MU-NLPC/Calc-aqua_rat huggingface dataset:
Two trains start from P and Q respectively and travel towards each other at a speed of 50 km/hr and 40 km/hr respectively. By the time they meet, the first train has traveled 100 km more than the second. The distance between P and Q is?	Choose the correct choice from the following answers:
A) 767 km
B) 975 km
C) 678 km
D) 900 km
E) 546 km

Solution: At the time of meeting, let the distance traveled by the second train be x km. Then, distance covered by the first train is (x + 100) km.   x/40 = (x + 100)/50   50x = 40x + 4000 => x = 400   So, distance between P and Q = (x + x + 100)km =900 km.   Answer: 900 km
Answer: D
All of the students of the Music High School are in the band, the orchestra, or both. 90 percent of the students are in only one group. There are 84 students in the band. If 60 percent of the students are in the band only, how many students are in the orchestra only?	Choose the correct choice from the following choices.
A) 24 B) 27 C) 30 D) 33 E) 36

Solution: 60% of students are in the band only, so 30% of students are in the orchestra only.   Since 10% of students are in both, then 70% of students are in the band which is 84 students.   The number of students in the orchestra is  (30/70)*84= 
 (30/70)*84 = 36
36.   The answer is 36.
Answer: E
Danny bought 2Q steaks for W dollars. Jerome buys R steaks for a 50% discount, how much will the steaks cost him in cents? Choose the correct choice:
A) 50RW/Q.
B) 50QR/W.
C) 25RQ/W.
D) 25RW/Q.
E) RW/(4Q).

Solution: 25RW/Q.anny bought 2Q steaks for W dollars, so 1 steak = W/2Q   Jerome buys R steaks for a 50% discount: r* (W/4Q)   in cents the answer will be : r* (100 W/4Q)= 25 RW/Q
Answer: D
The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is? Answers
A) 23  B) 21  C) 52  D) 56  E) 12

Solution: Let the total number of workers be x. Then,   8000x   = (12000 * 7) + 6000(x - 7)   = 2000x = 42000   = x =21.   Answer:21
Answer: B
When a certain perfect square is increased by 148, the result is another perfect square. What is the value of the original perfect square? Pick one:
A) 1296  B) 1369  C) 1681  D) 1764  E) 2500

Solution: Let’s call the two perfect squares x^2 and y^2, respectively. Then the given information translates as x^2+148=y^2. Subtracting x^2 gives 148=y^2−x^2, a difference of squares. This, in turn, factors as (y+x)(y−x)=148.   The next step is tricky. It begins with factoring 148, which breaks down as 2∗2∗37. Since we’re dealing with perfect squares, x and y are positive integers, and (y+x) and (y−x) must be paired integer factors of 148. The options are 148∗1,74∗2, and 37∗4. But our number properties establish that (y+x) and (y−x) must be either both odd or both even, so only 74∗2 is an actual possibility. And because for any positive integers (y+x)>(y−x), we can conclude that y+x=74 and y–x=2. Solving by elimination, 2y=76, y=38, and x=36.   Finally, we just need to square 36 . But rather than multiplying it out, note that 36^2 ends in 6 – as does only one answer, choice A. This answer must be the one we want.
Answer: A
If population of certain city increases at the rate of 5%. If population in 1981 was 138915, then population in 1978 was?	Choose the correct choice from the following answers:  A) 120000  B) 120029  C) 187899  D) 178968  E) 789698

Solution: X * (105/100) * (105/100) * (105/100) = 138915   X = 138915/1.157625= 
138915/1.157625 = 120_000
120000   120000nswer:120000
Answer: A
If G = 775 × 778 × 781, what is the remainder when G is divided by 14?  Choose the correct choice from the following answers
A) 6
B) 7
C) 8
D) 9
E) 10

Solution: G 775/14 leaves a remainder 5   778/14 leaves a remainder 8   781/14 leaves a remainder 11   5*8*11= 
5*8*11 = 440
440   So the remainder will be the remainder of 440/14 which is 6   6ns 6
Answer: A
How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?  Choose the correct choice from the following:	A) 1245	B) 4175	C) 5412	D) 4712	E) 6400

Solution: Number of bricks = Volume of the wall/Volume of 1 brick = (800 x 600 x 22.5) /(25 x 11.25 x 6)=6400.   Ans: 6400
Answer: E
ABCDEFGHI is a regular polygon with nine sides. What is the measure in degrees of angle ACB?	Choose the correct choice from the following choices:
A) 18  B) 20  C) 25  D) 27  E) 30

Solution: the formula of sum of angles in a polygon of sides n=(n-2)*180   so sum of angles=7*180..   therefore each angle ,angle ABC=7*180/9=140..   when we join A and C to make a triangle ABC, it becomes an isosceles triangle with AB and BC equal..   so angle ACB=angleCAB=(180-140)/2=20..   ans 20
Answer: B
An uneducated retailer marks all his goods at 40% above the cost price and thinking that he will still make 25% profit, offers a discount of 25% on the marked price. What is his actual profit on the sales? Choose one:
A) 12.50 %  B) 13.50 %  C) 5 %  D) 14.50 %  E) None

Solution: Sol.   Let C.P. = Rs. 100. Then, marked price = Rs. 140.   S.P. = 75% of Rs. 140 = Rs. 105.   ∴ Gain% = 5%.   Answer 5 %
Answer: C
21 ball numbered 1 to 21. A ballis drawn and then another ball is drawn without replacement.  Choose the most appropriate option
A) 1/15  B) 3/53  C) 9/42  D) 6/15  E) 7/12

Solution: The probability that first toy shows the even number,   =1021=1021   Since, the toy is not replaced there are now 9 even numbered toys and total 20 toys left.   Hence, probability that second toy shows the even number,   =920=920   Required probability,   =(1021)×(920)=(1021)×(920)   =9/42   9/42
Answer: C
The maximum numbers of students among them 451 pens and 410 toys can be distributed in such a way that each student gets the same number of pens and same number of toys is	Options:
A) 41	B) 910	C) 1001	D) 1911	E) None

Solution: olution   Required number of students.   = H.C.F of 451 and 410.   â€¹=â€º41.   41nswer 41
Answer: A
If you cut a 18ft piece of wood into two pieces making one piece 4ft longer than the other. What size is the smaller piece? Pick:
A) 4ft
B) 6ft
C) 8ft
D) 7ft
E) 12ft

Solution: Total length is 18ft, one piece is 4ft longer (x+4), leaving the other piece to figure out (x).   (x)+ (x+4)=18   x+x+4-4=18-4   2x=14   2x/2=14/2= 
14/2 = 7
7   The piece is 7ft) 7ft.
Answer: D
When is |x-14| = 14-x?
Choose the most appropriate option.
A) x=14	B) x=0	C) x>14	D) x<=14	E) x< 0

Solution: When is |x-14| = 14-x?   Choice A: X=14, it is true but X cannot be always 14   Choice B: X=0, it is also true, but X cannot be always 0   Choice C: X>14, it is false, for e.g. X=6, then one side of equation is 2 and the other side is -2   Choice D: X<=14, this choice encapsulate Choice A, Choice B and for all other conditions and is true for above said equation. Hence the answer choice is x<=14.
Answer: D
The average age of a husband, wife and their child 5 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is?
Choose the most appropriate option
A) 10.1 years  B) 54 years  C) 11.4 years  D) 12.6 years  E) 14 years

Solution: Sum of the present ages of husband, wife and child   = (23 * 2 + 5 * 2) = 57 years.   Required average   = 57/5= 
57/5 = 57/5 = around 11.4
11.4 years.   Answer:11.4 years
Answer: C
What least no. must be subtracted from 427398 so that remaining no.is divisible by 10?  Choose the most appropriate option:
A) 8 B) 9 C) 7 D) 6 E) 3

Solution: Explanation:   On dividing 427398 by 10 we get the remainder 8, so 8 should be subtracted   Option 8
Answer: A
If the selling price of 50 articles is equal to the cost price of 30 articles, then the loss or gain percent is:	Select the correct option
A) 40% B) 23% C) 20% D) 60% E) 56%

Solution: C.P. of each article be Re. 1.   Then, C.P. of 50 articles = Rs. 50;   S.P. of 50 articles = Rs. 30.   Loss % = 20/50 * 100= 
20/50 * 100 = 40
40%   40%NSWER 40%
Answer: A
If 4 spiders make 3 webs in 9 days, then how many days are needed for 1 spider to make 1 web?	Choose the correct choice:	A) 9	B) 12	C) 27	D) 24	E) 16

Solution: Explanation:   Let, 1 spider make 1 web in x days.   More spiders, Less days (Indirect proportion)   More webs, more days (Direct proportion)   Hence we can write as   (spiders)4:1   (webs) 1:9}::x:3   â‡’4Ã—1Ã—9=1Ã—3 Ã— x   â‡’x=12   Answer: Option 12
Answer: B
A man on tour travels first 160 km at 72 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:
Choose the correct choice from the following choices.
A) 31.11 km/hr	B) 35.55 km/hr	C) 71.11 km/hr	D) 36 km/hr	E) 75.8 km/hr

Solution: Total time taken = 160/72 + 160/80 = 3040/720 = 38/9 hours   --> Average speed = 320 x 9/38 = 75.8 km/hr.   Answer : 75.8 km/hr.
Answer: E
Find out the C.I on Rs.9000 at 4% p.a. compound half-yearly for 1 1/2 years
Choices.
A) 550.87  B) 506.07  C) 506.04  D) 506.03  E) 306.01

Solution: 550.87 = 9000(51/50)3   = 9550.87   9000   -----------   550.87   550.87nswer:550.87
Answer: A
A customer bought a product at the shop. However, the shopkeeper increased the price of the product by 10% so that the customer could not buy the required amount of the product. The customer managed to buy only 80% of the required amount. What is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase? Choose the correct choice.
A) 10% B) 12% C) 14% D) 16% E) 18%

Solution: Let x be the amount of money paid for the first purchase.   The second time, the customer paid 0.8(1.1x)=0.88x.   The difference is 12%.   The answer is 12%.
Answer: B
The population of a town increased from 75,000 to 2,25,000 in a decade. The average percent increase of population per year is : Pick
A) 20%	B) 5%	C) 6%	D) 8.75%	E) None of these

Solution: Solution   Increase in 10 year= (225000 - 75000)= 
(225000 - 75000) = 150_000
150000.   Increase%=( 150000/75000x 100 )% = 200%   âˆ´ Required average = ( 200/10 )= 
( 200/10 ) = 20
20%   20%nswer 20%
Answer: A
In how many ways can 4 men & 3 women can be made from a gang of 6 men & 7 women ? Select the correct option
A) 10 hr
B) 50
C) 20
D) 250
E) 260

Solution: Explanation:   6C4 * 7C3 = 50   50
Answer: B
The side of a square is increased by 10% then how much % does its area increases?
Pick one:
A) 40.00 %
B) 10.00 %
C) 25.00 %
D) 21.00 %
E) 15.00 %

Solution: a = 100 a2 = 10000   a = 110 a2 = 12100   ----------------   10000 --------- 2100   100 -------? => 21.00 %   Answer:21.00 %
Answer: D
What is the sum of the different positive prime factors of 550?	Choose the correct choice from the following options.
A) 10	B) 11	C) 15	D) 16	E) 18

Solution: I think answer is 18: 27   550 = 55 * 10 = (5 * 11) * (2 * 5)   Sum of theDIFF18R18NTpositive prime factors = 2 + 5 + 11= 
2 + 5 + 11 = 18
18
Answer: E
Two dice are tossed. The probability that the total score is a prime number is:	Choose the correct choice from the following
A) 5/12 B) 5/10 C) 6/12 D) 9/12 E) 4/12

Solution: Clearly, n(S) = (6 x 6) = 36.   Let E = Event that the sum is a prime number.   Then E	= { (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3),   (5, 2), (5, 6), (6, 1), (6, 5) }   n(E) = 15.   P(E) = n(E)/n(S) = 15/36	= 5/12.   5/12nswer:5/12
Answer: A
The average (arithmetic mean) of y numbers is x. If 10 is added to the set of numbers, then the average will be x - 5. What is the value of y in terms of x ?
Choose one.
A) x/6 - 6
B) x/6 - 5
C) x/7 - 5
D) x/5 - 3
E) x/5 - 6

Solution: (A1 + A2 + .. + Ay)/y = x   (A1 + A2 + .. + Ay + 10)/(y+1) = x - 5   => (xy + 10)/(y+1) = x - 5   => xy +10 = yx -5y + x - 5   => 15 = x - 5y   => 5y = x - 15   => y = x/5 - 3   Answer - x/5 - 3
Answer: D
The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 3025 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
Answers.
A) 140 B) 150 C) 160 D) 170 E) 220

Solution: Given that the area of the square = 3025 sq.units   => Side of square = √3025 = 55 units   The radius of the circle = side of the square = 55 units   Length of the rectangle = 2/5 * 55= 
2/5 * 55 = 22
22 units   Given that breadth= 10 units   Area of the rectangle = lb = 22 * 10= 
22 * 10 = 220
220 sq.units   Answer: Option 220
Answer: E
The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is?  Options
A) 36.3
B) 36.7
C) 36.5
D) 36.2
E) 36.1

Solution: Correct sum = (36 * 50 + 48 - 23)= 
(36 * 50 + 48 - 23) = 1_825
1825.   36.5orrect mean= 1825/50= 
1825/50 = 73/2 = around 36.5
36.5   Answer:36.5
Answer: C
A division of a company consists of six men and five women. If two of these employees are randomly selected as representatives of the division, what is the probability that both representatives will be female?	Choose the correct answer
A) 1/6
B) 2/5
C) 2/11
D) 5/12
E) 7/15

Solution: Total number of ways to select 2 members = 112/112 = 55   Total number of ways to select 2 females = 52/112 = 10   P(two females) = 10/55 = 2/11   The answer is 2/11.
Answer: C
HOW MANY KGS OF TEA WORTH RS.20/KG MUST BE BLENDED WITH 30 KGS OF TEA WORTH RS.30/KG SO THAT BY SELLING THE BLENDED VARIETY AT RS.30/KG THERE SHOULD BE A GAIN OF 10%
Choose the correct choice from the following answers
A) 3	B) 4	C) 6	D) 5	E) 2

Solution: (x+30)*30=(110/100)(20x+30*30)   Solving we get 3.   3nswer is 3.
Answer: A
If the reciprocals of two consecutive positive integers are added together, what is the sum in terms of the greater integer d?	Choose the correct choice:  A) (3d-1)/(d^2- d)  B) (2d-1)/(d^4- d)  C) d^2- d  D) 2d-1  E) (2d-1)/(d^2- d)

Solution: Let two consecutive positive integers be d and d-1 (Greater integer is d)   So,   (1/d) + [1/(d-1)]   = (2d-1)/d(d-1)   =(2d-1)/(d^2- d)   Answer : (2d-1)/(d^2- d)
Answer: E
Find the natural number nearest to 9217 which completely divides 88 without giving any remainder.	Choose the correct choice from the following answers:
A) 9240 B) 9064 C) 9184 D) 9152 E) 9169

Solution: Explanation:   These types of questions are to be solved by trial and error. Make sure minimum amount of time is wasted and your calculations are quick. Devote maximum 1 minute to such questions.   Here in this case clearly 9240 is the closest number which divides 88.   9240NSWER: 9240
Answer: A
If 15 students in a class average 70% on an exam and 10 students average 90% on the same exam, what is the average in percent for all 25 students?
Choices.
A) 78%	B) 79%	C) 80%	D) 81%	E) 82%

Solution: (15*70 + 10*90) / 25= 
(15*70 + 10*90) / 25 = 78
78%   The answer is 78%.
Answer: A
If X,Y is 24%,30% smaller than Z then how much percentage is Y greater than X?
Choose the correct choice from the following choices.
A) 7 17/19 %  B) 13%  C) 13 1/2%  D) 14%  E) 15%

Solution: X = 76%   Y = 70 %   Z = 100 %   X-Y/X × 100 = 6/76 × 100 = 7 17/19 % greater than X   7 17/19 %)
Answer: A
The difference between a number and its two-fifth is 510. What is 40% of that number?  Answers.
A) 342
B) 340
C) 344
D) 346
E) 348

Solution: Let the number be x. Then,   x - 2/5 x = 510   x = (510 * 5)/3= 
(510 * 5)/3 = 850
850   40% of 850= 340.   Answer:340
Answer: B
If a boat goes 7 km upstream in 42 minutes and the speed of the stream is 4 kmph, then the speed of
the boat in still water is  Choose the correct choice from the following options.
A) 12 kmph
B) 13 kmph
C) 14 kmph
D) 15 kmph
E) None of these

Solution: Explanation:   Rate upstream = (7/42)*60= 
(7/42)*60 = 10
10 kmph.   Speed of stream= 4 kmph.   Let speed in still water is x km/hr   Then, speed upstream = (x ï¿½4) km/hr.   x-4 = 10 or x = 14 kmph   Answer: 14 kmph
Answer: C
There 3 kinds of books in the library physics, chemistry and biology. Ratio of physics to chemistry is 3 to 2; ratio of chemistry to biology is 4 to 3, and the total of the books is more than 3000. Which one of following can be the total R of the book?
Choose the correct choice from the following:	A) 3003	B) 3027	C) 3024	D) 3021	E) 3018

Solution: First, you have to find the common ratio for all 3 books. You have:   P:C:B   3:2 --> multiply by 2 (gives you row 3)   4:6   6:4:3   Hence:   P:C:B:T(Total)R   6:4:3:13 ----> This means, the Total Number must be a multiple of 13.   3003nswer 3003 is correct since 299 is divisible by 13, hence is 2990 and so is 3003 (2990+13).
Answer: A
If x, y, and z are consecutive odd integers, with x < y < z, then which of the following must be true?
I. x + y is odd
II. (x+z)/y is an integer
III. xz is even Answers:
A) I only  B) II only  C) III only  D) I and II only  E) I, II, and III

Solution: consecutive odds are:   2x+1, 2x+3, 2x+5   I. 2x+1+2x+3=4x+4=2(2x+2), so divisible by 2 and even - NOT TRUE   II. 2x+1+2x+5=4x+6/2x+3=2(2x+3)/2x+3=2, so integer - TRUE   III. (2x+1)*(2x+5)=4x^2+10x+2x+5=4x^2+12x+5=(2x(x+6)+5)/2 is not integer, so NOT TRUE   ANSWER: II only
Answer: B
If A = c% of y and B = y% of c, then which of the following is true?  Choose the correct option.
A) 1) A is smaller than B.	B) 2) A is greater than B	C) 3) Relationship between A and B cannot be determined.	D) 4) If x is smaller than y, then A is greater than B.	E) 5) None of the above

Solution: Basically A = B = cy/100   None of the options mentions this; hence 5) None of the above.
Answer: E
Riya and Priya set on a journey. Riya moves eastward at a speed of 25kmph and Priya moves westward at a speed of 40 kmph.How far will be priya from Riya after 15 minutes Pick
A) 18kms B) 16kms C) 50kms D) 30kms E) 40kms

Solution: total eastward distance= 25kmph*1/4hr=6.25 km   total westward distance= 40kmph*1/4hr=10 km   total distn betn them= 6.25+10= 
6.25+10 = 16.25
16.25km   ans 16km   ANSWER:16kms
Answer: B
An unbiased die is tossed. Find the probability of getting a multiple of 4 Choose the correct choice
A) A)1/3 B) B)2/5 C) C)1/4 D) D)1/6 E) E)3/7

Solution: Here S = {1,2,3,4,5,6}   E = event of getting a multiple of 4   E = {4}   P(E) = 1/6   Answer is 1/6
Answer: D
A number of 53 marbles is to be divided and contain with boxes. If each box is to contain 3, 4, or 5 marbles, what is the largest possible number of boxes?	Choices
A) 10 B) 12 C) 15 D) 16 E) 17

Solution: To maximize # of boxes we should minimize marbles per box: 16*3+1*5= 
16*3+1*5 = 53
53 --> 16+1=17.   Answer: 17.
Answer: E
The hen lays 3 eggs then she lays 6 eggs more. Totally how many eggs she lays? Choose the correct choice from the following:	A) 3	B) 9	C) 19	D) 11	E) 23

Solution: 3+6= 
3+6 = 9
9. Answer is 9.
Answer: B
The operation T is defined by x T y=1/x+1/y for all nonzero numbers x and y. If z is a number greater than 1, which of the following must be true.
I. x T (-z)=0
II. 2/z T 2/z=z
III. z T z/z-1=1 Choose the correct choice from the following answers:
A) a.) I B) b.) I and II only C) c) I and III only D) d) II and III only E) e) I, II and III only

Solution: Statement I is TRUE   Statement II is TRUE   Statement III is not TRUE   Answer : b.) I and II only
Answer: B
N is an even 3-digit number such that the last 3 digits of N^2 are N itself. What is the value of N? Choose the most appropriate option.
A) 141376	B) 241376	C) 141476	D) 181376	E) 141396

Solution: 376*376= 
376*376 = 141_376
141376   141376NSWER:141376
Answer: A
Sheik Abdullah decides to buy 2 new cars for his collection. If he has to choose between nine different cars, what is the number of purchasing possibilities he has?
Pick one
A) A)1312	B) B)1412	C) C)1512	D) D)1612	E) E)1712

Solution: Sheik Abdullah decides to buy 2 new cars for his collection. He has to choose between nine different cars   815123= 9*8*7*6/(2*1)= 
9*8*7*6/(2*1) = 1_512
1512 ANS:1512
Answer: C
At a certain school, the ratio of the number of English majors to the number of Sociology majors is 5 to 2, and the ratio of the number of Psychology majors to the number of Sociology majors is 3 to 4. If the ratio of the number of History majors to the number of English majors is 5 to 3, what is the ratio of the number of Psychology majors to the number of History majors	Choices.
A) 25 to 3	B) 10 to 9	C) 9 to 50	D) 6 to 25	E) 3 to 10

Solution: Correct   25 to 3
Answer: A
If p = ||q – 3| – 2|, for how many values of q is m = 6?	Choose the most appropriate option.
A) 5  B) 4  C) 3  D) 2  E) 1

Solution: p = ||q – 3| – 2| can be 4 only and only when q-3= +/-8. so there are 2 values of q   Answer : 2
Answer: D
x% of y is y% of ?  Select the correct option.
A) x	B) 100x	C) x/100	D) y/100	E) None

Solution: xnswer   Let x% of y = y% of x, then   ⇒ xy / 100 = yx/100   ∴ x = (xy/100) x (100/y) = x   Correct Option: x
Answer: A
How many odd three-digit integers greater than 400 are there such that all their digits are different?
Choose the correct choice from the following choices
A) 140	B) 156	C) 172	D) 181	E) 200

Solution: 5 (hundred's digit) * 9 (ten's digit) * 8 (unit's digit) = 360   Now take numbers in the range 400 - 900.   Total numbers where all digits are different = 360 (as before)   [highlight]Number of odd numbers = 5 * 8 * 5= 
5 * 8 * 5 = 200
200[/highlight] (now there are 5 possibilities for the unit's digit)   200
Answer: E
In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
A. 40  Choose the correct choice from the following choices:
A) 87  B) 8  C) 46  D) 44  E) 64

Solution: Explanation:   Let the capacity of the can be T litres.   Quantity of milk in the mixture before adding milk = 4/9 (T - 8)   After adding milk, quantity of milk in the mixture = 6/11 T.   6T/11 - 8 = 4/9(T - 8)   10T = 792 - 352 => T = 44.   Answer: Option 44
Answer: D
g is a negative number and h is a positive number, which of the following options must be positive?  Choose the correct choice from the following options
A) 2g/h
B) h/g
C) (a + b)^4
D) g/h
E) gh

Solution: A. 2g/h   -ve/+ve=-ve   B.h/g   -ve/+ve=-ve   (a + b)^4.(a + b)^2   will be positive irrespective of the absolute values of x and y   will be positive always   D.g/h   -ve/+ve=-ve   B.gh   -ve*+ve=-ve   (a + b)^4orrect answer (a + b)^4
Answer: C
In a right angled triangle, two sides are consecutive whole number in which one side is hypotenuse. what could be the possible length of third side?  Choose the correct choice from the following choices: A) 277 B) 361 C) 269 D) 171 E) 112

Solution: Explanation:   Pythagorean triplets are generated with each "odd number" greater than 1 by using a formula.   If n is an odd number, then Pythagorean triplet = n,n2−12,n2+12n,n2−12,n2+12.   Here 361 is an odd number. So the triplet is 361, 65160, 65161.   Answer:361
Answer: B
In 1990 a total of p earthquakes occurred worldwide, some but not all of which occurred in Asia. If r of these earthquakes occurred in Asia, which of the following represents the ratio of the number of earthquakes that occurred in Asia to the number that did NOT occur in Asia?	Choices.
A) p/r
B) r/p
C) r/(p-r)
D) p/(p-r)
E) 1- (r/p)

Solution: We're given a couple of facts to work with:   1) There were a total of p earthquakes   2) Of those earthquakes, r of them occurred in Asia   We're asked for the ratio of the number of earthquakes that occurred IN ASIA to the number of earthquakes that DID NOT occur in Asia.   Let's TEST VALUES   p = 5 total earthquakes   r = 2 occurred in Asia   Thus, there were 3 earthquakes that DID NOT occur in Asia....   The answer to the question is 2:3   We just need to plug in the values for p and r and find the match...   Answer A: p/r = 5/2 NOT a match   Answer B: r/p = 2/5 NOT a match   Answer r/(p-r): r/(p-r) = 2/(5-2) = 2/3 This IS a match   Answer D: p/(p-r) = 5/(5-2) = 5/3 NOT a match   Answer E: 1 - (r/p) = 1-2/5 = 3/5 NOT a match   r/(p-r)
Answer: C
The length of a rectangle is double its width. If the length is diminished by 5cm and the width is increased by 5cm then its area is increased by 75cm square. What is the length of the rectangle?	Choose the most appropriate option:
A) 20
B) 30
C) 40
D) 56
E) 65

Solution: Sol. According to question   (l-5)(b+5)-lb = 75   And l = 2b   So, b = 20, l = 40   Ans.(40)
Answer: C