MU-NLPC/Calc-aqua_rat huggingface dataset:
Find the compound interest on Rs.16,000 at 20% per annum for 9 months, compounded quarterly Select the correct option:
A) Rs 2520	B) Rs 2521	C) Rs 2522	D) Rs 2523	E) None of these

Solution: Explanation:   Please remember, when we have to calculate C.I. quarterly then we apply following formula if n is the number of years   Amount=P(1+R/4 /100)4n   Principal	= Rs.16,000;   Time=9 months	= 3 quarters;   Rate = 20%, it will be 20/4= 
20/4 = 5
5%   So lets solve this question now,   Amount=16000(1+5/100)3=18522   Rs 2522.I=18522−16000=2522   Option Rs 2522
Answer: C
Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?	Choose the correct option:
A) 900 sq.cm.
B) 700 sq.cm.
C) 800 sq.cm.
D) 400 sq.cm.
E) 600 sq.cm.

Solution: Explanation:   Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus.   BE2 + AE2 = AB2   252 = 152 + AE2 AE = √(625 - 225)= 
(625 - 225) = 400
√400= 20,   AC = 20 + 20= 
20 + 20 = 40
40 cm.   Area of a rhombus= 1/2 * d1d2   = 1/2 * 40 * 30= 
1/2 * 40 * 30 = 600
600 sq.cm.   Answer: Option 600 sq.cm.
Answer: E
In the coordinate plane, the points F (-1,1), G (1,3), and H (3,1) lie on a circle with center P. What are the coordinates of point P ?
Select
A) (0,0)	B) (1,1)	C) (1,2)	D) (1,-2)	E) (2.5, -2.5)

Solution: I thought I need to find the 4th point that would lie on the circle   Hence my answer was D (1,-1)   (1,1)ut the the center of the circle will lie on (1,1)
Answer: B
A man rows to a place 48 Km distance and back in 14 hours. He finds that he can row 4 Km with the stream in the same time 3 Km against the stream. The rate off the stream is?  Pick.
A) 5	B) 3	C) 2	D) 1	E) 4

Solution: Let be moves 4km downstream in X Hours   Then in speed downstream = Kmph   Speed in upstream = 4/X Kmph   ==> 48/4/X + 48/3/X = 14   ==> 12X + 16X =14   ==> X = 1/2   Speed in downstream = 8 Kmph   Speed in up stream = 6 Kmph   Then the Rate of stream = 1/2 (8 - 6) = 1 Kmph   Answer is 1.
Answer: D
If a(a + 8) = 9 and b(b + 8) = 9, where a ≠ b, then a + b =  Options.
A) −8 B) −2 C) 2 D) 46 E) 48

Solution: a(a + 8) = 9   => we have a = 1 or -9   also b(b + 8) = 9   => b = 1 or -9   given a ≠ b   1) when a =1, b= -9 and a + b = -8   1) when a = -9, b= 1 and a + b = -8   −8nswer choice −8
Answer: A
A man took a loan from a bank at the rate of 10% p.a. simple interest.After 3 years he had to pay Rs. 5400 interest only for the period.The principal amount borrowed by him was :  Choose the correct choice from the following answers
A) Rs. 2000
B) Rs. 10,000
C) Rs. 18,000
D) Rs. 20,000
E) None

Solution: Solution   Principal = Rs.(100x5400/10x3)= Rs. 18000.   Answer Rs. 18,000
Answer: C
The speed of a boat in upstream is 100 kmph and the speed of the boat downstream is 170 kmph. Find the speed of the boat in still water and the speed of the stream? Pick one:  A) 10 kmph  B) 17 kmph  C) 19 kmph  D) 35 kmph  E) 29 kmph

Solution: Speed of the boat in still water   = (100+170)/2= 
(100+170)/2 = 135
135 kmph. Speed of the stream= (170-100)/2= 
(170-100)/2 = 35
35kmph.   Answer: 35 kmph
Answer: D
If the average (arithmetic mean) of x + 3, x + 4, and x + 5 is 0, then x =	Select:
A) –4
B) –3
C) –2
D) –1
E) 0

Solution: (x+3 + x+4 + x+5)/3 = 0   =>3x + 12 = 0   =>x = -4   –4nswer –4
Answer: A
If population of certain city increases at the rate of 5%. If population in 1981 was 277830, then population in 1978 was?  Choose the correct option.
A) 120000 B) 120029 C) 187899 D) 178968 E) 240000

Solution: X * (105/100) * (105/100) * (105/100) = 277830   X = 277830/1.157625= 
277830/1.157625 = 240_000
240000   Answer:240000
Answer: E
There is an unlimited stock of blue, red, white, and grey coloured balls. What is the number of ways of selecting 12 balls from the stocks? Choose the correct choice from the following answers.
A) 735
B) 445
C) 455
D) 475
E) 854

Solution: Let us say that we have selected 'x1' blue balls, 'x2' red balls, 'x3' white balls and 'x4' grey coloured balls.   This means, x1+x2+x3+x4 = 12   Now, for an intance, 1+2+3+6 can be an answer. 0+0+0+12 can also be another answer   Hence, we need to find the non-negative integral solution for the equation   x1+x2+x3+x4 = n is   (n+k-1)455(k-1)   Here, n=12 and k=4   (12+4-1)455(4-1) = 154553 = 455   ANSWER:455
Answer: C
There are 4 more women than there are men on a local co-ed softball team. If there are a total of 20 players on the team, what is the ratio of men to women?	Answers:
A) 10/16
B) 6/16
C) 4/16
D) 6/10
E) 8/12

Solution: w = m+4   w+m = 20   m+4+m = 20   2m = 16   m = 8   w = 12   ratio:8:12   Ans: 8/12
Answer: E
The vertex of a rectangle are (1, 0), (5, 0), (1, 2) and (5, 2) respectively. If line L passes through the origin and divided the rectangle into two identical quadrilaterals, what is the slope of line L?
Choose the correct choice from the following answers.
A) 3 B) 6 C) 1/3 D) 1/2 E) 1/6

Solution: If line L divides the rectangle into two identical quadrilaterals, then it must pass through the center (3, 1). The slope of a line passing through (0,0) and (3, 1) is 1/3.   The answer is 1/3.
Answer: C
The value of land increases by r% during June and decreases by s% during July. If the value of the land is the same at the end of July as at the beginning of June, what is s in terms of r?  Pick one:	A) 200r/(100+2r)	B) 100r/(100+r)	C) r(2+r)/(1+r)2	D) r(200+r)/10000	E) 2r/r+2r

Solution: The simplest pairing is a 25% increase will be offset by a 20% decrease.   Here's the proof:   Starting value = 100   25% increase = 100 + (.25)(100) = 125   20% decrease = 125 - (.2)(125) = 100   Ending value = 100   So we would be looking for an answer that equals 20 when A=25. While the answers might appear 'complex', you can actually avoid much of the 'math' if you just fill in the parts and take a good look at what you have...   Answer A: (200)(25)/(150) ... since 200>150, this answer will be greater than 25. ELIMINATE A.   Answer B: (100)(25)/125) = (100)(1/5) = 20 This is a MATCH.   Answer C: (25)(27)/(26)2 ... nothing 'cancels out', so this cannot = 20. ELIMINATE C.   Answer D: (25)(225)/10000... the 'units' digit of the numerator is a 5; when dividing by 10,000, this won't end in a 0. ELIMINATE D.   Answer E:  (50/25) + 50= 
 (50/25) + 50 = 52
52. ELIMINATE E.   ans 100r/(100+r)
Answer: B
A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 19.36, the number of the member is the group is:  Answers.
A) 57 B) 67 C) 77 D) 87 E) 44

Solution: Money collected = (19.36 x 100) paise = 1936 paise.   Number of members =Square root of 1936 = 44   Answer: Option 44
Answer: E
Jayant opened a shop investing Rs. 30,000. Madhu joined him 2 months later, investing Rs. 45,000. They earned a profit of Rs. 54,000 after completion of one year. What will be Madhu's share of profit?  Choose one.
A) Rs. 27,000  B) Rs. 24,000  C) Rs. 30,000  D) Rs. 36,000  E) None of these

Solution: 30,000 *12=45,000*8   1:1   Madhu's share=1/2*54,000   i.e. Rs. 27,000   Rs. 27,000NSWER:Rs. 27,000
Answer: A
If â€˜MANIPURâ€™ is coded as â€˜DAEIGCI', then â€˜MIZORAMâ€™ is coded as  Choose the correct choice from the following choices.
A) DDFIHIA B) HIADDFI C) DFIHIAD D) DHIFIAD E) DIHFIAD

Solution: M=13,1+3=4=D   A=1=A   SIMILARLY,   M=13=1+3= 
1+3 = 4
4=D   I=9=I   Z=26=2+6= 
2+6 = 8
8=H   O=15=1+5= 
1+5 = 6
6=F   R=18=1+8= 
1+8 = 9
9=I   A=1=A   M=13=1+3= 
1+3 = 4
4=D   SO ANS IS   DIHFIAD   ANSWDIHFIADR:DIHFIAD
Answer: E
Jack purchased two chairs at a discount of 50%. Sally purchased a table at a discount of 80%. Jack spent more on his two chairs than Sally did on her table. If Jack had purchased his two chairs at a discount of 60%, he would have spent less than Sally. If z represents the undiscounted price of Sally's table, which of the following could be the average undiscounted price of Jack's two chairs, in terms of z?
Choose the correct choice.
A) 0.25z
B) 0.22z
C) 0.19z
D) 0.15z
E) 0.13z

Solution: Let the average undiscounted price of Jack's two chairs be x, so 2 undiscounted chairs cost 2x.   Jack purchased two chairs at a discount of 50% --> he paid 0.5*2x = x.   Sally purchased a table at a discount of 80% --> she paid 0.2z.   Jack spent more on his two chairs than Sally did on her table --> x > 0.2z. Eliminate options C, D and E.   If Jack had purchased his two chairs at a discount of 60%, so for   0.4*2= 
  0.4*2 = 0.8
0.8x, he would have spent less than Sally --> 0.8x < 0.2z --> x < 0.25z. Eliminate A.   Answer: 0.22z.
Answer: B
In measuring the sides of a rectangle, one side is taken 5% in excess and the other 4% in deficit. Find the error percent in the area, calculate from the those measurements. Choose the correct choice from the following
A) 0.9%
B) 0.8%
C) 0.3%
D) 0.2%
E) 0.5%

Solution: Explanation:   let x and y be the sides of the rectangle then   correct area =   =   Error% =   Answer: 0.8%) 0.8%
Answer: B
The ratio of the earnings of P and Q is 9 : 10. If the earnings of P increases by one-fourth and the earnings of Q decreases by one-fourth, then find the new ratio of their earnings?	Choose the most appropriate option:	A) 3/9	B) 3/2	C) 3/5	D) 3/6	E) 3/1

Solution: Let the earnings of P and Q be Rs. 9x and Rs. 10x respectively.   New ration = [9x + 1/4(9x)]/[10x - 1/4(10x)]   => [9x(1 + 1/4)]/[10x(1 - 1/4)]   = 9/10 * (5/4)/(3/4) => 3/2.   Answer:3/2
Answer: B
When x is divided by 2, the quotient is y and the remainder is 1. When x is divided by 5, the quotient is z and the remainder is 6. Which of the following is the value of y in terms of z?  Choose one:  A) 4z/7 + 5  B) (7z + 5) / 6  C) (6z + 7) / 4  D) (5z + 5) / 2  E) (4z + 6) / 7

Solution: When x is divided by 2, the quotient is y and the remainder is 1: x = 2y + 1.   When x is divided by 5, the quotient is z and the remainder is 6: x = 5z + 6.   Equate those two:   2y + 1 = 5z + 6;   y = (5z + 5)/2.   Answer: (5z + 5) / 2.
Answer: D
A lighting store is stocked with 410 fixtures. Some of the fixtures are floor lamps and the rest are table lamps. If 5% of the floor lamps and 30% of the table lamps are imported, what is the smallest possible number R of imported lamps stocked at the store?	Pick one: A) 3 B) 10 C) 13 D) 20 E) 23

Solution: We want to minimize not maximize the expression,.   R=x/20+(410-x)*3/10=123+x/20-3x/10=123-5x/20 --> maximize x to minimize the expression --> x must be the greatest multiple of 20 less than 410, so 400 --> 123-5*400/20=23.   But i'm guessing 123-5x/20 can be written as 123- x/4   if x has to be the greatest multiple of 4 less then 410, then it would be 408.   Hence 123-408/4 --> 123-102 -->21   Yes, you cannot reduce in this case. If x=408, then 5/100*x and (410-x)*3/10 won't be integers.23
Answer: E
In February Wilson’s earnings were 40 percent of his family’s total income. In March Wilson earned 25 percent less than in February. If the rest of his family’s income was the same in both months, then, in March, Wilson’s earnings were approximately what percent X of his family’s total income?	Choose one: A) 15% B) 17% C) 24% D) 30% E) 33%

Solution: Lets suppose the Total Family income in Feb = 100x   Wilson's earning in Feb = 40% of 100x = 40x   33%arnings of remaining family in Feb = 100x - 40x = 60x   Wilson's earning in March 100  - 40= 
100  - 40 = 60
60x   Wilson's earning in March= 75% of Wilson's Feb earnings = 75% of 40x = 30x   33%arnings of remaining family in March = 33%arnings of remaining family in Feb = 60x   Thus Wilson's earning as % of Total family income in March X= 30x/ (30+60)x = 30x/90x = 33.33%   Thus Answer is 33%
Answer: E
If a > 1, which of the following is equal to (2a + 4)/(a^2 + 2a - 3)?  Choose the correct choice from the following answers.
A) 2(a+2)/(a+3)(a-1) B) a + 3 C) 2/(a - 1) D) 2a/(a - 3) E) (a - 1)/2

Solution: Here's the algebraic approach:   (2A + 4)/(A^2 + 2A - 3) can be rewritten as...   2(A + 2)/(A+3)(A-1)   We can simplify the fraction, which leaves us with...   2(a+2)/(a+3)(a-1)ns : 2(a+2)/(a+3)(a-1)
Answer: A
If you write down all the numbers from 1 to 100, then how many multiples of 3 ?	Select.
A) A)32  B) B)38  C) C)30  D) D)31  E) E)33

Solution: Division rule for 3 - sum of all digits is multiple of 3   3 6 9 12 15 18 21 24 27 30   33 36 39 42 45 48 51 54 57 60   63 66 69 72 75 78 81 84 87 90   93 96 99   Ans - 33
Answer: E
What is the CP of Rs 100 stock at 7 discount, with 1/5% brokerage?	Choose the correct option:
A) 93.2
B) 96.2
C) 97.5
D) 98.25
E) None of these

Solution: Explanation:   Use the formula,   CP= 100 â€“ discount + brokerage%   CP= 100-7+1/5   93.2   Thus the CP is Rs 93.2.   93.2NSWER 93.2
Answer: A
If a fair die is rolled five times, what is the probability that a 3 occurs on at least one roll?
Answers:
A) 25/36  B) 125/216  C) 64/107  D) 11/36  E) 36/216

Solution: Questions such as these that talk aboutat leastormaximumorminimumin probability questions should make sure realize that probability of any event (N) to occur = 1- P(Not N)   Thus, the probability of at least 1 roll = 1- Probability of NO 3s = 1-(5/6)(5/6)(5/6)(5/6)(5/6) = 1-43/107 = 64/107.   5/6 is the probability of NOT getting a 3 in any 1 roll with 5 allowed numbers (=1,2,4,5,6) out of a total of 6 possibilities.   C is thus the correct answer.   Hope this helps.
Answer: C
A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?	Choose the correct choice from the following options:
A) 160 m  B) 190 m  C) 120 m  D) 180 m  E) 150 m

Solution: Length of the train be ‘X’   X + 120/15 = X + 180/18   6X + 720 = 5X + 900   X = 180m   Answer: 180 m
Answer: D
Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit ?
Choices.
A) 10590 B) 10500 C) 10129 D) 11129 E) 10510

Solution: Simran : Nanda = (50000 * 36) : (80000 * 30) = 3 : 4.   Simran's share = Rs. ( 24500 * 3/7)   = Rs. 10500.   Answer: 10500
Answer: B
3 men and 8 women complete a task in same time as 6 men and 2 women do. How much fraction of work will be finished in same time if 2 men and 2 women will do that task.	Select.
A) 3/7  B) 3/10  C) 3/18  D) 3/16  E) 3/11

Solution: 3 m + 8 w = 6 m + 2 w   3 m = 6 w   1 m = 2 w   Therefore 3 m + 8 w = 14 w   2 m + 2 w =6 w   3/7nswer is 6/14 =3/7   3/7nswer: 3/7
Answer: A
What is the probability for a family with three children to have a girl and two boys (assuming the probability of having a boy or a girl is equal)? Answers
A) 1/8	B) 1/4	C) 1/2	D) 3/8	E) 5/8

Solution: One possible case is: girl - boy - boy   The probability of this is 1/2*1/2*1/2= 1/8   There are 3C2 = 3 such cases so we should multiply by 3.   P(one girl and two boys) = 3/8   The answer is 3/8.
Answer: D
Which of the following fractions is greater than 1/2 and less than 9/10?
1. 1/2 2. 9/10 3. 1/3 4. 1/9 5. 3/4 6. 1/10 Choose the correct choice.
A) 1/2	B) 3/5	C) 1/10	D) 1/3	E) 9/10

Solution: 1/2= 
1/2 = 1/2 = around 0.5
0.5, 9/10= 0.9, 1/3= 0.33, 1/9= 0.11, 3/5= 0.6, 1/10= 0.1   Clearly, 0.6 lies between 0.50 and 0.9.   Therefore, 3/5 lies between 1/2 and 9/10   Answer is 3/5.
Answer: B
The difference between the squares of two consecutive odd integers
is a square<1000 whose root equals the combined sum of the digits
of the two integers. What is the sum of the digits of the larger integer?  Select:
A) 2
B) 5
C) 8
D) 10
E) 11

Solution: Assume two odd integers to be (2x-1) and (2x+1).   Difference of their squares = (2 x+1)^2 - (2x-1)^2   = 4x^2 + 1 + 4x - (4x^2 + 1 - 4x)   = 4x^2 + 1 + 4x - 4x^2 - 1 + 4x   = 8x   Now root of 8x needs to be an integer such that it is equal to the sum of the digits of the two odd integers.   8 = 2^3, so x needs to be such that it "completes" a perfect square.   If we find x, we can find the value of 2x+1 (larger integer) and then sum of its digits.   Let's check the options, starting with c.   For sum to be 8, few possibilities are: 17, 35, 53, 71   If we take 17, the pair is 15 and 17, meaning x = 8.   8x = 64   root of 64 = 4 but 4 is not equal to 1+5+1+7.   Reject.   If we take 35, the pair is 33 and 35, meaning x = 17.   8x = 8*17   Reject since perfect square is not possible.   If we take 53, the pair is 51 and 53, meaning x = 26.   8x = 8*26   Reject since perfect square is not possible.   If we take 71, the pair is 69 and 71, meaning x = 35.   8x = 8*35   Reject since perfect square is not possible.   I tried each option and the possibilities and then got lost.   Then, it occurred to me that I was only checking 2-digit integers. What about 3-digits?   Starting with option a, only 2-digit odd integer whose sum is 2 is 101.   If we take 101, the pair is 99 and 101, meaning x = 50.   8x = 8*50= 
8*50 = 400
400   root of 400= 20 which is indeed equal to 9+9+1+1.   2nswer (2).
Answer: A
P , Q and R started a business by investing Rs 120000 , Rs 135000 & Rs 150000 respectively. Find the share of each, out of the annual profit of Rs 56700	Pick one.
A) 16800 , 18900 , 21000 B) 17850 , 18900 , 21000 C) 16800 , 18900 , 22000 D) 17850, 18500 , 22000 E) None of these

Solution: Explanation :   P : Q : R = 120000 : 135000 : 150000 = 120:135:150   = 24:27:30   = 8:9:10   Share of P= 56700*8/27 = 2100*8= 
2100*8 = 16_800
16800   Share of Q= 56700*9/27 = 2100*9= 
2100*9 = 18_900
18900   Share of R= 56700*10/27 = 2100*10= 
2100*10 = 21_000
21000. 16800 , 18900 , 21000nswer : Option 16800 , 18900 , 21000
Answer: A
The arithmetic mean and standard deviation of a certain normal distribution are 15.5 and 1.5, respectively. What value is exactly 2 standard deviations less than the mean?  Choose the most appropriate option.
A) 10.5  B) 11  C) 11.5  D) 12  E) 12.5

Solution: The value which isexactlytwo SD less than the mean is:mean-2*SD=15.5-2*1.5=12.5.   Answer: 12.5.
Answer: E
A bookseller has two display windows. She plans to display 5 new fiction books in the left window, and 3 new non-fiction books in the right window. Assuming she can put the three fiction books in any order, and separately, the three non-fiction books in any order, how many total configurations will there be for the two display windows?  Select the correct option.
A) 240  B) 720  C) 144  D) 336  E) 420

Solution: Two displays books could be arranged n! # of total arrangements are combinations multiplied together,   5!*3! =120*6= 
120*6 = 720
720   Answer is 720
Answer: B
A student multiplied a number by 3/5 instead of 5/3, What is the percentage error in the calculation ?
Choose the correct choice from the following:
A) 22
B) 64
C) 365
D) 29
E) 36

Solution: Let the number be x.   Then, ideally he should have multiplied by x by 5/3. Hence Correct result was .   By mistake he multiplied x by 3/5 . Hence the result with error =   Then, error =   Error % = = 64 %   Answer: 64
Answer: B
Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 4 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?  Choose the correct choice from the following choices
A) 5 : 1  B) 10 : 5  C) 15 : 2  D) 20 : 2  E) 25 : 2

Solution: U/I = 4/2   I/B = 5/1   Since I is multiple of both 2 (as per first ratio) and 5 (as per second ratio) so let's assume that I = 10   i.e. Multiplying teh first ratio by 5 and second ration by 2 in each numerator and denominator   then, U : I : B = 20 : 10 : 2   i.e. U : B = 20 : 2   Answer: Option 20 : 2
Answer: D
If A speaks the truth 20% of the times, B speaks the truth 80% of the times. What is the probability that at least one will tell the truth
Choose the most appropriate option
A) 0.82  B) 0.84  C) 1.5  D) 1.2  E) 1.4

Solution: probability of A speaks truth p(A)=2/10;false=8/10   probability of 0.84 speaks truth p(0.84)=8/10;false=2/10.For given qtn   Ans=1-(neither of them tell truth).0.84ecause A & 0.84 are independent events   =1-[(8/10)*(2/10)]=1-16/100=1-0.16= 
1-0.16 = 0.84
0.84   ANSWER:0.84
Answer: B
A man saved $2.50 in buying some lumber on sale. If he spent $25 for the lumber, which of
the following is closest to the percentage he saved?	Choose the correct choice from the following choices
A) 8% B) 9% C) 10% D) 11% E) 12%

Solution: 2.5/27.5 = 1/11 = 9/99 which is close to 9%.   correct answer 9%
Answer: B
If a student loses 6 kilograms, he will weigh twice as much as his sister. Together they now weigh 126 kilograms. What is the student's present weight in kilograms?	Choose the correct answer:
A) 82 B) 84 C) 86 D) 88 E) 90

Solution: Let x be the weight of the sister.   Then the student's weight is 2x+6.   x + (2x+6) = 126   3x = 120   x = 40 kg   Then the student's weight is 86 kg.   The answer is 86.
Answer: C
If (x + 1) times (2x + 1) is an odd integer, then x must be Choices.
A) an odd integer B) an even integer C) a prime number D) a composite number E) a negative integer

Solution: (x + 1) times (2x + 1) means (x + 1) * (2x + 1)..   (x + 1)*(2x + 1)= 2x^2+3x+1...   for 2x^2+3x+1 to be odd, 3x+1 should be odd..   hence 3x should be even, which further leads to x as even..   so x is even integer..   ANSWER:an even integer
Answer: B
A certain sum of money doubles itself in 15 years in how much many years will it trible itself at the same rate?
Answers
A) 20 years	B) 30 years	C) 88 years	D) 44 years	E) 11 years

Solution: 100 ---- 100 --- 15   100 --- 15   --------------------   300 ---- 30 years   Answer: 30 years
Answer: B
If a·b·c·d=330, where a, b, c and d are positive integers, and a<b<c<d, which of the following could be the value of d−a? Select the correct option:
A) 9  B) 10  C) 11  D) 13  E) 15

Solution: prime factorize : 330 = 2*3*5*11   Hence a = 2 and d = 11 .   Hence answer is  11 - 2= 
 11 - 2 = 9
9   9nswer 9
Answer: A
Evaluate: 983 x 207 - 983 x 107 Choose the most appropriate option:  A) 98300  B) 98500  C) 98600  D) 98900  E) 98100

Solution: 983 x 207 - 983 x 107 = 983 x (207 - 107) = 983 x 100 = 98300.   98300nswer is 98300.
Answer: A
Caleb and Kyle built completed the construction of a shed in 10 and half days. If they were to work separately, how long will it take each for each of them to build the shed, if it will take Caleb 2 day earlier than Kyle?  Choose the correct choice
A) 10 and 12
B) 9 and 11
C) 20 and 22
D) 8 and 10
E) 19 and 21

Solution: Work = (A)(B)/(A+B) where A and B are the individual times of each entity.   Here, we're told that (working together) the two workers would complete a job in 12 days. This means that (individually) each of them would take MORE than 10 days to do the job.   Answers E, A and C are illogical, since the individual times must both be greater than 10 days.   so we can TEST the values for Answers B and D.   Using the values for Answers B and D...   Answer B: (20)(22)/(20+22) = 440/42 = 10.5 This is a match   Final Answer:   20 and 22
Answer: C
A & B started a partnership business. A's investment was thrice the investment of B and the period of his investment was two times the period of investments of B. If B received Rs 6000 as profit , what is their total profit? Choose the correct choice from the following
A) 28000 B) 30000 C) 42000 D) 34000 E) None of these

Solution: Explanation :   Suppose B's investment = x. Then A's investment= 3x   Suppose Bs period of investment = y, then A's period of investment = 2y   A : B = 3x * 2y : xy   = 6 : 1   Total profit * 1/7 3  * 2= 
3  * 2 = 6
6 : 1   Total profit * 1/7= 6000   => Total profit = 6000*7= 
6000*7 = 42_000
42000. Answer : Option 42000
Answer: C
In one hour, a boat goes 9 km along the stream and 5 km against the stream. The speed of the boat in still water (in km/hr) is:	Pick
A) 2	B) 4	C) 7	D) 12	E) 15

Solution: Sol.   Speed in still water = 1/2 (9+5) kmph = 7 kmph.   Answer 7
Answer: C
Mahesh marks an article 15% above the cost price of Rs. 540. What must be his discount percentage if he sells it at Rs. 496.80?	Select the correct option
A) 18% B) 21% C) 20% D) 19% E) None of these

Solution: CP = Rs. 540, MP = 540 + 15% of 540 = Rs. 621   SP = Rs. 496.80, Discount = 621 - 496.80= 
621 - 496.80 = 124.2
124.20   Discount %= 124.2/621 * 100= 
124.2/621 * 100 = 20
20%   ANSWER:20%
Answer: C