MU-NLPC/Calc-aqua_rat huggingface dataset:
How much time will take for an amount of Rs. 360 to yield Rs. 81 as interest at 4.5% per annum of simple interest? Choose the correct choice from the following:  A) 8 years  B) 4 years  C) 3 years  D) 9 years  E) 5 years

Solution: Time = (100 * 81) / (360 * 4.5)= 
(100 * 81) / (360 * 4.5) = 5
5 years   Answer: 5 years
Answer: E
Two buses and a van were employed to transport a class of students on a field trip. 2/5 of the class boarded the first bus. 2/3 of the remaining students boarded the second bus, and the rest of the students boarded the van. When the second bus broke down, 1/2 of the students on the second bus boarded the first bus. What fraction of the class was on board the first bus?
Choose the correct choice from the following answers:
A) a) 1/2  B) b) 2/3  C) c) 11/15  D) d) 6/10  E) e) 4/5

Solution: This is a pure ratio question (we aren't given any numbers for anything), so you can just choose any starting number you like, and use it to solve the problem. The best number to pick is almost always the product of all the denominators of your fractions, so here we could start with 30 students. Then we have:   • 2/5 of these, or 12 students, board the first bus   • there are 18 students left. 2/3 of these, or 12 students, board the second bus   • this bus breaks down, and 1/2 of the 12 students, or 6 students, board the first bus   • the first bus now contains 18 out of the original 30 students, so the answer is 18/30 = 6/10   Answer d) 6/10
Answer: D
Ravi purchased 20 dozens of toys at the rate of Rs. 380 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit? Choose one:	A) 23%	B) 1.2%	C) 5.6%	D) 4.21%	E) 12.2%

Solution: D   C.P. of 1 toy = 380/12 = Rs. 31.6   S.P of 1 toy = Rs. 33   Profit = 1.33/31.25 * 100 = 4.21%   Answer is 4.21%
Answer: D
The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally?	Choose the most appropriate option
A) 36 B) 24 C) 12 D) 6 E) 8

Solution: x, 2x   (x-2):(2x-2) = 1:3   ANSWER 12
Answer: C
A firm has 4 senior partners and 5 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner. (2 groups are considered different if at least one group member is different) Select:
A) 66 B) 74 C) 82 D) 90 E) 98

Solution: The total number of ways to form a group of 3 is 9C3 = 84   The number of groups without a senior partner is 5C3 = 10   The number of groups which include a senior partner is  84-10= 
 84-10 = 74
74   The answer is 74.
Answer: B
By mixing two brands of tea and selling the mixture at the rate of Rs. 177 per kg. a shopkeeper makes a profit of 18%. If to every 2 kg of one brand costing Rs. 200 per kg, 3 kg of the other brand is added, then how much per kg does the other brand cost? Pick one
A) Rs. 110 B) Rs. 120 C) Rs. 140 D) None of these E) Not determined

Solution: Explanation:   Let the cost of the brand be Rs. X per kg.   C.P. of 5 kg = (2 * 200 + 3 * x) = Rs. (400 + 3x)   S.P of 5 kg = Rs. (5 * 177) = Rs. 885   [885 - (400 + 3x)]/(400 + 3x) * 100 = 18   24250 - 150x = 3600 + 27x   177x = 20650 => x = 116 2/3   So, cost of the other brand = Rs. 116.66.   Answer is None of these
Answer: D
A certain experimental mathematics program was tried out in 2 classes in each of 42 elementary schools and involved 55 teachers. Each of the classes had 1 teacher and each of the teachers taught at least 1, but not more than 3, of the classes. If the number of teachers who taught 3 classes is n, then the least and greatest possible values of n, respectively, are Choices
A) 0 and 13  B) 0 and 14  C) 1 and 10  D) 1 and 9  E) 2 and 8

Solution: One may notice that greatest possible values differ in each answer choice in contrast to the least values, which repeat.   To find out the greatest value you should count the total classes (42*2=84), then subtract the total #of teachers since we know from the question that each teacher taught at least one class (84-55=29). Thus we get a number of the available extra-classes for teachers, and all that we need is just to count how many teachers could take 2 more classes, which is 29/2 = 14.5. So the greatest possible value of the # of teachers who had 3 classes is 14.   Only answer 0 and 14 has this option.
Answer: B
If the number 617*324 is completely divisible by 3, then the smallest whole number in the place of * will be:
Choose the correct option
A) 3
B) 1
C) 2
D) 4
E) 5

Solution: Sum of digits = (6 + 1 + 7 + x + 3 + 2 + 4) = (23 + x), which must be divisible by 3.   x = 1.   1
Answer: B
The compound interest on Rs.30,000 at 7% per annum is Rs.4347. The period (in years) is  Choose the correct choice from the following answers: A) 2 B) 2½ C) 3 D) 4 E) 5

Solution: Solution   Amount	=Rs(30000 + 4347)   = Rs.34347.   Let the time be n years.   Then, 30000(1+7/100)^n   = 34347.   =34347/3000   =11449/1000   =(107/100)^n   n= 2years.   2nswer 2
Answer: A
A certain company had a total annual expenditure of 2.1∗10^7 on employee salaries last year. If the company employed 420 people, what was the average employee salary?
Choose the correct choice:
A) $20,000
B) $25,000
C) $35,000
D) $40,000
E) $50,000

Solution: Given: Total annual expenditure of 2.1∗10^7 on employee salaries   Total employees = 420   Observe that  420*5= 
 420*5 = 2_100
2100   Therefore try to bring the numerator in terms of 2100   Average salary= (2100*10^4) /420 = 5*10^4 = 50,000   Option $50,000
Answer: E
Three years ago the average age of a class of six members was 19 years. A boy have been added, the average age of the class is the same today. What is the age of the boy? Choose the correct choice from the following answers.
A) 1	B) 2	C) 3	D) 4	E) 5

Solution: 6 * 22= 
6 * 22 = 132
132   7 * 19= 
7 * 19 = 133
133   `1   1
Answer: A
The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 75 kg. What might be the weight of the new person?	Choose one:
A) 95 kg
B) 90 kg
C) 85 kg
D) Data inadequate
E) None of these

Solution: A   95 kg   Total weight increased = (8 x 2.5) kg = 20 kg.   Weight of new person = (75 + 20)= 
(75 + 20) = 95
95 kg.
Answer: A
If y > 0, which of the following could be true?
I. y^3 > y^2
II. y^2 = y
III. y^2 > y^3	Choose one
A) I only	B) III	C) IIIII	D) All of the above	E) None of the above

Solution: 1. y^3 > y^2 Well this is true for all y > +1 (but not for values 0 < y < 1)   2. y^2 = y This is true for only one positive number, 1   3. y^2 > y^3 Again this is true only for values of x such that 0 < y < 1   So the answer is All of the above, since there exists at least one value of y which satisfies the equation/ in equation(s)
Answer: D
The length of a room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of Rs. 600 per sq. metre.
Answers:
A) Rs. 12375
B) Rs. 15550
C) Rs. 15600
D) Rs. 16500
E) None of these

Solution: Solution   Area of the floor = (5.5 × 3.75) m2 = 20.625 m2   ∴ Cost of paving = Rs. (600 × 20.625) = 12375. Rs. 12375nswer Rs. 12375
Answer: A
Bhajan Singh purchased 120 reams of paper at Rs.80 per ream. He spent Rs.280 on transportation, paid octroi at the rate of 40 paise per ream and paid Rs.72 to the coolie. If he wants to have a gain of 8% , what must be the selling price per ream ?
Choices:
A) Rs.86  B) Rs.87.48  C) Rs.89  D) Rs.90  E) None

Solution: Explanation:   C.P of 120 reams = Rs.(120×80+280+72+120×0.40)= Rs.10000.   C.P. of 1 ream = 10000/120= Rs.250/3   S.P. of 1 ream = Rs.108/100×250/3=Rs.90   Correct Option : Rs.90
Answer: D
2.205 divided by 0.3 gives
Pick
A) 7.35	B) 6.25	C) 8.15	D) 6.95	E) None of these

Solution: Explanation :   2.205/0.3 = 22.05/3 = 7.35. 7.35nswer : Option 7.35
Answer: A
The average of 11 results is 52, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?  Choose the correct answer
A) A)46 B) B)34 C) C)66 D) D)76 E) E)74

Solution: 1 to 11 = 11 * 52= 
11 * 52 = 572
572   1 to 6= 6 * 49= 
6 * 49 = 294
294   6 to 11= 6 * 52= 
6 * 52 = 312
312   6th= 294 + 312 – 572 = 34   Answer:34
Answer: B
A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is?  Select the correct option:
A) 34500
B) 24000
C) 24098
D) 23007
E) 24098

Solution: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6   Total profit = Rs. 52000   Share of B = 6/13 (52000)   = Rs. 24000   Answer:24000
Answer: B
Of the 5 numbers, whose average is 75, the first is one-fourth of the sum of the last 4. The first number is?
Choose the correct choice from the following options:
A) 75  B) 80  C) 78  D) 56  E) 67

Solution: Total of 5 numbers = 5 * 75= 
5 * 75 = 375
375   Let total of last 4 numbers= x   1st number = x/4   x+ x/4 = 375   5x = 1500 => x =300   1st number = 300/ 4= 
300/ 4 = 75
75   75nswer :75
Answer: A
The students of a particular class were given two tests for evaluation. Twenty Five percent of the class cleared both the tests and forty five percent of the students were able to clear the first test.
You have to calculate the percentage of those students who passed the first test and were also able to pass the second test. How will you do it?  Choose the correct choice:  A) 39%  B) 41%  C) 60%  D) 70%  E) 88%

Solution: C   60%   In all such cases where you have to find out the probability of anything with an already given situation, you have to use the formula for conditional probability.   In this case, you have to find out the probability that the second test was passed by a student given that he passed the first test already.   Therefore, P(Second/First) = P (First and Second)/ P (First)   = 0.25/0.42   =0.60   =60 %
Answer: C
Let a, b, c, d be four integers such that a + b + c + d = 4m + 1 where m is a positive integer. Given m, which one of the following is necessarily true?  Select the correct option.
A) The minimum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 – 2m + 1 B) The maximum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 – 2m + 1. C) The minimum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 + 2m + 1 D) The maximum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 + 2m + 1 E) None

Solution: Explanation :   Given,   => a + b + c + d = 4m + 1. now squaring this equation:   => (a+b+c+d)2 = 16m2 + 8m + 1.   => a2 + b2 + c2 + d2 + 2*( ab + ac + ad + bc + bd + cd ) = 16m2 + 8m + 1.   using the fact that product of two numbers is maximum when they are equal / nearly equal,   expression ab + ac + ad + bc + bd + cd will be maximum when ab , ac , ad, bc , bd , cd will be maximum and this is possible when a, b, c, d are nearly equal to each other. i.e. m , m , m , m+1.   when ab + ac + ad + bc + bd + cd is maximum , obviuosly , a2 + b2 + c2 + d2 will be minimum.   Put values in the above equation we get that the minimum value of a2 + b2 + c2 + d2 comes out to be 4m2 + 2m + 1.   Answer : The minimum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 + 2m + 1
Answer: C
For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of odd all the integers between 1 and 50?
Options
A) 500 B) 625 C) 750 D) 550 E) 600

Solution: numbers are 1,3,5-------,47,49   Average of the set: (largest+smallest)/2=(49+1)/2= 
(49+1)/2 = 25
25;   # of terms: (largest-smallest)/2+1=(49-1)/2+1= 
(49-1)/2+1 = 25
25   The sum= 25*25= 
25*25 = 625
625   Answer: 625
Answer: B
Find the area of a cuboid of length 8cm , breadth 6 cm . and height 9cm.
Answers:
A) 400 cm cube
B) 410 cm cube
C) 420 cm cube
D) 432 cm cube
E) 480 cm cube

Solution: Area of a cuboid = lxbxh =8cm x 6cm x 9cm = 432 cm cube   answer :432 cm cube
Answer: D
Positive integer x has n factors; 3x has 3 factors; Which of the following values can n take?
I. 1
II. 2
III. 3	Choices
A) I only
B) II only
C) I or II
D) II or III
E) I or III

Solution: Squares have odd number of factors.The square which is a multiple of 3 is 9.   3 has factors 1,3 .   Therefore 2 factors   Answer II only
Answer: B
In how many different ways can the letters of the word 'LEADING' be arranged such that the vowels should always come together?  Answers
A) 720  B) 420  C) 320  D) 520  E) None of these

Solution: The word 'LEADING' has 7 letters. It has the vowels 'E','A','I' in it and these 3 vowels should always come together. Hence these 3 vowels can be grouped and considered as a single letter. that is, LDNG(EAI).   Hence we can assume total letters as 5 and all these letters are different. Number of ways to arrange these letters   =5!=5×4×3×2×1=120   In the 3 vowels (EAI), all the vowels are different. Number of ways to arrange these vowels among themselves   =3!=3×2×1=6   Hence, required number of ways=120×6=720   720nswer : 720
Answer: A
If P(A) = 2/15, P(B) = 7/15, and P(A âˆª B) = 16/15 Find P(A|B)
Select:
A) 1/2
B) 16/7
C) 3/2
D) 4/5
E) 4/7

Solution: P(A|B) = P(A âˆª B)/P(B)   P(A|B) = (16/15)/(7/15) = 16/7.   16/7
Answer: B
Two different solutions of alcohol with respective proportions of alcohol to water of 3:1 and 2:3 were combined. What is the concentration of alcohol in the new solution if the first solution was 6 times the amount of the second solution? Choose one:  A) 62  B) 65  C) 68  D) 70  E) 72

Solution: SOL:   Lets assume that 60L of sol1 was mixed with 10L of sol2.   Alcohol in Sol1: 60*3/4 = 45L   Alcohol in Sol2: 10*2/5 = 4L   Total Alcohol in the mixed solution of 70L = 45 + 4= 
45 + 4 = 49
49L   Alcohol concentration in the new sol: (49/70)*100= 
(49/70)*100 = 70
70%   ANSWER:70
Answer: D
A train covers a distance of 12 km in 16 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?  Choose the correct choice from the following:
A) 80
B) 90
C) 60
D) 75
E) 85

Solution: Speed = (12/16 * 60) km/hr = (45 * 5/18) m/sec = 12.5 m/sec.   Length of the train = 12.5 * 6= 
12.5 * 6 = 75
75 m.Answer:75
Answer: D
A machine puts c caps on bottles in m minutes. How many E hours will it take to put caps on b bottles?  Select the correct option:
A) 60bm/c
B) E=bm/60c
C) bc/60m
D) 60b/cm
E) b/60cm

Solution: The machine puts c caps in m minutes or c caps in m/60 hours.   Rate = c/m/60 = 60c/m.   To put b caps the machine will take:-   Time = Work/Rate   T = b/60c/m = bm/60c   Answer is E=bm/60c.
Answer: B
What least number should be added to 1056, so that the sum is completely divisible by 23?
A. B. 3
C. 2	D. 1 Choose the correct choice from the following answers
A) 4  B) 3  C) 2  D) 0  E) 5

Solution: 1056 ÷ 23 = 45 with remainder = 21   21 + 2= 
21 + 2 = 23
23.   Hence 2 should be added to 1056 so that the sum will be divisible by 23   Answer: Option 2
Answer: C
What is the ratio between the volumes of a cylinder and cone of the same height and of the same diameter Choose the most appropriate option
A) 2:1
B) 3:1
C) 4:1
D) 5:1
E) None of these

Solution: Explanation:   Volume of cylinder/Volume of cone=3/1   Answer: 3:1
Answer: B
What is the probability of getting a King and a Queen in a single draw of two cards from a pack of well-shuffled cards? Choose the correct option.
A) 1/16 B) (4C1 * 4C1) / 52C2 C) 4/52 * 4/51 D) 8C2 / 52 C 2 E) (8 * 7) / 52C2

Solution: there are 4 kings, so we can choose a king in 4C1 way..   there are 4 Queens, so we can choose a Queen in 4C1 way..   total possible way = 4C1∗4C152C24C1∗4C152C2   (4C1 * 4C1) / 52C2
Answer: B
If a boy lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?
Choose the most appropriate option
A) 6	B) 8	C) 9	D) 10	E) 12

Solution: 96% ---- 12   144% ---- ?     96/144 * 12= 
  96/144 * 12 = 8
8   8
Answer: B
On four consecutive flips of a coin, what is the probability that all four produce the same result? Choose the correct choice from the following:
A) 1/16
B) 1/8
C) 1/4
D) 3/8
E) 1/2

Solution: TTTT case --> P = (1/2)^4 = 1/16   HHHH case --> P = (1/2)^4 = 1/16   P(TTTT or HHHH) = 1/16 + 1/16 = 2/16=1/8   Answer: 1/8
Answer: B
What is the greatest positive integer x such that 4^x is a factor of 64^10?	Options:	A) 5	B) 9	C) 10	D) 20	E) 30

Solution: 64^10 = (4^3)^10 = 4^30   ANSW30R:30
Answer: E
The average of 6 no.'s is 6.40. The average of 2 of them is 6.2, while the average of the other 2 is 6.1. What is the average of the remaining 2 no's?
Answers.
A) 2.3
B) 2.6
C) 6.9
D) 4.5
E) 4.6

Solution: Sum of the remaining two numbers = (6.4 * 6) - [(6.2 * 2) + (6.1 * 2)]   = 38.40 - (12.4 + 12.2) = 38.40 - 24.6= 
38.40 - 24.6 = 13.8
13.80   Required average= (13.8 / 2)= 
(13.8 / 2) = 6.9
6.9   Answer : 6.9
Answer: C
A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?	Choose the correct option:
A) 1:2 B) 1:0 C) 1:87 D) 1:6 E) 1:1

Solution: T = 192/32= 
192/32 = 6
6 h   T= 6 - 3= 
6 - 3 = 3
3   Time Ratio= 6:3 = 2:1   Speed Ratio = 1:2   1:2nswer: 1:2
Answer: A
The average monthly income of A and B is Rs. 5050. The average monthly income of B and C is Rs. 6250 and the average monthly income of A and C is Rs. 5200. What is the monthly income of A?	Pick one.
A) 2000  B) 3000  C) 4000  D) 5000  E) 6200

Solution: Explanation:   Let monthly income of A = a   monthly income of B = b   monthly income of C = c   a + b = 2 × 5050 .... (Equation 1)   b + c = 2 × 6250 .... (Equation 2)   a + c = 2 × 5200 .... (Equation 3)   (Equation 1) + (Equation 3) - (Equation 2)   => a + b + a + c - (b + c) = (2 × 5050) + (2 × 5200) - (2 × 6250)   => 2a = 2(5050 + 5200 - 6250)   => a = 4000   i.e., Monthly income of A = 4000   ANSWER IS 4000
Answer: C
If W is the set of all the integers between 10 and 332, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?	Choose the correct choice from the following answers:
A) 111
B) 28
C) 160
D) 213
E) 107

Solution: Official Solution:   Number of multiples of 3   Step 1. Subtract the extreme multiples of 3 within the range (The greatest is 330, the smallest is 12): 330 - 12 = 318   Step 2. Divide by 3: 318 / 3 = 106   Step 3. Add 1: 106 + 1 = 107.   So there are 107 multiples of 3 within the range: examples are 51, 54, 57, 60, etc.   Number of multiples of 2   Step 1. Subtract the extreme multiples of 2 within the range (The greatest is 330, the smallest is 12): 330 - 12 = 318   Step 2. Divide by 2: 318 / 2 = 159   Step 3. Add 1: 159 + 1 = 160.   So there are 160 multiples of 2 within the range: examples are 50, 52, 54, 56, 58, 60 etc.   Add the 107 multiples of 3 and the 160 multiples of 2: 107+160=267.However, by adding the multiples of 2 and the multiples of 3, we are effectively counting several numbers twice: for example, 54 and 60 are parts of both the lists above. So we can't just take   107+160= 
  107+160 = 267
267. Find the Number of multiples of 6 (which are the double counted, as 6 is divisible by both 2 and 3), and subtract it from 25:   Step 1. Subtract the extreme multiples of 6 within the range (The greatest is 72, the smallest is 54): 330 - 12= 318   Step 2. Divide by 6: 318 / 6 = 53   Step 3. Add 1: 53 + 1 =54.   So there are 54 multiples of 6 within the range: we counted 54 numbers twice.   Subtract the 54 multiples of 6 from the sum of the multiples of 2 and 3:   = 107+160 - 54   = 267 - 54= 
267 - 54 = 213
213   Therefore, the final number of multiples of 2, 3 or 6 is 213.   Hence, this is the correct answer. (213)
Answer: D
For any positive integer N, the sum of the first N positive integers equals N(N+1)/2 . If M and N are positive integers and M > N, what is the sum of all the integers between M and N, inclusive? Choose the most appropriate option:
A) M(M+1)/2 + N(N+1)/2	B) M(M+1)/2 - N(N-1)/2	C) M(M+1)/2 - N(N+1)/2	D) M(M+1)/2 + N(N-1)/2	E) M(N+1)/2 - N(M-1)/2

Solution: The sum of all the integers between M and N,inclusiveis the sum of the first M positive integersminusthe sum of the first N-1 positive integers.   The sum of the first M positive integers is M(M+1)/2;   The sum of the first N-1 positive integers is (N-1)N/2;   Therefore the answer is M(M+1)/2 - (N-1)N/2.   Answer: M(M+1)/2 - N(N-1)/2.
Answer: B
A women purchased 3 towels @ Rs.100 each, 5 towels @ Rs.150 each and two towels at a certain rate which is now slipped off from his memory. But she remembers that the average price of the towels was Rs.155. Find the unknown rate of two towels? Choose the correct choice from the following answers:
A) A)400  B) B)450  C) C)500  D) D)550  E) E)600

Solution: 10 * 155= 
10 * 155 = 1_550
1550   3 * 100 + 5 * 150= 
3 * 100 + 5 * 150 = 1_050
1050   1550 – 1050= 500   500
Answer: C
A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?	Options
A) 5	B) 6	C) 8	D) 7	E) 4

Solution: 7 * 8 : 9 * x   = 8:9 => x= 7   Answer:7
Answer: D
Which of the following describes all values of x for which 1–x^2 = 0?
Choose one:
A) x >= 1  B) x <= –1  C) x=1; x=–1  D) x =2  E) x=-2

Solution: Which of the following describes all values of x for which 1–x^2 = 0?   (A) x >= 1   Plugged in 2. 1–(2)^2 >= 0 -3>=0? NO. Wrong   (B) x <= –1   Plugged in -2. 1–(-2)^2 >= 0 -3>=0? NO. Wrong   (C) x=1; x=–1   Plugged in 1. 1–1^2 = 0. Also -1. 1–(-1)^2 = 0. Since both are correct, answer is c.   (D) x =2   1–(2)^2 = -3. Wrong.   (E) –1 <= x <= 1   1–(-2)^2 = -3. Wrong   Answer is x=1; x=–1.
Answer: C
5005 - 5000 ÷ 10.00 = ?	Choose the correct choice.
A) 0.5  B) 50  C) 5000  D) 4505  E) None

Solution: Answer   Given expression = 5005 - 5000 ÷ 10.00   = 5005 - 500= 
5005 - 500 = 4_505
4505   Correct Option: 4505
Answer: D
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 answers
A) 1:6  B) 1:0  C) 1:9  D) 1:2  E) 1:1

Solution: r1: r2 = 1: 3   Πr12: Πr22   r12: r22 = 1:9   Answer:1:9
Answer: C
What is the greater of the two numbers whose product is 1280, given that the sum of the two numbers exceeds their difference by 32? Pick.
A) A)90 B) B)100 C) C)110 D) D)70 E) 80

Solution: Let the greater and the smaller number be g and s respectively.   g*s = 1288   g + s exceeds g - s by 32 i.e., g + s - (g - s) = 32   i.e., 2s = 32 => s = 16.   g = 1280/s = 80.   ANSW80R:80
Answer: E
Find the fraction which has the same ratio to 2/3 that 3/5 has to 6/7 Choose the correct choice from the following answers.
A) 1/5
B) 2/22
C) 3/4
D) 7/15
E) 5/6

Solution: P : 2/3 = 3/5 : 6/7   As the product of the means is equal to the product of the extremes.   P*6/7 = 2/3 * 3/5   P*6/7 = 6/15   P = 7/15 => P = 7/15   ANSWER:7/15
Answer: D
An amount of Rs. 3000 becomes Rs. 3600 in four years at simple interest. If the rate of interest was 1% more, then what was be the total amount?	Choose the correct choice:
A) 3728
B) 3726
C) 3720
D) 3722
E) 3721

Solution: A = P(1 + TR/100)   => 3600 = 3000[1 + (4 * R)/100] => R = 5%   Now R = 6%   => A = 3000[1 + (4 * 6)/100] = Rs. 3720.   Answer: 3720
Answer: C
If a quarter Kg of potato costs 60 paise, How many paise will 200 gm cost?  Choose the most appropriate option.
A) 48 Paise  B) 26 Paise  C) 28 Paise  D) 11 Paise  E) 12 Paise

Solution: Explanation:   Let the Required cost be X paise. Less Weight , Less cost (Direct Proportion)   \inline \fn_jvn \therefore \inline \fn_jvn 250:200:: 60:x \inline \fn_jvn \Leftrightarrow \inline \fn_jvn 250\times X =(200\times 60) \inline \fn_jvn \Leftrightarrow \inline \fn_jvn x=\frac{(200\times 60)}{250} \inline \fn_jvn \Leftrightarrow x= 48   48 Paisenswer: 48 Paise
Answer: A
In the set of positive integers from 1 to 80, what is the sum of all the odd multiples of 5? Choose the correct answer:	A) 180	B) 245	C) 320	D) 260	E) 270

Solution: reduce to 1 - 80   5 - 15 - 25 - 35 - 45--55--65--75 are valid multiples. Add them --> 320   320
Answer: C
The difference between the two numbers is 1/3 of the larger number. If the smaller one is 48 the larger one is	Choose the correct option
A) 72 B) 60 C) 32 D) 96 E) 65

Solution: Explanation:   Let the larger number be x. Then,   x - 48 = 1/3 x   x - x/3 = 48   => 2x/3 = 48 => x = 72   72nswer: Option 72
Answer: A