games for the week?
Pick:
A) 36  B) 42  C) 48  D) 54  E) 60

Solution: Let x be the number of additional games the gambler needs to play.   0.4(30) + 0.7x = 0.6(x+30)   0.1x = 6   x = 60   The answer is 60.
Answer: E
If 8^z is a factor of 256!, which of the following could be the value of z? Choose the correct answer.
A) 32
B) 42
C) 30
D) 52
E) 36

Solution: 8^z is a factor of 256!, what values can z take.   Powers of 8 in 256! = [256/8] + [256/64] , where [x] is the integral part of x   Powers of 8 in 256! = 32 + 4= 
32 + 4 = 36
36   Hence the maximum value of 8^z in 256!= 8^36   Correct Option: 36
Answer: E
The sale price at which a store sells an article is 25% more than its cost price. If the sale price is an integer, which of the following cannot be the cost price?
Options:	A) $20	B) $37	C) $48	D) $60	E) $84

Solution: Sale Price = (5/4)*(Cost Price)   If the sale price is an integer, then the cost price must be divisible by 4.   The answer is $37.
Answer: B
A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 62 now, the son age 5 years back was  Choose the correct answer.
A) 14	B) 17	C) 11	D) 19	E) 26

Solution: Let the son's present age be x years .Then, (62 - x) = x x= 31.   Son's age 5 years back = (31 - 5)= 
(31 - 5) = 26
26 years   Answer: 26
Answer: E
In how many ways can a committee consisting of three men and four women be formed from a group of six men and seven women?  Choose the correct option: A) ⁶C₄ ⁷C₃ B) ⁶C₃ ⁷C₅ C) ⁶C₃⁷C₄ D) ⁷C₅ ⁶C₄ E) ⁶C₃ ⁷C₃

Solution: The group contain six men and seven women   Three men can be selected from six men in ⁶C₃ ways.   Four women can be selected from seven women in ⁷C₄ ways.   Total number of ways = (⁷C₄)(⁶C₃).   ANSWER:⁶C₃⁷C₄
Answer: C
There are 5 physics books and 1 chemistry book on shelf P and 4 physics books on shelf Q. One book is moved from shelf P to shelf Q. A student picks up a book from shelf Q. What is the probability that the chemistry book is taken by the student? Choose the most appropriate option
A) 1/40	B) 1/35	C) 1/30	D) 1/25	E) 1/20

Solution: P(a chemistry book is moved to shelf Q) = 1/6   P(a chemistry book is then chosen from shelf Q) = 1/5   P(the student takes a chemistry book) = 1/6 * 1/5 = 1/30   The answer is 1/30.
Answer: C
A man gets a simple interest of Rs.600 on a certain principal at the rate of 5% p.a in two years. Find the compound interest the man will get on twice the principal in two years at the same rate?
Choose the correct answer:  A) s.1000  B) s.1056  C) s.1150  D) s.1230  E) s.1256

Solution: Let the principal be Rs.P   S.I at 5% p.a in 2 years on Rs.P = Rs.600   (P)(2)(5)/100 = 600   P = 6000   C.I on Rs.2P i.e., Rs.12000 at 5% p.a in two years   =12000{ [1 + 5/100]^2 - 1}   = 12000(41/ 400)   = Rs.1230   Answer:s.1230
Answer: D
A rower can row upstream at 20 kph and downstream at 34 kph. What is the speed of the rower in still water?	Choices
A) 26 B) 27 C) 28 D) 29 E) 30

Solution: Let V be the rower's speed in still water.   Let S be the speed of the current in the stream   V-S = 20   V+S = 34   When we add the two equations, we get: 2V = 54   Then V = 27 kph.   The answer is 27.
Answer: B
The diagonals of a rhombus are 15 cm and 20 cm. Find its area?	Choose the most appropriate option.
A) 277 B) 266 C) 150 D) 288 E) 212

Solution: 1/2 * 15 * 20= 
1/2 * 15 * 20 = 150
150   Answer: 150
Answer: C
8+88+888+.....+8888........8888. There are 21 “8” digits in the last term of the series.
Find the last three digits of the sum.  Choose the correct choice from the following answers:
A) 384	B) 584	C) 784	D) 968	E) 768

Solution: 21*8= 
21*8 = 168
168 carry 16   20*8= 
20*8 = 160
160+16= 
160+16 = 176
176 carry 17   19*8= 
19*8 = 152
152+17= 
152+17 = 169
169   the value is 968   ANSWER:968
Answer: D
A librarian has 4 identical copies of Hamlet, 3 identical copies of Macbeth, 2 identical copies of Romeo and Juliet, and one copy of Midsummer’s Night Dream. In how many distinct arrangements can these ten books be put in order on a shelf? Answers:
A) 720 B) 1,512 C) 2,520 D) 6,400 E) 12,600

Solution: If the ten books were all different, the arrangements would be (10!), a very big number. Because we have repeats of identical copies, not all 10! arrangements will be unique. For a subset of k identical members, those k members could be interchanged in k! orders, and the resulting arrangements would be the same, so we have to divide by k! to remove repetitions. In this example, we need to divide 10! by 4! and 3! and 2!:   10!/4!3!2!=12600   Answer : 12,600
Answer: E
Find 12 ×× 19	Options:
A) 238  B) 228  C) 208  D) 277  E) 101

Solution: Mentally imagine this number as (10 + 2 ) ×× 19 = 190 + 38= 
190 + 38 = 228
228.   Answer:228
Answer: B
The average age of a class of 19 students is 20 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher? Choose the correct choice from the following.
A) 39
B) 41
C) 40
D) 42
E) 43

Solution: Total age of all students =19Ã—20   Total age of all students + Age of the teacher =20Ã—21   Age of the teacher   =20Ã—21âˆ’20Ã—19=20(21âˆ’19)=20Ã—2=40   Answer is 40.
Answer: C
The distance between a sports store and a recreation center is approximately 3.34 x 10^5 inches. Which of the following is closest to the distance between the sports store and a recreation center, in kilometers? (1 kilometer is approximately 3.9 x 10^4 inches.) Options
A) 9.33 B) 8.98 C) 8.56 D) 9.21 E) 9.03

Solution: We know that 1 kilometer = 3.9x10^4 inches. Therefore, we now have a ratio of (1 kilometer/3.9x10^4 inches).   We also know that the distance between the sports store and a recreation center is approximately 3.34x10^5 inches. To convert inches to kilometers, we need to multiply 3.34x10^5 inches by the ratio we just found out.   kilometers = 3.34x10^5 inches x (1 kilometer/3.9x10^4 inches) [note: "inches" cancel out, leaving us with just km]   km = 3.34x10^5/3.9x10^4 km   km = 8.56 km   Therefore, we can see that the closest answer is 8.56.
Answer: C
If 25% of a class averages 80% on a test, 50% of the class averages 65% on the test, and the remainder of the class averages 90% on the test, what is the overall class average?
Choose the correct choice from the following options:
A) 60%
B) 65%
C) 70%
D) 75%
E) 80%

Solution: This question is a Weighted Average question with a series of dependent variables.   The remaining portion of the class represents 100% - 25% - 50% = 25% of the class   Converting the portions of the class population to decimal weights, we find:   Class Average  100  - 25  - 50= 
 100  - 25  - 50 = 25
25% of the class   Converting the portions of the class population to decimal weights, we find:   Class Average= 0.25x80 + 0.50x65 + 0.25x90 = 75   The class average is 75%   Final Answer   75%) 75%
Answer: D
Two numbers x and y are such that the sum of 3% of x and 4% of y is one-third of the sum of 2% of of x and 8% of y. Find the ratio of x : y.	Choose the correct choice.
A) 3:8
B) 6:7
C) 4:7
D) 2:5
E) None of these

Solution: Explanation :   Solution: 3% of x+ 4% of y=1/3(2% of x+8% of y)   3x/100 + 4y/100 = 2x/300 + 8y/300   (3x+4y)3 = 2x+8y   7x = 4y   x/y = 4/7   Answer : 4:7
Answer: C
How many five digit numbers can be formed using digits 0,1,2,3,4,5, Which are divisible by 7, without any of the digits repeating? Choose the correct choice from the following answers
A) 96
B) 98
C) 100
D) 81
E) 72

Solution: 0,1,2,3,4,5   One digit will have to remain out for all 5 digit numbers;   if 0 is out; Leftover digits will be 1,2,3,4,5 = Sum(1,2,3,4,5)=15.Ignore   if 1 is out; Leftover digits will be 0,2,3,4,5 = Sum(0,2,3,4,5)=14. divisible by 7)   if 3 is out; Leftover digits will be 0,1,2,4,5 = Sum(0,1,2,4,5)=12. Ignore   if 4 is out; Leftover digits will be 0,1,2,3,5 = Sum(0,1,2,3,5)=11. Ignore   if 5 is out; Leftover digits will be 0,1,2,3,4 = Sum(0,1,2,3,4)=10. Ignore   Total count of numbers divisible by 7 = 4*4! = 96   96
Answer: A
20 people going to one temple. (some time waste data) They want Rs. 20. For men-Rs.3, women-Rs.2, children-50 paisa. How much money spends for men, children and women?	Choose the correct choice from the following answers.
A) 3,7,10
B) 4,7,10
C) 5,7,10
D) 6,7,10
E) 7,7,10

Solution: M=1 => 1*3= 
1*3 = 3
3   W=5 => 5*2= 
5*2 = 10
10   C=14 => 14*.5= 
14*.5 = 7
7   1+5+14= 
1+5+14 = 20
20 & 3+10+7= 
3+10+7 = 20
20   3,7,10NSWER:3,7,10
Answer: A
Number of students in institutes A and B were in the ratio of 7 : 15 respectively in 2012. In 2013, the number of students in institute A increased by 25% and number of students in institutes B increased by 26%, then what was the respective ratio between number of students in institutes A and B? Pick one: A) 25 : 56 B) 24 : 55 C) 24 : 53 D) 25 : 53 E) 25 ratio 54

Solution: Solution:   Ratio of students in 2012 in institutes A and B,   = 7 : 15.   Let number of students in institute A in 2012 = 700.   And Number of students in institutes B in 2012 = 1500.   25% increase in the number of students in 2013,   Now, number of students in Institute A,   = 700 + 25% of 700. = 875.   Number of students in B in 2013 as 26% students increased in B,   = 1500 + 26% of 1500 = 1890.   Current Ratio of the students,   = 875 /1890 = 25 : 54.   Answer: Option 25 ratio 54
Answer: E
A land owner needs to fence his semicircular land leaving an opening of length of 3m for access. The radius of the semicircular plot is 7m. How long would be the fence in meters?  Options.
A) 22
B) 33
C) 36
D) 44
E) 51

Solution: Perimeter of the semicircle= Ï€xD/2 + D   = Ï€x7 + 14   =22+14= 
22+14 = 36
36m   Length of the fence= 36-3= 
36-3 = 33
33m   Answer: 33
Answer: B
A man has Rs. 560 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?  Choose the correct choice from the following options: A) 45 B) 60 C) 75 D) 105 E) 120

Solution: Let number of notes of each denomination be x.   Then x + 5x + 10x = 560   16x = 560   x = 35.   Hence, total number of notes = 3x = 105.   Answer = 105
Answer: D
What is the smallest of six consecutive odd integers whose average (arithmetic mean) is x + 2?
Pick.
A) x - 5 B) x - 3 C) x - 1 D) x E) x + 1

Solution: Assume the integers to be   n - 5, n - 3, n- 1, n+1, n + 3, n + 5   AM = 6n/6 = n   Given n = x + 2   Therefore, smallest term = n - 5 = x + 2 - 5 = x - 3   Correct Option: x - 3
Answer: B
The grade point average of one third of the classroom is 60; the grade point average of the rest is 66. What is the grade point average of the whole class? Choose the most appropriate option.
A) 55 B) 56 C) 64 D) 65 E) 66

Solution: Let n=total students in class   total points for 1/3 class=60n/3=20n   total points for 2/3 class60 /3= 
60 /3 = 20
20n   total points for 2/3 class=66*2n/3=44n   total points for whole class66*2 /3= 
66*2 /3 = 44
44n   total points for whole class=20n+44n=64n   64n total class points/n total students20 +44= 
20 +44 = 64
64n   64n total class points/n total students=64 grade point average for total class   Answer : 64
Answer: C
If half of 5 were 3, that would one-third of 10 be Choose the correct option:
A) 2
B) 4
C) 6
D) 8
E) 1

Solution: Explanation:   Half of 5 is 2.5. But given as 3. So take 1/2 of 5x = 3 ⇒ x = 6/5   Now 1/3 (10x) = 1/3 × 10 × 6/5 = 4.   Answer: 4
Answer: B
An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
Choose the correct choice from the following:  A) 33 1/7%  B) 33 2/3%  C) 33 1/3%  D) 37 1/3%  E) 23 1/3%

Solution: 675 ---- 225   100 ---- ? =>   =33 1/3%   Answer:33 1/3%
Answer: C
Cream costs twice as much as skim milk. A certain brand of milk is 1/3 cream and 2/3 skim milk. What fraction of the cost of this brand is due to the cream?	Select the correct option
A) 1/3 B) 1/2 C) 2/5 D) 3/5 E) 3/4

Solution: Let x be the cost of the skim milk in the mixture.   The cost of the cream is (1/2)*x*2 = x.   The total cost is x+x = 2x and the fraction due to the cream is x/2x = 1/2   The answer is 1/2.
Answer: B
The number 110 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?  Choose the correct choice from the following choices
A) 18	B) 16	C) 15	D) 14	E) 13

Solution: 7^2+5^2+6^2=49+25+36= 
49+25+36 = 110
110   7+5+6= 
7+5+6 = 18
18   Hence answer is 18
Answer: A
Given two sets A = {1,1,4,4,5,5} and B = {0,1}, if one number is chosen from each set at random, what is the probability that the sum of both numbers is an even number
Choose the most appropriate option
A) 1/4  B) 1/8  C) 1/7  D) 1/2  E) 3

Solution: One way to look at it:   The number from set A can be ANYTHING.   The number selected from set B will determine whether the sum is odd or even.   For example, if a 4 is selected from set A, we need a 0 from set B to get an even sum.   If a 5 is selected from set A, we need a 1 from set B to get an even sum.   And so on.   So, P(sum is even) = P(select ANY number from set AAN1/2select the number from set B that makes the sum even)   = P(select ANY number from set A)xP(select the number from set B that makes the sum even)   = 1x1/2   = 1/2   = 1/2
Answer: D
For 2consecutive yrs, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the 2nd yr is Rs. 42000 & my expenses in the first yr in Rs.22000, my total savings for the two-year is
Choose one:
A) s. 8000 B) s. 9000 C) s. 9900 D) s. 9990 E) s. 10000

Solution: Sol. Income in first year = * x 42000 = Rs. 24000   Expenses in second year = \ x 21000 = Rs. 35000 Total savings = Total income - Total expenses = (42000 + 24000)- (22000 + 35000)   = 66000 - 57000 = Rs. 9000   s. 9000
Answer: B
If the SI on a certain sum of money is 4/25 of the sum and the rate per cent equals the number yrs, then the rate of interest/annum is?  Choose the correct choice: A) 4% B) 5% C) 6% D) 7% E) 8%

Solution: Sol Let the prmcipal be Rs. x   Then the simple interest (1)   Let the me ofinterestp 3 be 1%,   than tune m : ryears   max! max   pm   ‘X:5   4%   4%
Answer: A
A boy multiplied 987 by a certain number and obtained 559981 as his answer. If in the answer both 98 are wrong and other digits are correct, then the correct answer would be:	Choose one.
A) 553681  B) 555181  C) 555681  D) 556581  E) 555581

Solution: 987 = 3 x 7 x 47.   So, the required number must be divisible by each one of 3, 7, 47   553681 --> sum of digits = 28, not divisible by 3   555181 sum of digits = 25, not divisible by 3   555681 is divisible by each one of 3, 7, 47.   556581 sum of digits = 30, not divisible by 7   555581 sum of digits = 29, not divisible by 3   so the answer is 555681.
Answer: C
One side of a rectangular field is 15m and one of its diagonal is 17m. Find the area of field?  Options
A) 120 sq. m	B) 140 sq. m	C) 125 sq. m	D) 130 sq. m	E) 110 sq. m

Solution: Other side = [(17 x 17) - (15 x 15)] = (289 - 225) = 8m   Area = 15 x 8 =120 sq. m   120 sq. mNSWER:120 sq. m
Answer: A
Sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum. Sandy attempts 30 sums and obtains 60 marks. How many sums did Sandy get correct?	Pick.
A) 18
B) 20
C) 22
D) 24
E) 26

Solution: Let x be the correct sums and (30-x) be the incorrect sums.   3x - 2(30-x) = 60   5x = 120   x = 24   The answer is 24.
Answer: D
The distance between two planets is 4 × 10^6 light years. What is the distance between the two planets, in parsecs? (1 parsec = 3.26 light years)
Pick:
A) 9.3 × 10^5	B) 9.9 × 10^6	C) 9.3 × 10^7	D) 9.9 × 10^7	E) 1.2 × 10^6

Solution: 4*10^6 light years = 4*10^6/3.26 parsecs.   4/3.26 is a little bit less than 1, something like 0.9, thus 4*10^6/3.26 = ~1.2*10^6.   Answer: 1.2 × 10^6.
Answer: E