# Elitmus previous questions

1. How many five digit numbers can be formed by using the digits 0,1,2,3,4,5 such that the number is divisible by 4?
Explanation:
If a number has to be divisible by 4, the last two digit of that number should be divisible by 4.
So _ _ _ x y.  Here xy should be a multiple of 4.
There are two cases:
Case 1: xy can be 04, 20 or 40
In this case the remaining 3 places can be filled in 4×3×2 = 24.  So total 24×3 = 72 ways.
Case 2: xy can be 12, 24, 32, 52.
In this case, left most place cannot be 0.  So left most place can be filled in 3 ways.  Number of ways are 3×3×2 = 18.  Total ways = 18×4 = 72.
Total ways = 144

2. Data sufficiency question:
There are six people. Each cast one vote in favour of other five. Who won the elections?
i)  4 older cast their vote in favour of the oldest candidate
ii) 2 younger cast their vote to the second oldest
Explanation:
Total possible votes are 6.  Of which 4 votes went to the oldest person.  So he must have won the election. Statement 1 is sufficient.

3.
(Image taken while taking eLitmus Test, as you see eLitmus Test has New Layout from 2016)

4. Decipher the following multiplication table: (See and learn how to solve cryptographical elitmus problem here:)
M A D
B E
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M A D
R A E
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A M I D
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Explanation:
From the hundred's line, M + A = 10 + M or 1 + M + A = 10 + M
As A = 10 not possible, A = 9
So I = 0.
and From the thousand's line R + 1 = A. So R = 8.
M 9 D
B 1
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M 9 D
8 9  1
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9 M 0 D
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As B×D = 1, B and D takes 3, 7 in some order.
If B = 7 and D = 3, then M93×7 =   _51 is not satisfying. So B = 3 and D = 7.
2 9 7
3 1
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2 9 7
8  9  1
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9 2 0 7
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5. If
${\mathrm{log}}_{3}N+{\mathrm{log}}_{9}N$ is whole number, then how many numbers possible for N between 100 to 100?
Explanation:
${\mathrm{log}}_{3}N+{\mathrm{log}}_{9}N$ = ${\mathrm{log}}_{3}N+{\mathrm{log}}_{{3}^{2}}N$ = ${\mathrm{log}}_{3}N+\frac{1}{2}{\mathrm{log}}_{3}N$ =$\frac{3}{2}{\mathrm{log}}_{3}N$
Now this value should be whole number.
Let $\frac{3}{2}{\mathrm{log}}_{3}N$ = w
$⇒{\mathrm{log}}_{3}N=\frac{2}{3}w$
$N={3}^{\left(\frac{2}{3}w\right)}$
As N is a positive integer, So for w = 0, 3, 6 we get N = 1, 9, 81.
Three values are possible.

Ques. What will be obtained if 8 is subtracted from the HCF of 168, 189, and 231?
Op 1: 15
Op 2: 10
Op 3: 21
Op 4: None of these
Op 5:

Correct Op : 4

7. If a4 +(1/a4)=119 then a power 3-(1/a3) =
a. 32
b. 39
c.  Data insufficient
d.  36
Explanation:
Given that ${a}^{4}+\frac{1}{{a}^{4}}=119$ , adding 2 on both sides, we get : ${\left({a}^{2}+\frac{1}{{a}^{2}}\right)}^{2}=121$
$⇒{a}^{2}+\frac{1}{{a}^{2}}=11$
Again, by subtracting 2 on both sides, we have, $⇒{\left(a-\frac{1}{a}\right)}^{2}=9$
$⇒a-\frac{1}{a}=3$
Now, $⇒{a}^{3}-\frac{1}{{a}^{3}}$ = $\left(a-\frac{1}{a}\right)\left({a}^{2}+\frac{1}{{a}^{2}}+1\right)$ = 12×3 = 36