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Express 2^20-2^19-2^18-2^17 as a power of 2.

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Express 2^20-2^19-2^18-2^17 as a power of 2.

by Max@Math Revolution » Thu Mar 21, 2019 11:19 pm

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[GMAT math practice question]

Express 2^20-2^19-2^18-2^17 as a power of 2.

A. 2^15
B. 2^16
C. 2^17
D. 2^18
E. 2^19
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by Brent@GMATPrepNow » Fri Mar 22, 2019 6:48 am
Max@Math Revolution wrote:[GMAT math practice question]

Express 2^20 - 2^19 - 2^18 - 2^17 as a power of 2.

A. 2^15
B. 2^16
C. 2^17
D. 2^18
E. 2^19
2^20 - 2^19 - 2^18 - 2^17 = 2^17(2^3 - 2^2 - 2^1 - 1)
= 2^17(8 - 4 - 2 - 1)
= 2^17(1)
= 2^17

Answer: C

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by GMATGuruNY » Fri Mar 22, 2019 8:38 am
Max@Math Revolution wrote:[GMAT math practice question]

Express 2^20-2^19-2^18-2^17 as a power of 2.

A. 2^15
B. 2^16
C. 2^17
D. 2^18
E. 2^19
Test an analogous case with easier values:
2� - 2³ - 2² - 2¹ = 16 - 8 - 4 - 2 = 2¹
The matching blue portions imply the following:
2²� - 2¹� - 2¹� - 2¹� = 2¹�

The correct answer is C.
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by Max@Math Revolution » Sun Mar 24, 2019 5:05 pm
=>

2^20-2^19-2^18-2^17
=2^32^17- 2^22^17-2^12^17-2^17
= 2^17 (8-4-2-1)
= 2^17(1)
= 2^17

Therefore, the answer is C.
Answer: C
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by Scott@TargetTestPrep » Sun Mar 24, 2019 5:16 pm
Max@Math Revolution wrote:[GMAT math practice question]

Express 2^20-2^19-2^18-2^17 as a power of 2.

A. 2^15
B. 2^16
C. 2^17
D. 2^18
E. 2^19
Simplifying we have:

2^17(2^3 - 2^2 - 2^1 - 1) = 2^17(8 - 4 - 2 - 1) = 2^17

Answer: C

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