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How many of the integers from 100 to 999, inclusive, do NOT contain ei

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soumyap09
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How many of the integers from 100 to 999, inclusive, do NOT contain ei [#permalink] How many of the integers from 100 to 999, inclusive, do NOT contain ei   04 Dec 2023, 11:49
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69% (01:55) correct 31% (02:36) wrong based on 268 sessions
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How many of the integers from 100 to 999, inclusive, do NOT contain either the digit 2 or the digit 5?

A. 343
B. 448
C. 512
D. 648
E. 700
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B
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gmatophobia
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Re: How many of the integers from 100 to 999, inclusive, do NOT contain ei [#permalink] How many of the integers from 100 to 999, inclusive, do NOT contain ei   04 Dec 2023, 12:05
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soumyap09 wrote:
How many of the integers from 100 to 999, inclusive, do NOT contain either the digit 2 or the digit 5?

A. 343
B. 448
C. 512
D. 648
E. 700


_ _ _

The hundreds digit can be filled by 1, 3, 4, 6, 7, 8, or 9. Hence, the hundreds digits can be filled in 7 ways

The tens digit can be filled by 0, 1, 3, 4, 6, 7, 8, or 9. Hence, the tens digits can be filled in 8 ways

The unit digit can be filled by 0, 1, 3, 4, 6, 7, 8, or 9. Hence, the unit digits can be filled in 8 ways

Total number of combinations = 8 * 8 * 7 = 448

Option B
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MartyMurray
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How many of the integers from 100 to 999, inclusive, do NOT contain ei [#permalink] How many of the integers from 100 to 999, inclusive, do NOT contain ei   10 May 2024, 08:47
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­How many of the integers from 100 to 999, inclusive, do NOT contain either the digit 2 or the digit 5?

Many GMAT Quant questions can be solved in multiple ways. For instance, in the case of this question, if you didn't know how to use the approach gmatophobia used, you could use brute force.

Starting number of integers: 900

Take away all the 200 and 500s: 700

Take away all the remaining 20s and 50s: 700 - 7(10 + 10) = 560

Take away a 2 and a 5 for each of the remaining 10s: 560 - 7(8 × 2) = 560 - 112 = 448

A. 343
B. 448
C. 512
D. 648
E. 700

Correct answer: B­
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Account9855
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Re: How many of the integers from 100 to 999, inclusive, do NOT contain ei [#permalink] How many of the integers from 100 to 999, inclusive, do NOT contain ei   09 Jun 2024, 15:39
­Why doesnt this approach work?

Use either equation (for non mutually exclusive events)

=> Total # of integers = # of integers that dont have 2 + # of integers that dont have 5 - # of integers that dont have 2 and 5

Since the problem is asking for # of integers that dont have EITHER a 2 or 5, wont this also include integers that dont have a 2 but have a 5 and integers that dont have a 5 but have a 2?

What logical mistake am I making?

I appreciate any response!!!
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Bunuel
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Re: How many of the integers from 100 to 999, inclusive, do NOT contain ei [#permalink] How many of the integers from 100 to 999, inclusive, do NOT contain ei   10 Jun 2024, 00:38
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Account9855 wrote:
­Why doesnt this approach work?

Use either equation (for non mutually exclusive events)

=> Total # of integers = # of integers that dont have 2 + # of integers that dont have 5 - # of integers that dont have 2 and 5

Since the problem is asking for # of integers that dont have EITHER a 2 or 5, wont this also include integers that dont have a 2 but have a 5 and integers that dont have a 5 but have a 2?

What logical mistake am I making?

I appreciate any response!!!

­The phrase "do NOT contain either the digit 2 or the digit 5" means we are looking for numbers that do not contain either of these digits.­
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Re: How many of the integers from 100 to 999, inclusive, do NOT contain ei [#permalink]
10 Jun 2024, 00:38
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Bunuel
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