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This question, and its explanation, do not make sense.

A shopper came to a store to purchase 4 items. What were the prices of the four items?

1) The total cost was $5.11 2) The product of the prices was $5.11

The explanation says:

This problem has 4 variables and two equations. It is impossible to solve it.

This is not a two-equation, four-variable situation. If we call the prices a, b, c and d, we know:

a+b+c+d = 5.11 abcd = 5.11

But we also know:

* a, b, c and d are all positive; * 100a, 100b, 100c and 100d are all integers- they are prices in a shop, after all. You can't see a price of an item in a shop that is equal to \sqrt{2}, \Pi or 3.44417.

If we let A, B, C and D be the prices in cents, so that A = 100a, B = 100b, C = 100c and D = 100d, we have:

Thus, A, B, C and D need to be positive integer factors of (2^3)(5^3)(7)(73), their product needs to be (2^3)(5^3)(7)(73), and they need to add to 511. These are extreme restrictions- this is not a 2-equation, 4-variable problem. In fact, there are no possible values for A, B, C and D, if my calculations are correct.
_________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

So you're saying E is what you choose for your answer?

IanStewart wrote:

This question, and its explanation, do not make sense.

A shopper came to a store to purchase 4 items. What were the prices of the four items?

1) The total cost was $5.11 2) The product of the prices was $5.11

The explanation says:

This problem has 4 variables and two equations. It is impossible to solve it.

This is not a two-equation, four-variable situation. If we call the prices a, b, c and d, we know:

a+b+c+d = 5.11 abcd = 5.11

But we also know:

* a, b, c and d are all positive; * 100a, 100b, 100c and 100d are all integers- they are prices in a shop, after all. You can't see a price of an item in a shop that is equal to \sqrt{2}, \Pi or 3.44417.

If we let A, B, C and D be the prices in cents, so that A = 100a, B = 100b, C = 100c and D = 100d, we have:

Thus, A, B, C and D need to be positive integer factors of (2^3)(5^3)(7)(73), their product needs to be (2^3)(5^3)(7)(73), and they need to add to 511. These are extreme restrictions- this is not a 2-equation, 4-variable problem. In fact, there are no possible values for A, B, C and D, if my calculations are correct.

_________________

------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

So you're saying E is what you choose for your answer?

Logically, there is no good answer: C is 'correct', because the situation is impossible, and therefore we know with both statements that the prices are impossible to find. That is, using both statements, we know the answer is 'no solution'. But E is also 'correct', because even with both statements, we can't find the prices. The statements in a DS question should never be contradictory. Still, more importantly, the explanation provided is a gross oversimplification of the problem, which is what I was pointing out.
_________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

I agree with your answer of E. I think it would be C if the question were a yes/no answer where we have to find out if the answer is always Yes, or always no, but when the question asks for values and we still have multiple possible values...that is E and not C. Besides, I've never heard of a "no solution" on the real GMAT.

IanStewart wrote:

jallenmorris wrote:

So you're saying E is what you choose for your answer?

Logically, there is no good answer: C is 'correct', because the situation is impossible, and therefore we know with both statements that the prices are impossible to find. That is, using both statements, we know the answer is 'no solution'. But E is also 'correct', because even with both statements, we can't find the prices. The statements in a DS question should never be contradictory. Still, more importantly, the explanation provided is a gross oversimplification of the problem, which is what I was pointing out.

_________________

------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

I agree with your answer of E. I think it would be C if the question were a yes/no answer where we have to find out if the answer is always Yes, or always no, but when the question asks for values and we still have multiple possible values...that is E and not C. Besides, I've never heard of a "no solution" on the real GMAT.

We do not have multiple possible values here- there is no possible solution, if you use both statements. And yes, as you say, that never happens on the real GMAT (in a real GMAT DS question that asks for a value, there is always at least one solution when you combine both statements), for precisely the reason I pointed out above- it leaves both C and E as logically 'correct' answers. This is one of the problems with the question that I am pointing out.
_________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Thanks guys, +2 for you both. If you have any suggestions on how to improve the question we encourage you to share your ideas. Any help will be greatly appreciated.

This question, and its explanation, do not make sense.

A shopper came to a store to purchase 4 items. What were the prices of the four items?

1) The total cost was $5.11 2) The product of the prices was $5.11

The explanation says:

This problem has 4 variables and two equations. It is impossible to solve it.

This is not a two-equation, four-variable situation. If we call the prices a, b, c and d, we know:

a+b+c+d = 5.11 abcd = 5.11

But we also know:

* a, b, c and d are all positive; * 100a, 100b, 100c and 100d are all integers- they are prices in a shop, after all. You can't see a price of an item in a shop that is equal to \sqrt{2}, \Pi or 3.44417.

If we let A, B, C and D be the prices in cents, so that A = 100a, B = 100b, C = 100c and D = 100d, we have:

Thus, A, B, C and D need to be positive integer factors of (2^3)(5^3)(7)(73), their product needs to be (2^3)(5^3)(7)(73), and they need to add to 511. These are extreme restrictions- this is not a 2-equation, 4-variable problem. In fact, there are no possible values for A, B, C and D, if my calculations are correct.

HAs the forum been updated? as i have totally different question for M01 number 27

Max's current monthly salary is $2,000, and will be raised by 25% next month. If he decides to save exactly 25% of his salary each month, how many months will it take for Max to save $5,500?

Max's current monthly salary is $2,000, and will be raised by 25% next month. If he decides to save exactly 25% of his salary each month, how many months will it take for Max to save $5,500?