Problem Solving

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.

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

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!

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?

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!

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!

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

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