What is the units digit of 6^15 - 7^4 - 9^3 ?

Question

What is the units digit of  6^{15} - 7^4 - 9^3 ?

A. 8
B. 7
C. 6
D. 5
E. 4

CareerGeek · Answer

6^{15} - 7^4 - 9^3 
 6 - (1 + 9) 
 6 - 0 = 6

Option C

ScottTargetTestPrep · Answer

The pattern of units digits of powers of 6 is 6, so 6^15 has a units digit of 6.

The pattern of units digits of powers of 7 is 7-9-3-1, so 7^4 has a units digit of 1.

The pattern of units digits of powers of 9 is 9-1,so 9^3 has a units digit of 9.

Thus, we have:

6 - 1 - 9

5 - 9

-4

Recall that we can add 10 (or multiples of 10) to a “negative” units digit to make it positive. Therefore, the actual units digit is -4 + 10 = 6.

Answer: C

Abhishek009 · Answer

6^{15} - 7^4 - 9^3

= 6 - 1 - 9

= 6 - 10

= -4

Thus, Answer must be (C) 6

DaniyalAlwani · Answer

ScottTargetTestPrep 
"Recall that we can add 10 (or multiples of 10) to a “negative” units digit to make it positive. Therefore, the actual units digit is -4 + 10 = 6"

Can you explain me this rule please?

dave13 · Answer

hi guitarist Abhishek009

how is it possible that answer is 6 and not -4, can you pls explain the concept thanks and have a great weekend

AnirudhaS · Answer

Just concentrating on the unit digits..
6-1-9
=6-(1+9)
=6-(0)
=6

Answer:  C

AnirudhaS · Answer

I can help. So when we talk about numbers it is in the decimal system.
For e.g let us take the example of 20 - 11. So the unit place here would be 9. Or the unit place can be mathematically written as -1. But in the number form you won't write a negative integer.

ScottTargetTestPrep · Answer

Response: 
 
Of course, a negative integer cannot be the units digit of any number; however, if a calculation involving units digit turns out to be a negative number, we can use the fact that adding 10 to any number does not change units digits to find an equivalent positive number.
 
Here’s an alternate explanation:
 
We found that the units digits of 6^15, 7^4 and 9^3 are 6, 1 and 9, respectively. To find the units digit of 6^15 - 7^4 - 9^3, rather than calculating 6 - 1 - 9, we can instead calculate 16 - 1 - 9 and find 6. Notice that we could also have taken 26 (or any number with a units digit of 6) instead of 16 and we would have found 26 - 1 - 9 = 16, which also has a units digit of 6.

Kinshook · Answer

Asked: What is the units digit of  6^{15} - 7^4 - 9^3 ?

Unit digit of  6^{15} = 6 
Unit digit of  7^4 = 1 
Unit digit of  9^3 = 9

Unit digit of  6^{15} - 7^4 - 9^3 = 16 - 1 - 9 = 6

IMO C

DhanyaAbhirami · Answer

ScottTargetTestPrep Bunuel
Why wasn't comparison of the exponent terms not done here, like it's done for https://gmatclub.com/forum/what-is-the- ... 51159.html and https://gmatclub.com/forum/m26-184441.html

Bunuel · Answer

Yes, if 7^4 + 9^3 were greater than 6^{15} , the answer would have been 4 instead of 6. However, it's easy to see that 6^{15} is a much larger number than 7^4 + 9^3 : 6^{15} > 3^{15} > 3^{14} = 9^7 While: 7^4 + 9^3 < 9^4 + 9^4 < 2*9^4 < 9^5 Therefore, 6^{15} > 7^4 + 9^3 . Hope it helps.

What is the units digit of 6^15 - 7^4 - 9^3 ?

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What is the units digit of 6^15 - 7^4 - 9^3 ?

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