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Three digits have been removed from each of the following nu

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GMAT Club Legend
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Joined: 07 Jun 2014
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Three digits have been removed from each of the following nu [#permalink] New post 27 Mar 2018, 16:25
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Question Stats:

63% (00:52) correct 36% (01:31) wrong based on 11 sessions
Three digits have been removed from each of the following numbers. If n = 25, which of the numbers is equal to \(3 * 2^{n - 1}\) ?

A. 47, __ __6, __23
B. 47, __ __6, __32
C. 49, __ __2, __64
D. 49, __ __2, __36
E. 50, __ __1, __48

Drill 2
Question: 12
Page: 551
[Reveal] Spoiler: OA

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Last edited by Carcass on 28 Mar 2018, 12:47, edited 1 time in total.
Edited by Carcass
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Re: Three digits have been removed from each of the following nu [#permalink] New post 29 Mar 2018, 14:11
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They've deleted part of each number in the answer choices, and although it is possible (but painful) to figure out what digits are missing, it's not necessary. In fact, all we need is the last digit.

It's useful to know that any number, when multiplied by itself over and over and over, will form a pattern with the units digits of each successive term. For example, here are the first 8 powers of 2:
2
4
8
16
32
64
128
256
etc

Notice that the last digits form a pattern: 2, 4, 8, 6... etc. So, if we plug n into 3*2^(n-1), we get 3*2^24. Let's figure out what the units digit of 2^24 is. Since we know that every 4th term ends in 6, and we know that 2 to the 24th power will go through exactly 6 cycles of the pattern, and will therefore end with a 6. Only one of the answers ends in 6, but that's a trap.

We still need to deal with that 3. Any number you can think of that ends in 6, if multiplied by 3, will produce a number that ends in 8. Try it! So, since 2^24 ends in a 6, if we multiply it by 3, then the resulting huge number, even with a bunch of digits missing, must end in 8. Thus the answer is E.
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GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4722
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1630 [0], given: 390

CAT Tests
Re: Three digits have been removed from each of the following nu [#permalink] New post 06 Apr 2018, 15:12
Expert's post
Explanation

The equation \(3 \times 2^{n–1}\) follows a pattern.

When n = 1, the result is 3. When n = 2, the result is 6.

When n = 3, the result is 12. When n = 4, the result is 24. When n = 5, the result is 48. When n = 6, the result is 96. Beginning with the second term, the final digit in each result follows the pattern: 6, 2, 4, 8, 6, 2, 4, 8, etc.

The 25th term will thus end in the same digit as all the other kth terms, where k is one greater than a multiple of 4.

Thus, the (4 + 1)th, (8+1)th, (12+1)th.…(24+1)th terms all have a final digit of 8, and the only answer in which that is true is choice (E).
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Re: Three digits have been removed from each of the following nu   [#permalink] 06 Apr 2018, 15:12
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