14 June Aptitude Test

Aptitude test Dr. T.K. Jain. AFTERSCHOOOL M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk

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Find the value of (1-1/2) (11/3) (1-1/4) ….. (1-1/n)? • it can be simplified as: • ½*2/3 * ¾ …. Till we get (n-1/n) • We can observe that denominator of first gets cancelled from numerator of second, similarly denominator of second gets cancelled from numerator of third and so on. • Thus the final answer is 1 / n .

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What is the minimum and maximum no. of interaction points of 5 straight lines in the same plane? • Minimum is 0 = as it is possible that they may not interact. • Maximum could where each line interact with each other line separately. Thus first line may interact with 4 lines, 2nd may interact with 3 and so on. Thus we have : 4+3+2+1+0 = 10 interactions possible.

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How many 6 digit integers are perfect squares? • The minimum number of 6 digits is 100000 and maximum one is 999999. • Minimum 6 digit perfect square is 317*317 =100489 and 1000000 is square of 1000. Thus totol number of perfect squares are: 1000-317 = 683 ans. www.afterschoool.tk

A-B = 3; A^3-B^3 = 117; A+B =? (1)5 (2) 7 (3) 9 (4) 11 • • • • •

(A-B)^3 = A^3 – B^3 -3AB(A-B) 27=117-3AB(3) 27=117-9AB; 9AB = 90 AB = 10 Thus AB can be only 5 & 2. A+B = 7 ans.

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From a square sheet of side 16 cm maximum possible circles of radius 2 cm were to be cut. By mistake we read it as .5 instead of 2. what will be the ratio of area covered now v/s projected? • Earlier we could cut 4*4 = 16 circles. • Now we have cut 16*16 = 256 circles • The area of new circle is pie*.5*.5 =.7857 and total area of new circles is 256*.7857 = 201 sq. cm • The projected area was 16* pi*2*2=201 thus ratio is 1:1 ans. www.afterschoool.tk

A cylinder of maximum possible size is made out of a solid wooden cube. How much material is lost in the process in percentage approximately?

• Let us take cube of side of 2m. Volume is 2*2*2 = 8 • Radius of cylinder will be 1 and height will be 2. volume of cylinder will be : • Pi*1*1*2 = 6.2456; area lost is 1.7544 • In % the area is 21.9% approx.

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A committee of 7 persons has be formed out of 9 men and 6 women such that majority is of men and there is at least 1 women. In how many ways can we do it?

• The possible options are: 6 +1, 5+2, 4+3. we can find their possibilities using formulae of combinations. • 9c6*6c1 = (9*8*7/3*2*1) *6 = 504 • 9c5*6c2 = (9*8*7*6/4*3*2*1) *(6*5/2*1) = 126*15 =1890 • 9c4*6c3 = (9*8*7*6/4*3*2*1) *(6*5*4/3*2*1)=126* 20=2520 • Now add these: 504+1890+2520 = 4914.

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A defence code is assigned as per the grid below. Codes show numbers from 1 to 9. vertical and horizontal sum is 15 in each case. Y:S = 1:4; S:W = 2:1; W:O = 2:3. if code is 1159, how is it written?

S

Z

O

X

V

T

W

R

Y www.afterschoool.tk

Answer : decoded: 8

1

6

3

5

7

4

9

2

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Answer continued : • 1159 = ZZVR

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A can prepare a unit in 15 days and B in 12 days. This work is worth Rs. 270. They jointly undertake the work and share amount in proportion to their efficiency. They work for 20 days. How much will A get? • Their efficiency is in ratio of 4:5. • Together they will take :1/15 +1/12 = 27/180 =3/20 or 20/3 days to complete work. In 20 days they will complete 3 units and receive 3*270 = 810 Rs. • Share of A will be 4/9 *810 =360.

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2 chords of 16 cm and 17 cm are drawn perpendicular to each other on a circle of radius 10 cm. the distance of their points of intersection from centre is what? • Find mid points of chords and their distance from Centre • Mid points are 8 & 8.5 • Distance of mid points from centre: • sqrt(10^2-8^2) =6 • sqrt(10^2-8.5^2) = 5.26 • Sqrt(36+27.75) =7.98 • Or 8 approx.

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A sphere is cut into 2 bowls (hemispheres). 6 such bowls are used to fill up one conical structure. Conical structure has diameter of 12 and height of 12. what was the radius of sphere? • • • • • • • • •

Volume of conical structure: 1/3 pi*6*6*12 =452.57 Volume of sphere is: 452.57/3 =150.8 Volume of sphere is 4/3 pi *r*r*r=150.8 R = cubic root (150.8*3/4*3.142857) =cubic root of 355 = 7 approx. We can also solve it as 4/3*pi*r*r*r*3=1/3 pi*6*6*12.

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I bought some calculators. I sold half of them at Rs. 54 and others at a profit of 5%. My net loss was 2.5%. What was my cost?

• Suppose I purchased 2 calculators at 1000 each. My loss was : 50, • On one I earned 5% = 50. Thus on other I lost Rs. 100. Selling price of loss making calculator was 900. • If selling price is 900, cost is 1000. if selling price is 54, cost is: 1000/900*54 = 60 • Thus cost price was 60 each.

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In how many ways can we select 4 letters from English Alphabet, so that we don’t have 4 consecutive letters?

• We have 26C4 ways of selecting 4 letters. ; 26*25*24*23/ 4! = 14950 • We know that we have 23 ways of selecting 4 consecutive numbers as: • Abcd, bcde, cdef, defg .. So on. • Thus we have 14950-23 = 14927 ways. www.afterschoool.tk

How many different numbers of 4 digits can be made from digits 0 to 9. (repetition not allowed) • It is a question of permutation • We can select 4 digits out of 10 in the following manner: 10p4 • =10*9*8*7=5040; but these numbers will also have 0 as the beginning number, which is not permissible. Thus we will find out all the 4 digit numbers that we have made with 0 as beginning and deduct those. • Numbers with 0 as beginning: 9P3 = 9*8*7=504 • Thus we have5040-504 = 4536 numbers from 0 to 9 (repeatition not allowed).

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28 games were played in a tournament. Each played played 1 game against each other team. How many teams were there?

• Let us say the first team plays N matches. • N(N+1)/2 = 28 • N(N+1) =56 • N = 7. Thus there were 8 teams.

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