FDP chapter 7, question 7

[paraclete]

I'm confused about chapter 7, question 7 of the FDP guide (5th edition). It says only A and B could be correct, but I don't see why C and D can't be correct either (since 4*9*1 also equals 36). Moreover, it looks like answer B isn't actually correct when you look at all the information given. Am I just looking at this wrong? Please help!

Thanks!

[jnelson0612]

I'm confused about chapter 7, question 7 of the FDP guide (5th edition). It says only A and B could be correct, but I don't see why C and D can't be correct either (since 4*9*1 also equals 36). Moreover, it looks like answer B isn't actually correct when you look at all the information given. Am I just looking at this wrong? Please help!

Thanks!

Hey Kenneth,
Look at the far right (units) digits of all the numbers. You have a diamond * diamond which results in a number that also ends in a diamond. What digit when squared ends in the same number? 1, 5, and 6. 1*1=1 5*5 = 25 6*6=36 Every other number when squared results in a product with a DIFFERENT number in the units digit. So right off the bat only B and D are possible.

If you test out B, it works. Put in 2=circle, 3=square, 6=diamond. You'll get 936, so 9=diamond.

If you test D is doesn't work. You'll get 41 * 91 which will be a four digit number, not a three digit.

[jasonthomasyee]

I'm confused about chapter 7, question 7 of the FDP guide (5th edition). It says only A and B could be correct, but I don't see why C and D can't be correct either (since 4*9*1 also equals 36). Moreover, it looks like answer B isn't actually correct when you look at all the information given. Am I just looking at this wrong? Please help!

Thanks!

Hey Kenneth,
Look at the far right (units) digits of all the numbers. You have a diamond * diamond which results in a number that also ends in a diamond. What digit when squared ends in the same number? 1, 5, and 6. 1*1=1 5*5 = 25 6*6=36 Every other number when squared results in a product with a DIFFERENT number in the units digit. So right off the bat only B and D are possible.

If you test out B, it works. Put in 2=circle, 3=square, 6=diamond. You'll get 936, so 9=diamond.

If you test D is doesn't work. You'll get 41 * 91 which will be a four digit number, not a three digit.

I had the same question! I actually chose D - 491 as well, so thank you for your explanation it makes much more sense to me now.

With regards to the PROCESS for solving this question, the FDP strategy guide recommends breaking 36 out into its prime factors 2x2x3x3. The book then state "What different digits can you create using two 2's and two 3's? 2, 3, and 6. So these three symbols must equal 2,3,6 but which is which?"

In light of the fact that the prime factorization could also yield digits 4 and 9 (and the obvious 1 as well), the digits could also be 4,9,1, so the only answer choice we could eliminate right off the bat would be E. However, one should have already eliminated E given that the digits don't give us a product of 36. Sorry to be long winded, but ultimately would you say there may not be a benefit to spending time on the prime factorization of 36 since it doesn't eliminate any answer choices?

[RonPurewal]

I don't mean to spoil the party here, but we can't have any further discussion of this problem until the forum rules are followed "” i.e., please post the entire text of the question. If there are answer choices, we need those, too.

Thanks.