SOLUTION:

Last year, if Elena spent a total of $720 on newspapers, magazines, and books, what amount did she spend on newspapers?

Given that \(n + m + b = 720\), find the value of n.

(1) Last year, the amount that Elena spent on magazines was 80 percent of the amount that she spent on books --> \(m=0.8b\) --> \(n + 0.8b + b = 720\) --> \(n=720-\frac{9}{5}b\). Not sufficient.

(2) Last year, the amount that Elena spent on newspapers was 60 percent of the total amount that she spent on magazines and books --> \(n=0.6(m+b)\) --> \(\frac{5}{3}n=m+b\) --> substitute: \(n + m + b =n+\frac{5}{3}n =720\) --> we can solve for n. Sufficient.

Answer: B.
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Last year, if Elena spent a total of $720 on newspapers, magazines, and books, what amount did she spend on newspapers?

(1) Last year, the amount that Elena spent on magazines was 80 percent of the amount that she spent on books.
(2) Last year, the amount that Elena spent on newspapers was 60 percent of the total amount that she spent on magazines and books.



My Solution:
From Question: N(newspapers) + M (magazines) + B(books) = 720
From (1) : M =80/100(B)
M= 4/5B

Subs in Question: N+ 4/5B+B = 720 ( Two unknown values), So insufficient.
From(2): N=60/100(M+B)
N=3/5(M+B)
Since we need to find N, Keeping N in the equation. So M=5/3N-B
Subs in Main equation: N+ 5/3N-B +B= 720
N+5/3N= 720
So, can find N... Sufficient! My ANSWER : B

Statement 1) magazine = .8 of books. As newspaper expenditure is not provided. Hence Not sufficient.

Statement 2) Lets assume magazine expenditure = m, newspaper expenditure = n and book expenditure = b
then n = 0.6(m+b)
we know that m+n+b = $720
=> 1.6 (m+b) = $720
We can find out the value of (m+b) and from there we can find the value of n as well.
hence Option B)
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In regards to st2, is it the same as saying N = 60 % of 720 and M+B = 40% of 720?
We can't figure out exact values for M and B, but we can for M+B

Just so I have a better understanding for these types of questions

Thanks

given n$+m$+b$=720$ (amount spent on newspaper, magazines, books)

(1) Last year, the amount that Elena spent on magazines was 80 percent of the amount that she spent on books.

\(m= 0.80*(b)\)

\(n+0.80*b+b=720\)----> \(n+1.80b=720\) ------>\( n= 720-1.80b\) (we don't know b, so this is clearly insuff.)


(2) Last year, the amount that Elena spent on newspapers was 60 percent of the total amount that she spent on magazines and books.

\(n=0.60 (m+b)\) ---> \(0.60m+0.60b\) -----> \(n+m+b= 720\) ----- > \(0.60m+0.60b +m +b = 720\) ----> \(1.60m+1.60b = 720 \)-----> \(1.60(m+b)= 720 \)----> \(m+b= 720/1.60 \)

we got \(m + b\), now plug that value in the stem equation, \(n+m+b=720\) to get the value of n$

2 is sufficient. B is the answer.

Let the amount spent by Elena on newspapers be $n, on magazines be $m and on books be $b. From the question data, n + m + b = 720.
The value of n to be found.

From statement I alone, m = \(\frac{4}{5}\) * b. No information about n.

Statement I alone is insufficient to find the value of n. Answer options A and D can be eliminated. Possible answer options are B, C or E.

From statement II alone, n = \(\frac{3}{5}\) (m +b). We can rewrite this as \(\frac{n }{ (m+b)}\) = \(\frac{3}{5}\).

This means, n and (m+b) are in the ratio of 3:5, so n = 3k and (m+b) = 5k.

From question data, n + m + b = 720. Substituting the values of n and (m+b), we have,
3k + 5k = 720 i.e. k = 90. Therefore, n = 3k = 270.
Statement II alone is sufficient to find the value of n. Answer options C and E can be eliminated.

The correct answer option is B.

Hope that helps!
Aravind B T
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Solution:

Question Stem Analysis:

We need to determine the amount of money Elena spent on newspapers given that she spent a total of $720 on newspapers, magazines, and books. We can let n, m, and b be the amounts (in dollars) she spent on newspapers, magazines, and books, respectively. Therefore, we need to determine the value of n, given that n + m + b = 720.

Statement One Alone:

We are given that m = 0.8b. Substituting this in the equation in the stem analysis, we have:

n + 0.8b + b = 720

n + 1.8b = 720

We can’t determine the value of n since we don’t know the value of b. Statement one alone is not sufficient.

Statement Two Alone:

We are given that n = 0.6(m + b). Substituting this in the equation in the stem analysis, we have:

0.6(m + b) + m + b = 720

1.6(m + b) = 720

m + b = 450

Since n = 0.6(m + b), n = 0.6(450) = 270. Statement two alone is sufficient.

Answer: B

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