# Quant Boosters - Vikas Saini - Set 4

• Q26) There are 3 consecutive natural numbers such that square of the second is 19 more than 9 times of sum of first & third number. Find second number.

• Let 3 consecutive numbers are n-1, n and n+1.
=> n^2 – 19 = 9(n -1+n+1)
=> n^2 – 19 = 9 x 2n
=> n^2 – 18n + 19 = 0.
=> (n-19) (n+1) = 0.
=> n = 19, -1.
Second number is 19.

• Q27) Let N = 999999 ... 36 times. How many 9’s are there in N^2 ?

• 99^2 = 9801 (one 9)
999^2 = 998001 (two 9)
9999^2 = 99980001 (three 9)
Therefore (99999……….36 time)^2 should have 35 nines.

• Q28) How many positive numbers are there which is equal to 12 times sum of their digits ?

• For 2 digit number
Let the number is 10a+b.
10a + b = 12(a+b)
= > 10a + b = 12a + 12b
= > -2a = 11b
None two digit number exist here.

For 3 digit numbers
Let the number is 100a+10b+c.
100a + 10b + c = 12(a+b+c)
= > 100a + 10b + c = 12a + 12b + 12c
= > 88a – 2b = 11c.
b = 0.
= > 88 a = 11 c.
= > 8a = c.
a = 1, c = 8.
Number 108.

For 4 digit number
1000a+100b+10c+d
1000a+100b+10c+d = 12(a+b+c+d)
= > 1000 a + 100 b + 10 c + d = 12 a + 12 b + 12 c + 12 d
= > 988 a + 88b = 2c+11d
Not possible.

Hence only positive number is 108.

• Q29) If we arrange 4 different color balls like
1 red ball, 2 black balls, 3 green balls, 4 white balls
5 red balls, 6 black balls, 7 green balls, 8 white balls etc...
How many balls would be required to reach the 100th black ball ?

• Number\BallsRedBlackGreenWhite
11234
25678
39101112
413141516
517181920
621222324
725262728
8292--
Total120100105112

Total = 120 + 100 + 105 + 112 = 437.

437th ball is the 100th black ball.

• Q30) If A, B, C, D, E represent distinct digit from 1 to 5.
ABE = E x BE.
CDA = CA x AA.
BCA + CCD = EEE.
Find the value of AB x CE.

• Here given E x E = E and A x A =A.
So E = 1 or 5, A = 5 or 1.
Let’s put E = 1 and A = 5.
5B1 = 1 x B1
Not possible.
Let’s put E = 5 and A = 1.
1B5 = 5 x B5
So B = 2.
BBA + CCD = EEE.
221 + CCD = 555.
1 + D = 5.
D = 4.
2 + C = 5.
C = 3.
AB x CE = 12 x 35 = 420.

61

63

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61

34

54

46

45