If 20 Swiss Francs is enough to buy 9 notebooks and 3 pencils, is 40 Swiss Francs enough to buy 12 notebooks and 12 pencils? (inequalities)

(1) 20 Swiss Francs is enough to buy 7 notebooks and 5 pencils.
(2) 20 Swiss Francs is enough to buy 4 notebooks and 8 pencils.

Formal Answer:

Let n be the price of each notebook and p the price of each pencil. We need to know whether 12(n+p) < 40 i.e. n+p < 10/3.

1. 7n +5n < 20. This, combined with (a), means that 16n + 8p < 40. If notebooks are more expensive than pencils, 4 notebooks can be exchanged for 4 pencils, and the price of the resulting 12 notebooks and 12 pencils will be at most 40 francs. However, if pencils cost more than notebooks, when 4 notebooks are exchanged for 4 pencils, the total cost will rise, perhaps over 40 francs. For example is n=1 and p=2.5, (1) is True, but n+p> 10/3 NOT SUFF.

2. 4n+8p< 20. i.e. 2n+4p<10. (a) tells us that 3n+p < 20/3. Summing theses inequalities, we see that 5n+5p<50/3 and n+p< 10/3. It makes sense that (2) is sufficient, as even if pencils are more expensive than notebooks, 10 notebooks can be exchanged for 10 pencils without the price rising above 40 francs. SUFF

Formal Answer: A

I think the Answer should be D. Am I correct? If not, what did I do incorrectly?

Given 20 > 9n + 3p. Is 40 > 12n + 12p or 10 > 3(n+p)

(1) 20 > 9n + 3p =>
20 > 7n + 5p

100 > 45n + 15p
-60 > -21n -15p
40 > 24n
or 5/3 > n

20> 9(5/3) + 3p
20-15 > 3p
5/3 > p

n and p used to know which variable is being calculated….
12(5/3)n + 12(5/3)p =
20n + 20p = 40 SUFF



(2) I got the same answer as formal answer here- SUFF

Am I correct... the answer is B?

[kevin]

The correct answer is indeed B. Do you see why (1) is not sufficient?

[kevin]

Originally Posted by wvspidermonkey

If 20 Swiss Francs is enough to buy 9 notebooks and 3 pencils, is 40 Swiss Francs enough to buy 12 notebooks and 12 pencils? (inequalities)

(1) 20 Swiss Francs is enough to buy 7 notebooks and 5 pencils.
(2) 20 Swiss Francs is enough to buy 4 notebooks and 8 pencils.

Formal Answer:

Let n be the price of each notebook and p the price of each pencil. We need to know whether 12(n+p) < 40 i.e. n+p < 10/3.

1. 7n +5n < 20. This, combined with (a), means that 16n + 8p < 40. If notebooks are more expensive than pencils, 4 notebooks can be exchanged for 4 pencils, and the price of the resulting 12 notebooks and 12 pencils will be at most 40 francs. However, if pencils cost more than notebooks, when 4 notebooks are exchanged for 4 pencils, the total cost will rise, perhaps over 40 francs. For example is n=1 and p=2.5, (1) is True, but n+p> 10/3 NOT SUFF.

2. 4n+8p< 20. i.e. 2n+4p<10. (a) tells us that 3n+p < 20/3. Summing theses inequalities, we see that 5n+5p<50/3 and n+p< 10/3. It makes sense that (2) is sufficient, as even if pencils are more expensive than notebooks, 10 notebooks can be exchanged for 10 pencils without the price rising above 40 francs. SUFF

Formal Answer: A

I think the Answer should be D. Am I correct? If not, what did I do incorrectly?

Given 20 > 9n + 3p. Is 40 > 12n + 12p or 10 > 3(n+p)

(1) 20 > 9n + 3p =>
20 > 7n + 5p

100 > 45n + 15p
-60 > -21n -15pChange the sign!
40 > 24n
or 5/3 > n

20> 9(5/3) + 3p
20-15 > 3p
5/3 > p

n and p used to know which variable is being calculated….
12(5/3)n + 12(5/3)p =
20n + 20p = 40 SUFF



(2) I got the same answer as formal answer here- SUFF

Remember to change the sign when multiplying by a negative number!

Yes,

Thank you... I see the error. A