If x is a positive integer, is the remainder 0 when 3^x + 1 is divided by 10?
(1) x = 4n + 2, where n is a positive integer.
(2) x > 4
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
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sana.noor
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3^x +1 is always divisible by 10 no matter what is the value of x. it is because 3 when raise to power (sign of the power must be postive) will always lead to answers that end with 9 and when you add 1, the unit digit will become 0 and thus divisible by 10.
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Atekihcan
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That is true only if x is of the form (4n + 2), i.e. 2 more than a multiple of 4.sana.noor wrote:3^x +1 is always divisible by 10 no matter what is the value of x. it is because 3 when raise to power (sign of the power must be postive) will always lead to answers that end with 9 and when you add 1, the unit digit will become 0 and thus divisible by 10.
For x = 1, 3^1 + 1 = 3 + 1 = 4 not divisible by 10
For x = 3, 3^3 + 1 = 27 + 1 = 28 not divisible by 10
For x = 4, 3^4 + 1 = 81 + 1 = 82 not divisible by 10 and so on
But if x = 2 (= 4*0 + 2), 3^2 + 1 = 10 divisible by 10
And if x = 6 (= 4*1 + 2), 3^6 + 1 = (3^2)*(3^4) + 1 = 9*81 + 1 divisible by 10 and so on
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ygdrasil24
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sana.noor
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sorry i missed this point Atekihcan, 3^x+1 is divisible by 10 when it is in the form of 4n + 2
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Brent@GMATPrepNow
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Target question: Is the remainder 0 when (3^x) + 1 is divided by 10?gibran wrote:If x is a positive integer, is the remainder 0 when 3^x + 1 is divided by 10?
(1) x = 4n + 2, where n is a positive integer.
(2) x > 4
Looks like a candidate for rephrasing the target question.
(Aside: We have a free video that offers some tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100)
So, we would rewrite the target question as "Is (3^x) + 1 divisible by 10?"
Another way to phrase it is, "Does (3^x) + 1 have units digit 0?" (since all integers divisible by 10 must have units digit 0)
Finally, if (3^x) + 1 has units digit 0 then 3^x must have units digit 9. So, let's go with . . .
Rephrased target question: Does 3^x have units digit 9?
Statement 1: = 4n + 2, where n is a positive integer.
To see whether or not this statement is sufficient, we need to make the following observations.
3^1 = 3 (the units digit is 3)
3^2 = 9 (the units digit is 9)
3^3 = 27 (the units digit is 7)
3^4 = 81 (the units digit is 1)
3^5 = 243 (the units digit is 3)
3^6 = ---9 (the units digit is 9)
3^7 = ---7 (the units digit is 7)
3^8 = ---1 (the units digit is 1)
3^9 = ---3 (the units digit is 3)
3^10 = ---9 (the units digit is 9)
.
.
.
So, 3^x = ---9 when x = 2, 6, 10, 14, 18, etc
In other words, 3^x = --9 whenever x is in the form 4n + 2, where n is a positive integer
Since statement 1 tells us that x = 4n + 2, where n is a positive integer, then it must be the case that the units digit of 3^x is 9
Since we can answer the rephrased target question with certainty, statement 1 is SUFFICIENT
Statement 2: x > 4
There are several values x that meet this condition. Here are two:
Case a: x = 5, in which case the units digit of 3^x is 3
Case b: x = 6, in which case the units digit of 3^x is 9
Since we cannot answer the rephrased target question with certainty, statement 2 is NOT SUFFICIENT
Answer = A
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