Great strategy for this OG problem with negative exponents!

[aleph777]

I love learning really elegant solutions to complex problems, and while I was studying this morning I came across one I had to share!

It's an OG12 question, but I can't recall what number, but the question goes something like this (and, sorry, I can't remember all the wrong answers off hand, but I've included the correct one, too):

(2^-14 + 2^-15 + 2^-16 + 2^-17)/5 is greater than 2^-17 by what factor?

a. 7
b. 3/8
c. 3/5
d. 5
e. 3

OA: 3

READ BELOW FOR THE TIP:

When I first went through the problem, I used distribution to extract 2^-14 from the numerator and then work out the awkward phrase [2^-14(1+2^-1+2^-2+2^-30]/5..... All those reciprocals take too long to break down and solve.

But the MGMAT Official Guide Companion had a great solution... I've always thought about distribution in terms of shrinking a phrase, but the MGMAT explanation actually extracts in reverse. Rather than pull the smallest phrase ( 2^-14 ), they recommend pulling 2^-17, so that you already have a match to the question at hand.

So the phrase becomes: [2^-17(2^3+2^2+2^1)]/5 -----> [2^-17(15)]/5 ------> 2^-17(5)!

I never thought about distribution this way, but it's great for a complex series of reciprocals like this! Using the rule of exponents that says when multiplying like bases, you add the exponents, there's no reason why you can't play with negatives and positives to reach the same results.

2^-14 = 2^-14(2^0) because -14+0=-14
but it could also be solved the MGMAT way
2^-14 = 2^-17(2^3) because -17+3=-14

And when dealing with such a complex phrase of reciprocals, it's much easier to convert to positive exponents and solve from there!

Hope that's as useful to some of you as it was to me!

[shashank.ism]

see the solution is very simple..
Acc. to question we have to compare (2^-14 + 2^-15 + 2^-16 + 2^-17)/5 with 2^-17
so go this way... we know that 2^17 x 2^-17 = 1
so multiply the given term with 1.
1 x (2^-14 + 2^-15 + 2^-16 + 2^-17)/5
= 2^17 x 2^-17 x (2^-14 + 2^-15 + 2^-16 + 2^-17)/5
take 2^17 inside the bracket
= 2^-17 x ( 2^17 x 2^-14 + 2^17 x 2^-15 + 2^17 x 2^-16 + 2^17 x 2^-17)/5
= 2^-17 x ( 2^3 + 2^2 + 2^1+ 1)/5
= 2^-17 x (8 + 4+ 2 + 1)/5
= 15/5 x 2^-17
= 3 x 2^-17

so when you compare 3 x 2^-17 with 2^-17 , clearly it is greater by a factor of 3.
hence correct answer is [spoiler]E = 3.[/spoiler]

[Night reader]

I love learning really elegant solutions to complex problems, and while I was studying this morning I came across one I had to share!

It's an OG12 question, but I can't recall what number, but the question goes something like this (and, sorry, I can't remember all the wrong answers off hand, but I've included the correct one, too):

(2^-14 + 2^-15 + 2^-16 + 2^-17)/5 is greater than 2^-17 by what factor?

a. 7
b. 3/8
c. 3/5
d. 5
e. 3

OA: 3

READ BELOW FOR THE TIP:

When I first went through the problem, I used distribution to extract 2^-14 from the numerator and then work out the awkward phrase [2^-14(1+2^-1+2^-2+2^-30]/5..... All those reciprocals take too long to break down and solve.

But the MGMAT Official Guide Companion had a great solution... I've always thought about distribution in terms of shrinking a phrase, but the MGMAT explanation actually extracts in reverse. Rather than pull the smallest phrase ( 2^-14 ), they recommend pulling 2^-17, so that you already have a match to the question at hand.

So the phrase becomes: [2^-17(2^3+2^2+2^1)]/5 -----> [2^-17(15)]/5 ------> 2^-17(5)!

I never thought about distribution this way, but it's great for a complex series of reciprocals like this! Using the rule of exponents that says when multiplying like bases, you add the exponents, there's no reason why you can't play with negatives and positives to reach the same results.

2^-14 = 2^-14(2^0) because -14+0=-14
but it could also be solved the MGMAT way
2^-14 = 2^-17(2^3) because -17+3=-14

And when dealing with such a complex phrase of reciprocals, it's much easier to convert to positive exponents and solve from there!

Hope that's as useful to some of you as it was to me!

you could also do (2^-14 + 2^-15 + 2^-16 + 2^-17)/(5*2^-17)= 1/5 * (2^3+2^2+2^1+2^0) OR 1/5 * 15 = 3

[shashank.ism]

Its simple mathematics question . I don't know why MGMAT has given such a long explanation.... It really creates confusion to a lot of people....Wiser one choose to do it correctly on their own...