Digit Dilemma

[arashyazdiha]

If (243)^x(463)^y = n, where x and y are positive integers, what is the units digit of n?

(1) x + y = 7

(2) x = 4

[n@resh]

If (243)^x(463)^y = n, where x and y are positive integers, what is the units digit of n?

(1) x + y = 7

(2) x = 4

Ans is C!

from 1 and 2 statements we get X = 4 and y = 3

now for the units digit we need to last digits of the product (243)^4(463)^3
i.e. 3^4 *3^3 => 7 which is the units digit of n.

Hence ans is C!

[prateek_guy2004]

Statement 1 is'int sufficient because it got 2 variables X and Y , to get to Unit digits of both the numbers we need their respectives powers.

statemt 2 is'int sufficint too. Is just got 1 variable.

evaluation 2 statements we get the value of both the variables.

dont bother to get the unit digit.....

Answer C

[Brent@GMATPrepNow]

If (243)^x(463)^y = n, where x and y are positive integers, what is the units digit of n?

(1) x + y = 7

(2) x = 4

Important aside: The units digit of (243)^x is the same as the units digit of 3^x (since we are only concerned with the last digit, the other digits are of no consequence). Similarly, the units digit of (463)^y is the same as the units digit of 3^y.

So, we can reword the target question as, "If (3^x)(3^y) = n (where x and y are positive integers), what is the units digit of n?"

Since we now have the two powers (3^x and (3^y) written with the same base, we can combine them to get 3^(x+y)

This means we can further reword the target question as, "If 3^(x+y) = n (where x and y are positive integers), what is the units digit of n?"

Okay, now the statements:

Statement 1: x+y=7
Given this, our target question becomes "What is the units digit of 3^7?"
Since we can answer the target question with certainty, statement 1 is sufficient

Statement 2: x=4
Given this, we are unable to determine the value of 3^(x+y).
So, statement 2 is not sufficient, and the answer is A.

Cheers,
Brent

[akhilsuhag]

Since we r looking at only digits digits lets just look at them:

so the prompt becomes 3^x*3^y => 3 ^ (x+y)

So IMO A is sufficient.

Tho I not not too great with quant so don't take my word for it!!

OA??

[akhilsuhag]

I hope this comes in helpful- "When it seems too obvious that C is the answer, it in most cases isn't"

When I initially saw the question I thought to myself- C is too easy to get to. GMAT will play it tricks. In this case it easily put C in front of you so that you don't chek for others.

So you when you see that C is an easy option. Think to yourself that the GMAT mit be at it again and go ahead and check the other choices.

Again this might not always be true. But you should know GMAT is setting traps and this is one of them.

Also I am no expert and maybe you already follow this but I just thot I shud share.

I hope it helps!!

Cheers!!

[prateek_guy2004]

Hi akhilsuhag

No you are right but i dont understand why i cant be C.

[akhilsuhag]

Prateek I didn't get your question.. are you asking why it can't be C??

[prateek_guy2004]

Prateek I didn't get your question.. are you asking why it can't be C??

Statement 1 is'int sufficient because it got 2 variables X and Y , to get to Unit digits of both the numbers we need their respectives powers.

statemt 2 is'int sufficint too. Is just got 1 variable.

evaluation 2 statements we get the value of both the variables.

dont bother to get the unit digit.....

Answer C

Ya i canot undstand why it cant be C....

[akhilsuhag]

Prateek lets look at the prmpt:

263^x * 463^y; We need to find the units digit of this.
Because we are interested in the units digit of a number, we should consider only the unit digits of the prompt. This is a simple rule. The units digit of 3^5 will be the same as that of 43^5 or 463^5.
You can check this.

So we can change the prompt as: 3^x * 3^y ; this gives us 3^(x+y).

So if we have the value of x+y; we can find the units digit of 3^(x+y); which is exactly what statement 1 gives us.

I hope you get it; if not write and I will try and do a better job at explaining!!

[prateek_guy2004]

Hi Akhil

Its a nice explanation and i understand as well but why my answer is wrong i dont understand that...

[n@resh]

If (243)^x(463)^y = n, where x and y are positive integers, what is the units digit of n?

(1) x + y = 7

(2) x = 4

Important aside: The units digit of (243)^x is the same as the units digit of 3^x (since we are only concerned with the last digit, the other digits are of no consequence). Similarly, the units digit of (463)^y is the same as the units digit of 3^y.

So, we can reword the target question as, "If (3^x)(3^y) = n (where x and y are positive integers), what is the units digit of n?"

Since we now have the two powers (3^x and (3^y) written with the same base, we can combine them to get 3^(x+y)

This means we can further reword the target question as, "If 3^(x+y) = n (where x and y are positive integers), what is the units digit of n?"

Okay, now the statements:

Statement 1: x+y=7
Given this, our target question becomes "What is the units digit of 3^7?"
Since we can answer the target question with certainty, statement 1 is sufficient

Statement 2: x=4
Given this, we are unable to determine the value of 3^(x+y).
So, statement 2 is not sufficient, and the answer is A.

Cheers,
Brent

Incredible point Brent! very true, somehow my numbmind messup.

[akhilsuhag]

Prateek you are not wrong. Yes we can solve the problem if we have both the statements aswell. But in GMAT we need to find the minimum info required to solve a prompt. And A is the minimum ino, additional info makes it easier to solve the promp but we r not interested in that. We are interested in what minimum is required.