Questions about the world of GRE Math from other sources and general math related questions.
Videoorchard
Prospective Students
 
Posts: 48
Joined: Thu Mar 06, 2014 2:58 am
 

Problem from FDP Guide

by Videoorchard Fri Feb 06, 2015 11:21 am

Hello,

Greetings of the day! Let's get straight to business! :)

Question:
The length of a rectangle is 3 inches, plus or minus an amount no greater than 1/2 inch, while its width is 2 inches, plus or minus an amount no greater than 1/4 inch. Which of the following could be the percentage by which the actual area of the rectangle is greater than or less than its nominal area of 6 square inches? Select all that apply.

A. -30%
B. -25%
C. +25%
D. +30%


Doubt:
I have understood most part of the question EXCEPT the second half of the question i.e

Which of the following could be the percentage by which the actual area of the rectangle is greater than or less than its nominal area of 6 square inches?


What does this even mean? How does the author conclude the answers to be B,C & D? Could you please help me decipher it?

I also wanted to ask you, i find the hard section of each strategy guide extremely tough. I find them similar to the monthly challenge problem. Although my main aim of doing this section(well any GRE problem for that matter) is build skills/have takeaways from each problem, the hard sections of the strategy guides are giving me really hard time. I end up writing almost all of the problems from this sections in my "Mistakes/Review log book".. Is this something that i should really worry about? Will i see problems of such difficulty level on the real test?
Last edited by Videoorchard on Sat Feb 07, 2015 11:55 am, edited 2 times in total.
n00bpron00bpron00b
Students
 
Posts: 89
Joined: Sun Apr 20, 2014 6:12 pm
 

Re: Problem from FDP Guide

by n00bpron00bpron00b Fri Feb 06, 2015 4:48 pm

Let's get straight to business! :)
Yes !

Given :
Length = 3
Width = 2
Area = 6 = "x" (consider this as the benchmark)

Possible Range -
Length : plus or minus an amount no greater than 1/2 inch
Width : plus or minus an amount no greater than 1/4 inch

Find the possible range of area's (Max - Min)

Max:
Length = 3 + 1/2 = 7/2
Width = 2 + 1/4 = 9/4
Area = 63/8 = 7.875 (Max area)

Min:
Length = 3 - 1/2 = 5/2
Width = 2 - 1/4 = 7/4
Area = 35/8 = 4.375 (Min area)

So the range is -
(min area) 4.375 -- 6 (benchmark : area of given rectangle) -- 7.895 (max area)

Which of the following could be the percentage by which the actual area of the rectangle is greater than or less than its nominal area of 6 square inches? Select all that apply.


So basically, we need to find the possible area's (in terms of percentage) above 6 (max being 7.895) and possible area's (in terms of percentage) below 6 (min being 4.375)

a) (4.375-6)/6 = x/100
=> -27.083 %

b) (7.895-6)/6 = x/100
=> 31.583 %

Total Percentage range => -27.083 % <= X <= +31.583 %

Ans. B, C, D

P.S - "A" is part of the solution ??
Videoorchard
Prospective Students
 
Posts: 48
Joined: Thu Mar 06, 2014 2:58 am
 

Re: Problem from FDP Guide

by Videoorchard Sat Feb 07, 2015 11:54 am

Hi Noob,

Thank you for your explanation! :)

I have understood most part of your explanation, but i still cannot wrap my head around the second part of the question... We know that the "range" for area of rectangle is between 4.375 --7.895..Now, how did you make use of the formula i.e new-old/old to convert the decimal representation to percent representation? I always thought that the above formula, to be used when the question revolves around percent change(increase/decrease)...

In the question, could you also tell me on what "actual area of rectangle" vs "nominal area (6)" means? what's the difference between the two?

P.S: Yes. you are right. The correct answers are B,C,D..Option A is not a part of it! I have corrected the typo for future reference! :)
n00bpron00bpron00b
Students
 
Posts: 89
Joined: Sun Apr 20, 2014 6:12 pm
 

Re: Problem from FDP Guide

by n00bpron00bpron00b Sat Feb 07, 2015 12:58 pm

Nominal Area in this case is 6 - by using the default condition of length = 3 and width = 2 ; Consider this area of 6 as the fixed point

Actual Area is the area that you arrive by using any value of length and width that satisfies the condition of

Length : plus or minus an amount no greater than 1/2 inch
Width : plus or minus an amount no greater than 1/4 inch

Actual length : pick any value within this range (3-1/2) to (3+1/2) - inclusive of end points

Actual Width : pick any value within this range (2-1/4) to (2+1/4) - inclusive on end points

Actual Area = Actual length x Actual Width

So we know for sure two things -

Nominal area is fixed = 6
Since we want the total range of actual area we have just considered the end points (max and min) i.e 4.375 - 7.895. But any point which lies between this range is also acceptable.

Now, about what the question means -

percentage by which the actual area of the rectangle is greater than or less than its nominal area of 6 square inches


Nominal Area acts as a fixed point and with respect to that point we have to find the % inc/dec of the actual area.

In other words 7.895 is what percent greater (% increase) than 6
=> 31.583 %

In other words 4.375 is what percent less (% decrease) than 6
=> -27.083 %

So any actual area value that lies within the range 4.375 - 7.895 and later when you find the % increase/decrease of that value with respect to 6 => will fall within the % range of -27.083 % to +31.583%

Hence the answer B,C,D

Hope this helps.
Videoorchard
Prospective Students
 
Posts: 48
Joined: Thu Mar 06, 2014 2:58 am
 

Re: Problem from FDP Guide

by Videoorchard Tue Feb 10, 2015 8:01 am

Thanx noob for clearing my doubt!

Hey,do you mind sharing on what resources you are using for your GRE Prep (Both verbal & Math)? Just curious! :) I have been using the MSG for my GRE Prep!

Tommy, could you please answer the below question? Thanx!

I also wanted to ask you, i find the hard section of each strategy guide extremely tough. I find them similar to the monthly challenge problem. Although my main aim of doing this section(well any GRE problem for that matter) is build skills/have takeaways from each problem, the hard sections of the strategy guides are giving me really hard time. I end up writing almost all of the problems from this sections in my "Mistakes/Review log book".. Is this something that i should really worry about? Will i see problems of such difficulty level on the real test?
n00bpron00bpron00b
Students
 
Posts: 89
Joined: Sun Apr 20, 2014 6:12 pm
 

Re: Problem from FDP Guide

by n00bpron00bpron00b Tue Feb 10, 2015 2:24 pm

Hey,

I think the number of problems present in Manhattan series should suffice. I tried to put more focus on basic concepts rather than solving from multiple books. (but it's a personal choice you may solve from other books if you feel you need more practice on a particular topic)

For basic/fundamental concepts -
-> khanacademy
-> Youtube - plethora of videos (just search for the difficult concept)
-> Google for free school grade worksheets (search for concept name + worksheets)

Verbal - Haven't started yet :)

basic stuff > gre level > gre level timed > mocks + ETS OG ..Hopefully should work
tommywallach
Manhattan Prep Staff
 
Posts: 1917
Joined: Thu Mar 31, 2011 11:18 am
 

Re: Problem from FDP Guide

by tommywallach Thu Feb 12, 2015 12:04 pm

As always, great answers across the board from Noob.

Never forget, there can be vocabulary words in quant too! In this case, we're using the definition of "nominal" meaning "stated or expressed but not necessarily corresponding exactly to the real value." In this case, the value would be 6 IF the stated/expressed side lengths were definitive. But then we are told they can vary a bit. That's what sends us down the rabbit hole of testing and then percent change solving.

As for the hard stuff, the short answer is YES, you can see a couple of hard problems on the real test. The longer answer consists of two parts:

1) If you see really hard questions on the test, you won't see all that many, so you could still ignore the hardest questions in the book (as long as you were really good at all the easy, medium, and kinda hard ones).

2) As Noob said (and you said too), you should always be focused on techniques/takeaways. If a hard question doesn't seem to have any of these, just let it be and move on to the next one.

Good luck!

-t