Quicker + alternate methods

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wongee: Senior | Next Rank: 100 Posts; Posts: 76; Joined: Sat Jul 28, 2007 1:55 pm; Thanked: 1 times

by wongee » Fri Oct 26, 2007 5:02 pm

First qtn on my Gmat prep test: relatively simple, and I got it correct, but I think i spent a little more time on it than I should have (I timed myself) because I tried to use factorization in some way, but didn't succeed. Is there any other solution other than working it out and guesstimating the result with the answer choices, coz thats what I did.

1. 2^5 + 2^5 + 3^5 + 3^5 +3^5 =

a. 5^6 b. 13^5 c. 2^6+3^6 d. 2^7 + 3^8 e. 4^5 + 9^5

2. If the two-digit integers M&N are positive and have digits but in reverse order, which of the following CANNOT be the sum of M & N?

a. 181 b. 165 c. 121 d. 99 e. 44

Qtn: According to a formula in the flashcards, which I was hoping to use says
AB
BA
CDC

But, the explanation solves this differently. Is there a way to solve this with the use of the formula above? Thanks.

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Source: Beat The GMAT — Problem Solving | Fri Oct 26, 2007 5:02 pm

ri2007: Master | Next Rank: 500 Posts; Posts: 258; Joined: Mon Aug 27, 2007 12:43 pm; Thanked: 15 times

by ri2007 » Fri Oct 26, 2007 7:00 pm

My asnwers were as follows -

1) c. 2^6+3^6

2^5 + 2^5 + 3^5 + 3^5 +3^5 = 2^5 (1+1) + 3^5 (1+1+1)

= 2^5 (2) + 3^5 (3) = 2^6+3^6

2) This one I actually saw earlier from Samir Pandeys reply -

Ans a. 181

If M = 10X + Y then

N = 10Y + X

So M + N = 11X + 11 Y = 11 (X+Y) so it has to be a multiple of 11. The only one from the ans choices which is not a multiple of 11 is a = 181

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wongee: Senior | Next Rank: 100 Posts; Posts: 76; Joined: Sat Jul 28, 2007 1:55 pm; Thanked: 1 times

by wongee » Sat Oct 27, 2007 10:48 am

hey! Thanks for the explanation on 1. For 2, yes the book explanation is the same, but I also wanted to know if that formula means anything? Anyone? Thanks!

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ri2007: Master | Next Rank: 500 Posts; Posts: 258; Joined: Mon Aug 27, 2007 12:43 pm; Thanked: 15 times

by ri2007 » Sat Oct 27, 2007 10:57 am

well,

since M & N are 2 digit numbers, assume the tens digit of M = 2 and the units digit of M = 4 so M = 10(2) + (4) = 24

Now if N has the same digits but in reverse order
what is N?

N = 42 which is the same as 10 (4) + 2

Since u do not know the actual digits in such a question you use variables x and Y and solve as shown earlier.

Hope this answers your question?

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wongee: Senior | Next Rank: 100 Posts; Posts: 76; Joined: Sat Jul 28, 2007 1:55 pm; Thanked: 1 times

by wongee » Thu Nov 01, 2007 11:50 am

Thanks for giving it a try. I get your point. I wanted to know if the std formula or tip ie
AB
BA
___=
CDC

And if so this means

24
42 =
88 - the formula works, if you try

38 and 83, it works again, 121 (CDC), but if you try 68 and 86, it doesn't...Is this a reliable formula/tip? Thanks for your help!

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Dakotakiki: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Thu Nov 28, 2013 8:21 am

by Dakotakiki » Sat Dec 28, 2013 2:13 am

Hi everyone. I have exactly the same question!

Can someone please explain the rationale behind the Flashcards formula :

AB
+ BA
-----
CDC

I've noticed similar inconsistencies (83+38 = 121 -> ok ; but 48+84 = 132 -> not ok)and would like to understand the rules / exceptions behind the above formula.

Thanks in advance!

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Sat Dec 28, 2013 2:59 am

Dakotakiki wrote:Hi everyone. I have exactly the same question!

Can someone please explain the rationale behind the Flashcards formula :

AB
+ BA
-----
CDC

I've noticed similar inconsistencies (83+38 = 121 -> ok ; but 48+84 = 132 -> not ok)and would like to understand the rules / exceptions behind the above formula.

Thanks in advance!

Hi!

No such general formula exists - that pattern comes from an old GMAT question that gave you that summation as a rule to help you answer that one specific question. Whoever put it on a flashcard managed to confuse a whole bunch of people, though (which is why you should be very wary of resources created by random folks!).

Stuart

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
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naseem_iqbal: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Fri Nov 29, 2013 5:46 am

by naseem_iqbal » Sat Dec 28, 2013 11:49 am

AB
+BA
----
=AA
+BB
That should help eliminate remembering most rules.

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