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How many factors of the number 2^3 x 3 x 5^2 are even?

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How many factors of the number 2^3 x 3 x 5^2 are even?  [#permalink]

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New post Updated on: 13 Aug 2018, 01:11
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

73% (00:48) correct 27% (01:23) wrong based on 113 sessions

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e-GMAT Question:



How many factors of the number \(2^3 * 3 * 5^2\) are even?

    A) 10
    B) 12
    C) 16
    D) 18
    E) 24

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Question 2 of The e-GMAT Number Properties Marathon




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Originally posted by EgmatQuantExpert on 27 Feb 2018, 08:42.
Last edited by EgmatQuantExpert on 13 Aug 2018, 01:11, edited 3 times in total.
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Re: How many factors of the number 2^3 x 3 x 5^2 are even?  [#permalink]

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New post 27 Feb 2018, 08:51
1
The total no: of factors are denoted by (p+1)(q+1)(r+1). Therefore it would be 4*2*3 = 24

Lets remove the powers of 2 as they give even factors , then we have 3*5^2 ,which has 2*3= 6 factors

To get the even no: of factors we need to subtract the odd no: of factors from the total , that is 24-6=18 even factors.

Hence answer is option D.
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Re: How many factors of the number 2^3 x 3 x 5^2 are even?  [#permalink]

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New post 27 Feb 2018, 08:54
D) 18

Total no. factors = 4x2x3 = 24
Now the no. of factors that will be odd will have no multiple of hence count the factors which are without 2, = 2x3 = 6

Therefore no. of even factors = 24 - 6 = 18




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Re: How many factors of the number 2^3 x 3 x 5^2 are even?  [#permalink]

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New post 27 Feb 2018, 09:05
2^3 * 3 *5^2

number of even factors = 3*(1+1)*(2+1)= 3*2*3=18
The first 3 comes from the 2 with power 1 and obove (2^1, 2^2, 2^3)

Answer: D
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Re: How many factors of the number 2^3 x 3 x 5^2 are even?  [#permalink]

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New post 27 Feb 2018, 22:11
1
1

Solution:



A factor of a number can either be even or odd.
Hence, we can write:
  • Total factors of a number = Even factors of the number + Odd factors of the number.
    • Total number of factors in \(2^3 * 3 * 5^2\) = \((3+1) * (1+1) * (2+1)\) =\(4*2*3\) = \(24\).
  • From our conceptual knowledge, any number written in its prime factorized form will have odd factors only if all the prime factors of the numbers are odd.
  • Similarly, here in this question, only \(3\) and \(5\) are such prime factors of the number.
    • Odd factors in \(2^3 * 3 * 5^2\) = number of factors in \(3 * 5^2\) = \((1+1) * (2+1) = 6\)
    Since the number of odd factors of \(2^3 * 3 * 5^2\) is \(6\), and we already have the total number of factors to be \(24\), the number of even factors of \(2^3 * 3 * 5^2 = 24-6 = 18\)
Hence, the correct answer is Option D.
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Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

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Re: How many factors of the number 2^3 x 3 x 5^2 are even? &nbs [#permalink] 27 Feb 2018, 22:11
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