metallicafan wrote:

At a certain bookstore, each notepad costs x dollars and each markers costs y dollars. If $10 is enough to buy 5 notepads and 3 markers, is $10 enough to buy 4 notepads and 4 markers instead?

1). each notepad cost less than $1

2). $10 is enough to buy 11 notepads

Given: 5x + 3y <= 10 .... (I)

Question: Is 4x + 4y <=10 ?....(II)

Statement (1) x < 1.

If x is a little less than 1 but almost 1, then 5x is little less than 5. Putting in (I) above, we get that y is less than \(\frac{5}{3}\).

Now we need to put these values in equation (II) and check.

4x will be a little less than 4 and 4y will be less than 4x\(\frac{5}{3}\) i.e. 6.66. Together, 4x + 4y will be less than 10.66. It may be less than 10 or a little more than 10, hence this is not sufficient.

Statement (2) x < \(\frac{10}{11}\)

If x is a little less than 10/11 but almost 10/11, then 5x is little less than 50/11. Putting in (I) above, we get that y is less than \(\frac{20}{11}\).

Now we need to put these values in equation (II) and check.

4x will be a little less than 40/11 and 4y will be less than 4x\(\frac{20}{11}\) i.e. \(\frac{80}{11}\). Together, 4x + 4y will be less than 120/11 i.e. less than 10.9. It may be less than 10 or more, we do not know, hence this is not sufficient.

Note: You didn't actually need to calculate the data in the second statement. This is because, if we compare 5x + 3y with 4x + 4y, the x term has reduced but the y term has increased. If x is as great as possible, it will keep y small and the extra y in second statement may not matter. We tried with x a little less than 1 in first statement. In second statement, x is smaller than 10/11. Hence, if first statement was not sufficient, no way could the second statement be sufficient.

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