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by oquiella » Sat Sep 05, 2015 11:18 am
S and T are two-digit positive integers that have the same digits but in reverse order. If the positive difference between S and T is less than 40, what is the greatest possible value of S minus T?


27

30

33

36

39
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by [email protected] » Sat Sep 05, 2015 1:42 pm
Hi oquiella,

This question is actually based on an issue that Accountants sometimes face (and that you might have learned about in an Accounting class) - it's what happens when digits are 'flip-flopped' in a number. When that type of accounting error occurs (or when you purposely reverse the digits in a number), the DIFFERENCE in those two numbers is ALWAYS a multiple of 9.

For example...
32 and 23 --> 32-23 = 9
41 and 14 --> 41-14 = 27
95 and 59 --> 95-59 = 36
Etc.

Knowing that rule would make solving this problem really easy. However, even if you didn't know that rule, you can TEST VALUES (in much the same way that I already showed with the examples above).

The largest difference you will ever be able to find is 36 (and you can find it with a variety of different 2-digit pairs: 95 and 59, 84 and 48, 73 and 37, 62 and 26, 51 and 15).

Final Answer: D

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by oquiella » Thu Oct 15, 2015 2:18 pm
[email protected] wrote:Hi oquiella,

This question is actually based on an issue that Accountants sometimes face (and that you might have learned about in an Accounting class) - it's what happens when digits are 'flip-flopped' in a number. When that type of accounting error occurs (or when you purposely reverse the digits in a number), the DIFFERENCE in those two numbers is ALWAYS a multiple of 9.

For example...
32 and 23 --> 32-23 = 9
41 and 14 --> 41-14 = 27
95 and 59 --> 95-59 = 36
Etc.

Knowing that rule would make solving this problem really easy. However, even if you didn't know that rule, you can TEST VALUES (in much the same way that I already showed with the examples above).

The largest difference you will ever be able to find is 36 (and you can find it with a variety of different 2-digit pairs: 95 and 59, 84 and 48, 73 and 37, 62 and 26, 51 and 15).

Final Answer: D

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

HI RICH I NOTICED B AND D YIELDS 27 AS THE DIFFERENCE. IS THERE A REASON WHY 36 IS BETTER. RATHER THAN 30?
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by oquiella » Thu Oct 15, 2015 2:18 pm
[email protected] wrote:Hi oquiella,

This question is actually based on an issue that Accountants sometimes face (and that you might have learned about in an Accounting class) - it's what happens when digits are 'flip-flopped' in a number. When that type of accounting error occurs (or when you purposely reverse the digits in a number), the DIFFERENCE in those two numbers is ALWAYS a multiple of 9.

For example...
32 and 23 --> 32-23 = 9
41 and 14 --> 41-14 = 27
95 and 59 --> 95-59 = 36
Etc.

Knowing that rule would make solving this problem really easy. However, even if you didn't know that rule, you can TEST VALUES (in much the same way that I already showed with the examples above).

The largest difference you will ever be able to find is 36 (and you can find it with a variety of different 2-digit pairs: 95 and 59, 84 and 48, 73 and 37, 62 and 26, 51 and 15).

Final Answer: D

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

HI RICH I NOTICED B AND D YIELDS 27 AS THE DIFFERENCE. IS THERE A REASON WHY 36 IS BETTER. RATHER THAN 30?
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by [email protected] » Thu Oct 15, 2015 11:48 pm
Hi oquiella,

Since the question asks for the GREATEST difference between S and T, we have to work until we find that GREATEST difference. While 27 is a possible difference, 36 is the greatest difference.

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by manik11 » Tue Oct 20, 2015 4:10 am
Here's an algebraic approach:

Since S and T are 2 digit numbers, let's consider the 1st digit x and the second digit y
This implies:

S=10x+y
T=10y+x (flipped the units and tens digit)

Positive diff is less than 40:

=>S-T<40
=>10x+y-(10y+x)<40
=>9x-9y<40
=>9(x-y)<40

The question mentions positive diff.
9 is positive so (x-y) will have to be positive too.

How much can you increase the value of (x-y) and keep the product 9(x-y) under 40
Well..turns out 9(x-y) can be maxed out till 36 for which (x-y)=4

Answer: D

-Manik
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