Of the integers between 100 and 799, inclusive

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 am; Followed by:3 members

Of the integers between 100 and 799, inclusive

by VJesus12 » Thu Jun 28, 2018 5:15 am

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Of the integers between 100 and 799, inclusive, how many do not have digit 2 and 5?

(A) 310
(B) 320
(C) 410
(D) 420
(E) 520

The OA is the option B.

Is there a fast way to solving this PS question? I don't have any good idea.

Please, someone, help me. <i class="em em-disappointed"></i>

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Thu Jun 28, 2018 5:23 am

VJesus12 wrote:Of the integers between 100 and 799, inclusive, how many do not have digit 2 and 5?

(A) 310
(B) 320
(C) 410
(D) 420
(E) 520

Number of options for the hundreds digit = 5. (Of the seven digits 1-7, any but 2 or 5.)
Number of options for the tens digit = 8. (Of the ten digits 0-9, any but 2 or 5.)
Number of options for the units digit = 8. (Of the ten digits 0-9, any but 2 or 5.)
To combine these options, we multiply:
5*8*8 = 320.

The correct answer is B.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Mon Apr 29, 2019 8:09 am

VJesus12 wrote:Of the integers between 100 and 799, inclusive, how many do not have digit 2 and 5?

(A) 310
(B) 320
(C) 410
(D) 420
(E) 520

The OA is the option B.

Is there a fast way to solving this PS question? I don't have any good idea.

Please, someone, help me. <i class="em em-disappointed"></i>

Let's start with the hundreds digit; we have 5 choices (1, 3, 4, 6, 7). Each of the tens and units digits has 8 choices (any of the 10 digits except 2 and 5). Thus, there are 5 x 8 x 8 = 320 numbers that do not contain 2 and 5.

Answer: B

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