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The product of 3,305 and the 1-digit integer xis a 5-digit integer. Th

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The product of 3,305 and the 1-digit integer xis a 5-digit integer. Th  [#permalink]

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New post 23 Jul 2017, 12:30
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The product of 3,305 and the 1-digit integer x is a 5-digit integer. The units (ones) digit of the product is 5 and the hundreds digit is y. If A is the set of all possible values of x and B is the set of all possible values of y, then which of the following gives the members of A and B?

A AND B


A. {1,3,5,7,9} (0,1,2,3,4,5,6,7,8,9}

B. {1,3,5,7,9} {1,3,5,7,9}

C. {3,5,7,9} {1,5,7,9}

D. {5,7,9} {1,5,7}

E. {5,7,9} {1,5,9}

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Re: The product of 3,305 and the 1-digit integer xis a 5-digit integer. Th  [#permalink]

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New post 23 Jul 2017, 15:11
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carcass wrote:
The product of 3,305 and the 1-digit integer x is a 5-digit integer. The units (ones) digit of the product is 5 and the hundreds digit is y. If A is the set of all possible values of x and B is the set of all possible values of y, then which of the following gives the members of A and B?

A AND B


A. {1,3,5,7,9} (0,1,2,3,4,5,6,7,8,9}

B. {1,3,5,7,9} {1,3,5,7,9}

C. {3,5,7,9} {1,5,7,9}

D. {5,7,9} {1,5,7}

E. {5,7,9} {1,5,9}


Wow. There are a lot of steps to this one. The key is going to be extremely careful organization (you should pick up on that when you see how many numbers there are in the answer choices, and the complexity of the question they're asking you.)

First, I read the whole thing. Then I approached the first sentence:

3305x is a 5-digit integer.

That probably limits the possible values for x. For instance, x can't be 1, 2, or 3, because the product would be too small. Is there an upper limit to the values of x? For instance, could x be 9? To check, I multiplied 3305*9 on my paper and found that the result had 5 digits. So, the acceptable values for x will be 4, 5, 6, 7, 8, and 9 (so far). I jotted those down on my scratch paper (large & clear).

4 5 6 7 8 9

The problem also says that the units digit of 3305x is 5. That means x must be odd. If x was even, the units digit would come out to 0. So, I crossed off all of the even numbers:

4 5 6 7 8 9

Now there are only three possible values for x. I don't see anything that limits it further than that, so I write down on my paper:

A = {5, 7, 9}

At this point, I also jot down the answer choices, A B C D E, and cross off everything except for D and E.

To figure out the values of y, we need to find the hundreds digit of 3305x. There's a rule that says that if you only want a particular digit, you can ignore everything past that digit. We can ignore the first 3 in 3305 and just treat it like 305, since it won't affect the hundreds digit of the result. That'll speed up the multiplication.

305 * 5 = 1525, hundreds digit = 5
305 * 7 = 2135, hundreds digit = 1
305 * 9 = 2745, hundreds digit = 7

So now I know B = {1, 5, 7}.

Finally, check this against the two remaining answer choices. D is correct.
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Re: The product of 3,305 and the 1-digit integer xis a 5-digit integer. Th  [#permalink]

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New post 30 Jul 2017, 07:31
looks difficult .. but easy equation to solve .
So challenge if any will be the language of the question .
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The product of 3,305 and the 1-digit integer xis a 5-digit integer. Th  [#permalink]

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New post 03 Aug 2017, 08:55
ccooley wrote:
carcass wrote:
The product of 3,305 and the 1-digit integer x is a 5-digit integer. The units (ones) digit of the product is 5 and the hundreds digit is y. If A is the set of all possible values of x and B is the set of all possible values of y, then which of the following gives the members of A and B?

A AND B


A. {1,3,5,7,9} (0,1,2,3,4,5,6,7,8,9}

B. {1,3,5,7,9} {1,3,5,7,9}

C. {3,5,7,9} {1,5,7,9}

D. {5,7,9} {1,5,7}

E. {5,7,9} {1,5,9}


Wow. There are a lot of steps to this one. The key is going to be extremely careful organization (you should pick up on that when you see how many numbers there are in the answer choices, and the complexity of the question they're asking you.)

First, I read the whole thing. Then I approached the first sentence:

3305x is a 5-digit integer.

That probably limits the possible values for x. For instance, x can't be 1, 2, or 3, because the product would be too small. Is there an upper limit to the values of x? For instance, could x be 9? To check, I multiplied 3305*9 on my paper and found that the result had 5 digits. So, the acceptable values for x will be 4, 5, 6, 7, 8, and 9 (so far). I jotted those down on my scratch paper (large & clear).

4 5 6 7 8 9

The problem also says that the units digit of 3305x is 5. That means x must be odd. If x was even, the units digit would come out to 0. So, I crossed off all of the even numbers:

4 5 6 7 8 9

Now there are only three possible values for x. I don't see anything that limits it further than that, so I write down on my paper:

A = {5, 7, 9}

At this point, I also jot down the answer choices, A B C D E, and cross off everything except for D and E.

To figure out the values of y, we need to find the hundreds digit of 3305x. There's a rule that says that if you only want a particular digit, you can ignore everything past that digit. We can ignore the first 3 in 3305 and just treat it like 305, since it won't affect the hundreds digit of the result. That'll speed up the multiplication.

305 * 5 = 1525, hundreds digit = 5
305 * 7 = 2135, hundreds digit = 1
305 * 9 = 2745, hundreds digit = 7

So now I know B = {1, 5, 7}.

Finally, check this against the two remaining answer choices. D is correct.



If I am a 600-650 scorer , then is it possible to solve this question in just 2 minutes?
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Re: The product of 3,305 and the 1-digit integer xis a 5-digit integer. Th  [#permalink]

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New post 09 Aug 2017, 12:43
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carcass wrote:
The product of 3,305 and the 1-digit integer x is a 5-digit integer. The units (ones) digit of the product is 5 and the hundreds digit is y. If A is the set of all possible values of x and B is the set of all possible values of y, then which of the following gives the members of A and B?

A AND B


A. {1,3,5,7,9} (0,1,2,3,4,5,6,7,8,9}

B. {1,3,5,7,9} {1,3,5,7,9}

C. {3,5,7,9} {1,5,7,9}

D. {5,7,9} {1,5,7}

E. {5,7,9} {1,5,9}


We are given that the product of 3,305 and the 1-digit integer x is a 5-digit integer, the units (ones) digit of the product is 5, and the hundreds digit is y. In order for the product to be a 5-digit integer, we see that x cannot be 1, 2, or 3. In order for the product to have 5 as its ones digit, we can also eliminate 4, 6, and 8 from consideration.

Thus, x can only be 5, 7, or 9.

Let’s now solve for y:

When x is 5, since 5 x 3,305 = 16,525, y is 5.

When x is 7, since 7 x 3,305 = 23,135, y is 1.

When x is 9, since 9 x 3,305 = 29,745, y is 7.

Thus, A = 5, 7, and 9 and B = 1, 5, and 7.

Answer: D
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Re: The product of 3,305 and the 1-digit integer xis a 5-digit integer. Th  [#permalink]

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New post 01 Sep 2017, 04:16
"The product of 3,305 and the 1-digit integer x is a 5-digit integer"

It is slightly confusing. I thought, above statement meant, product of three integers i.e. 3, 305 and another integer x.
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Re: The product of 3,305 and the 1-digit integer xis a 5-digit integer. Th  [#permalink]

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New post 10 Sep 2017, 04:03
2
carcass wrote:
The product of 3,305 and the 1-digit integer x is a 5-digit integer. The units (ones) digit of the product is 5 and the hundreds digit is y. If A is the set of all possible values of x and B is the set of all possible values of y, then which of the following gives the members of A and B?

A AND B


A. {1,3,5,7,9} (0,1,2,3,4,5,6,7,8,9}

B. {1,3,5,7,9} {1,3,5,7,9}

C. {3,5,7,9} {1,5,7,9}

D. {5,7,9} {1,5,7}

E. {5,7,9} {1,5,9}



_ _ Y _ 5 = 3305 x X
we know x cannot equal 1 or 3 because the product of that does not equal 5 digits, but only 4
therefore eliminate answers a,b,c

for x, we are left with 5,7,9 -- just plug these in for x

3305 x 5 = 16,525 wherein y = 5
3305 x 7 = 23,135 wherein y = 1
3305 x 9 = 29,745 wherein y = 7

therefore the answer is D

hope that helps
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Re: The product of 3,305 and the 1-digit integer xis a 5-digit integer. Th  [#permalink]

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New post 10 Sep 2017, 04:04
nareshlawadia wrote:
"The product of 3,305 and the 1-digit integer x is a 5-digit integer"

It is slightly confusing. I thought, above statement meant, product of three integers i.e. 3, 305 and another integer x.



When you are translating english to math, "product" means multiplication, and "is" translates to equals sign

so 3,305 x X = a five digit integer

hope that helps
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Re: The product of 3,305 and the 1-digit integer xis a 5-digit integer. Th  [#permalink]

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New post 24 Jun 2018, 05:33
niks18 chetan2u VeritasPrepKarishma

Can I skip calculation part as shown by JeffTargetTestPrep
knowing that 9*9 = 81 ?
All individual set elements must result in product as 5 in unit digit.
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Re: The product of 3,305 and the 1-digit integer xis a 5-digit integer. Th  [#permalink]

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New post 24 Jun 2018, 06:40
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adkikani wrote:
niks18 chetan2u VeritasPrepKarishma

Can I skip calculation part as shown by JeffTargetTestPrep
knowing that 9*9 = 81 ?
All individual set elements must result in product as 5 in unit digit.


Hi adkikani

Once you have identified the elements of set x, then only two options remain D & E.

concentrate on the last three digits of the number 3305 when you multiply 05 by x, then the product will not have any carry over for the hundred's digit. for e.g 05*9=45 and there is no carry forward.

Hence the hundreds digit of the resulting product will be simply unit's digit of 3*x

so y = 3*5=15

y=3*7=21 & y=3*9=27

so you can save yourself from calculation if you have visualized this step
Re: The product of 3,305 and the 1-digit integer xis a 5-digit integer. Th &nbs [#permalink] 24 Jun 2018, 06:40
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