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Three digits have been removed from each of the following

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by [email protected] » Tue Feb 05, 2019 10:49 am
Hi All,

We're told that three digits have been removed from each of the following numbers and n = 25. We're asked which of the numbers is equal to 3*2^(n-1).

To start, the fact that three digits have been removed from each answer is irrelevant. When a GMAT question presents information that appears to be a gigantic calculation, there is almost always a pattern behind the numbers. Here, the pattern is the 'units digit'; each of the 5 answers has a different units digit - and we'll use that, along with some basic Arithmetic, to answer this question.

(3)(2^24) = a big number

The GMAT won't expect us to physically calculate that number though, so let's look for a pattern in 2^24....

2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16

2^5 = 32
2^6 = 64
2^7 = 128
2^8 = 256

Notice the pattern that exists in the units digits: 2....4....8.....6.....2.....4....8....6

This means that for every 4 increasing "powers of 2", the same pattern will repeat. 2^24 would give us 6 sets of those repeating four digits, meaning that 2^24 will have a units digit of 6.

When we multiply a number that ends in 6 by the number 3, we end up with a product that ends in 8. There's only one answer that matches....

Final Answer: E

GMAT assassins aren't born, they're made,
Rich
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by swerve » Wed Feb 06, 2019 8:09 am
$$2^{24} \text{ can be re-written as } (2^8)^3 = 156^3.$$
$$\text{The units digit of } 156 \text{ raised to a positive power will remain as } 6.$$
$$6\cdot 3 = 18. \text{ So the answer will have a units digit of } 8.$$
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by Scott@TargetTestPrep » Wed Feb 06, 2019 6:33 pm
AAPL wrote:Princeton Review

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

OA E
Let's look at the pattern of powers of 2 when raised to positive integer exponents. We are concerned only with the units digit of each power of 2.

2^1 = 2

2^2 = 4

2^3 = 8

2^4 = 6

2^5 = 2

We see that the pattern is 2, 4, 8, 6. Thus, if 2 is raised to a power that is a multiple of 4, the answer has a units digit of 6.

Thus, we see that 2^24 has a units digit of 6.

Since n = 25, we have:

3 x 2^24

We therefore see that the product of 3 x 2^24 has a units digit of 8. Only one answer choice has a units digit of 8, so it must be the correct choice.

Answer: E

Scott Woodbury-Stewart
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