Not clear :(

Question

The sum of the digits of [(10^x)^y]-64=279. What is the value of xy A. 28 B. 29 C. 30 D. 31 E. 32 xy is positive integer Ans-E

Rich.C@EMPOWERgmat.com · Answer

Hi shibsriz,

This question has some awkward wording to it, but here's its intent: the number 10^(xy) - 64 has digits that add up to 279.

So, we need to figure out what THAT number is.

Here's what you need to "see" to solve this problem:

IF xy = 3, then 1,000 - 64 = 936 and the sum of digits = 18 = 2x9
If xy = 4, then 10,000 - 64 = 9,936 and the sum of digits = 27 = 3x9
If xy = 5, then 100,000 - 64 = 99,936 and the sum of digits = 36 = 4x9

Notice the pattern? The sum of digits is increasing by 9 every time.

So, how many times does 9 divide into 279? 31 times

As a reminder of the pattern:
xy = 3 --> 2x9
xy = 4 --> 3x9
xy = 5 --> 4x9

So, 31x9 --> xy = 32

Thus, the final answer is E

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

theCodeToGMAT · Answer

[(10^x)^y]-64=279 To find: xy 10^xy - 64 = 279 Let xy = 2 ==> 36 ==> Sum = 9 Let xy = 3 ==> 936 ==> Sum = 18 Let xy = 4 ==> 9936 ==> SUm = 27 So, using formula for AP 9 + (n-1)9 = 279 9n = 279 n = 31 So, 31+1 32 [spoiler]{E}[/spoiler]

kackerarnav · Answer

theCodeToGMAT wrote:[(10^x)^y]-64=279 To find: xy 10^xy - 64 = 279 Let xy = 2 ==> 36 ==> Sum = 9 Let xy = 3 ==> 936 ==> Sum = 18 Let xy = 4 ==> 9936 ==> SUm = 27 So, using formula for AP 9 + (n-1)9 = 279 9n = 279 n = 31 So, 31+1 32 [spoiler]{E}[/spoiler] Sorry, I was confused for a second because I didn't see a definition of n.

theCodeToGMAT · Answer

kackerarnav wrote:theCodeToGMAT wrote:[(10^x)^y]-64=279 To find: xy 10^xy - 64 = 279 Let xy = 2 ==> 36 ==> Sum = 9 Let xy = 3 ==> 936 ==> Sum = 18 Let xy = 4 ==> 9936 ==> SUm = 27 So, using formula for AP 9 + (n-1)9 = 279 9n = 279 n = 31 So, 31+1 32 [spoiler]{E}[/spoiler] Shouldn't that term in bold above be n-2, by the pattern? No, I just used the formula for AP term==> a + (n-1)d The part marked in green is what I did to cater that delta 1

Mathsbuddy · Answer

10^xy - 64 -> 279

So 10^xy - 100 + 36 -> 279

So 10^xy - 100 -> 270

But 9 * 30 = 270 therefore there need to be 30 digits of 9

So 10^xy = 100 + 99999...00 (with 30 digits of 9)

So 10^xy = 10^31

Hence xy = 31 (D)

???

Rich.C@EMPOWERgmat.com · Answer

Hi Mathsbuddy,

You made a conceptual math error in your work. Remember that we have to add up the digits in the calculation. When you change the calculation (by turning - 64 into "-100 +36"), you're changing the digits. Unless you do the necessary steps to "undo" those changes later, you're going to end up with the wrong power of 10.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Mathsbuddy · Answer

Rich.C@EMPOWERgmat.com wrote:Hi Mathsbuddy, You made a conceptual math error in your work. Remember that we have to add up the digits in the calculation. When you change the calculation (by turning - 64 into "-100 +36"), you're changing the digits. Unless you do the necessary steps to "undo" those changes later, you're going to end up with the wrong power of 10. GMAT assassins aren't born, they're made, Rich Edit Thanks Rich, Here's my corrected version (with some plagerism from your work!): sum of digits of (10^xy - 64) -> 279 So sum of digits of (10^xy - 100 + 36) -> 279 So sum of digits of (10^xy - 100) -> 270 But 9 * 30 = 270 therefore there need to be 30 digits of 9 Note (QUOTED): IF xy = 3, then 1,000 - 64 = 936 and the sum of digits = 18 = 2x9 If xy = 4, then 10,000 - 64 = 9,936 and the sum of digits = 27 = 3x9 If xy = 5, then 100,000 - 64 = 99,936 and the sum of digits = 36 = 4x9 So... If xy = N, then 10^N - 64 = "(N-2) nines" + 36 and the sum of digits = (N-2) * 9 If xy = 32, then 10^32 - 64 = "30 nines" + 36 and the sum of digits = 270 = 31x9 So 10^xy = 10^32 Hence xy = 32

Rich.C@EMPOWERgmat.com · Answer

Hi Mathsbuddy,

There you have it. The GMAT essentially "rewards" clever people (especially those who can "see" more than one way to solve a problem) with some easy-to-get points. However you choose to approach the Quant and Verbal sections, precision is a must, since the GMAT is also really good at punishing people who make silly mistakes. You're clearly a clever thinker, make sure that you keep your eye on the details.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Choose how you want to prepare

Get Ready for GMAT Test Day Faster with Live Online Classes

Target Test Prep EA OnDemand

Target Test Prep GMAT OnDemand

Not clear :(

GMAT/MBA Expert

GMAT/MBA Expert

GMAT/MBA Expert

Chicago Booth

GMAT Course Reviews

Admissions Consulting Reviews

FREE GMAT PREP RESOURCES

GMAT PREP DEAL TRACKER