The Italian size of a suit jacket is N centimeters, where N

[jonvindjohnsen]

The Italian size of a suit jacket is N centimeters, where N is the linear distance between the armpits when the jacket is laid on a flat surface. The American size of a suit jacket is P inches, where P is twice the linear distance between the armpits when the jacket is laid on a flat surface. If, for a particular jacket, N = P + 10, which of the following is closest to the value of N? (One inch is approximately 2.54 centimeters.)

a) 36
b) 47
c) 58
d) 65
e) 72

[jonvindjohnsen]

OA: B

I'm wondering about how we know that the answer should be expressed in inches?


Thanks.

[jonvindjohnsen]

Actually, I think I figured it out. Correct me if my reasoning is wrong.

Since we have this relationship: P=2N it doesn't matter if we convert inches to cm or vice versa.

e.g 2.54P = 2N or P = 2N / 2.54

But since the q. stem asks us to solve for N, then this equation should only consist of N's --> P = N - 10

And since we want only N's, we substitute for P.

(How I ballparked the answer as a side note for others):

N=1270/27 --> 1270/30 = 42,++ (30 times 40 = 1200 and 30 times 2 = 60)

Since we divide something on (I thought ppl) more ppl, it will be less for each person. So, when there are fewer ppl "fighting" for "apples" then it will be more for each person. So we should round up from 42,++.

[RonPurewal]

Actually, I think I figured it out. Correct me if my reasoning is wrong.

Since we have this relationship: P=2N it doesn't matter if we convert inches to cm or vice versa.

e.g 2.54P = 2N or P = 2N / 2.54

But since the q. stem asks us to solve for N, then this equation should only consist of N's --> P = N - 10

And since we want only N's, we substitute for P.

(How I ballparked the answer as a side note for others):

N=1270/27 --> 1270/30 = 42,++ (30 times 40 = 1200 and 30 times 2 = 60)

Since we divide something on (I thought ppl) more ppl, it will be less for each person. So, when there are fewer ppl "fighting" for "apples" then it will be more for each person. So we should round up from 42,++.

That can work.

The units are a non-issue. If you have a value for N, then, by definition, that's in centimeters. If you have a value for P, then, by definition, that's in inches.

Finally, your method of estimation here is fine, but you shouldn't be trigger-shy about just doing the long division. Look at the answer choices -- none of them even start with the same digit! Therefore, if you do long division, you can simply stop after you get the first digit (which will be a "4").
Ironically, that probably takes even less time than what you've done here.

[Johann.pacla]

I have a slight variation to this problem where the american size is already converted to CM.

"The Italian size of a suit jacket is N centimeters, where N is the linear distance between the armpits. The American size of a suit jacket is 2.5P centimeters, where P is twice the linear distance between the armpits. If, for a particular jacket, N = P + 10, which of the following is closest to the value of N?"

I was able to undstand and translate that P=2N, but I'm having a lot of trouble grasping why I can't just use P=2N and N=P+10 for solving N. When I use those 2 equations, I get N=-10 which is obviously the wrong answer.

Please help

[RonPurewal]

The equation N = P + 10 is only valid when P is expressed in inches. If you redefine the American size to be in centimeters, that equation is wrong.

If you put everything in centimeters, then you'd need to write N = P/2.5 + 10.
In that case you'll get N = 50, which is certainly close enough to work.

By the way, this is how real Italian and American suit sizes actually work. So, if you know your size in both systems, this is a problem on which you might be able to call on your own experience to help you out.

[Johann.pacla]

Understood. However, the question that was on my CAT exam doesn't state the sizes and formula in inches. Are the units in this equation (N=P+10) something I'm supposed to know/memorize?

[tim]

Any units you need will be given to you in the problem. Is that what you were asking?

[payal919]

I see the CAT Exam question a little differently. It says 2.5P is the twice the linear distance. Was the CAT exam question updated? I also see the American size provided in centimeters and not inches.

The Italian size of a suit jacket is N centimeters, where N is the linear distance between the armpits. The American size of a suit jacket is 2.5P centimeters, where 2.5P is twice the linear distance between the armpits. If, for a particular jacket, N = P + 10, which of the following is closest to the value of N?

Here is what I did:

2.5P = 2N
N= P+10 which would mean P= N-10

2.5 (N-10) = 2N
2.5N - 25 = 2N
.5N = 25
N = 25/.5
N=50

The closest answer is 47 which is B.

Please let me know if my process was accurate and if I should have approached it differently?

[RonPurewal]

I guess they must have updated the problem.

I wrote the original version of this problem"”I'm a fashion-head, and these are the actual definitions of the two countries' sizing systems.
I originally wrote the problem with inches, as quoted at the top of this thread. So, it must have been updated, most likely to make it easier to read/process quickly.

Your approach is absolutely correct.