Manhattan - Italian Suits

sparkles3144 wrote: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?

A. 36
B. 47
C. 58
D. 65
E. 72

I did this...

N = (1/2) (2.5 P) = 1.25 P

N = P + 10
1.25 P = P + 10
0.25 P = 10
P = 40
So, it is closest to A.

However, according to Manhattan solution, the answer is B.

N = 1.25P
N = 1.25(N – 10)
N = 1.25N – 12.5
12.5 = 1.25N – 1N
12.5 = 0.25N multiply both sides by 4
50 = N

The problem asks for the closest value. The closest answer choice to 50 is 47.

The correct answer is B.

Can someone please help me with this?

Thanks!

Sparkles,
What ever u did is exactly right. But, you didn't read question correctly. In question they asked to find the value of N not P.
So you found value of P that is 40.
N=P+10
=> N= 50 and closest to 50 is 47.
Hence OA is B

Regards,
Uva.

Oh my god! My bad. I was solving for wrong variable! I did not notice that.

Thanks!

sparkles3144 wrote: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?

A. 36
B. 47
C. 58
D. 65
E. 72

An alternate approach is to plug in the answers, which represent the linear distance.
When the correct answer choice is plugged in, N-P ≈ 10.

Answer choice C: 58
Since 2.5P is equal to twice the linear distance, we get:
(5/2)P = 2*58
P = (2*2)(58)/5) = 4 * (11.6) = 46.4.
Here, N-P = 58 - 46.4 ≈ 12.

Answer choice B: 47
Since 2.5P is equal to twice the linear distance, we get:
(5/2)P = 2*47
P = (2*2)(47/5) = 4 * (9.4) = 37.6.
Here, N-P = 47 - 37.6 ≈ 10.

Since the difference in B is closer to 10 than is the difference in C, eliminate C.
Notice the TREND:
The smaller the answer choice, the smaller the difference between N and P.
Thus, the correct answer cannot be D or E.
Eliminate D and E.

Answer choice A: 36
Since 2.5P is equal to twice the linear distance, we get:
(5/2)P = 2*36
P = (2*2)(36)/5) = 4 * (7.2) = 28.8.
Here, N-P = 36 - 28.8 ≈ 7.
Since the difference in B is closer to 10 than is the difference in A, eliminate A.

The correct answer is B.

Solving algebraically might be faster here, but when a problem involves two variables, there is a definite risk: more than a few test-takers will solve for the wrong variable.
A key advantage to plugging in the answers: the process virtually GUARANTEES that the correct answer will be chosen.