BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Not clear :(

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Sun Nov 24, 2013 7:40 pm
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]
Image
Top
User avatar
Legendary Member
Posts: 1556
Joined: Tue Aug 14, 2012 11:18 pm
Thanked: 448 times
Followed by:34 members
GMAT Score:650

by theCodeToGMAT » Sun Nov 24, 2013 9:59 pm
[(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]
R A H U L
Top
User avatar
Junior | Next Rank: 30 Posts
Posts: 18
Joined: Sat Sep 17, 2011 9:51 am
Thanked: 3 times
Followed by:3 members

by kackerarnav » Mon Nov 25, 2013 8:00 am
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. :)
Last edited by kackerarnav on Mon Nov 25, 2013 8:03 am, edited 1 time in total.
Top
User avatar
Legendary Member
Posts: 1556
Joined: Tue Aug 14, 2012 11:18 pm
Thanked: 448 times
Followed by:34 members
GMAT Score:650

by theCodeToGMAT » Mon Nov 25, 2013 8:03 am
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
R A H U L
Top
Master | Next Rank: 500 Posts
Posts: 447
Joined: Fri Nov 08, 2013 7:25 am
Thanked: 25 times
Followed by:1 members

by Mathsbuddy » Mon Nov 25, 2013 8:13 am
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)

???
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Mon Nov 25, 2013 2:45 pm
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]
Image
Top
Master | Next Rank: 500 Posts
Posts: 447
Joined: Fri Nov 08, 2013 7:25 am
Thanked: 25 times
Followed by:1 members

by Mathsbuddy » Tue Nov 26, 2013 12:02 am
[email protected] 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
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Tue Nov 26, 2013 1:24 am
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]
Image
Top
Post new topic Post Reply
• Page 1 of 1