The product of 3305 and the 1-digit integer x is a 5-digit integer.

Question

The product of 3305 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 numbers of A and B?

------------A----------------------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}

ccooley · Accepted Answer

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.

Carcass · Answer

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}

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}

rohit8865 · Answer

3305*A = xxBxx

option A,B,C are out as 3305 multiplied by 1 or 3 (which set A contains) never gives a 5 digit product value

working further

(D) 3305*5 = 16  5  25
3305*7 = 23  1  21
3305*9 = 29  7  45

so Set B contains all three above values

Ans D

TheKingInTheNorth · Answer

looks difficult .. but easy equation to solve . 
So challenge if any will be the language of the question .

rocko911 · Answer

If I am a 600-650 scorer , then is it possible to solve this question in just 2 minutes?

JeffTargetTestPrep · Answer

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

nareshlawadia · Answer

"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.

CyberStein · Answer

_ _ 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

CyberStein · Answer

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

adkikani · Answer

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.

niks18 · Answer

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 3 305  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=1 5

y=3*7=2 1  & y=3*9=2 7

so you can save yourself from calculation if you have visualized this step

hasnain3047 · Answer

If we look at the given answer, we can see than 5 digit number is possible for values of A greater than 3. So we are only left with option C and D.
now by working further, we have to determine whether we can get hundreds digit 9 or 7.
so if we multiply 3305 by 5 we get 16525 and hundreds digit is  5 
 if we multiply 3305 by 7 we get 22135 and hundreds digit is  1 
 if we multiply 3305 by 9 we get 29745 and hundreds digit is  7 
as 5,1 and 7 are members of set B in option (D) so 
 Answer is (D)

KarishmaB · Answer

The product of 3305 and the 1-digit integer x is a 5-digit integer.

3305*3 = 9915
So x is 4 or more. Since x is a 1 digit integer, it can be anything from 4 to 9.

If units digit of the product is 5, this means x must be odd (if x were even, the units digit will be 0)

So x must be 5/7/9

3305 * 5 = ...525
3305 * 7 = ...135
3305 * 9 = ...745

So the hundreds digit would be 5/1/7 (value of y)

Answer (D)

Salsanousi · Answer

To understand this we need to keep this thought in mind that x > 4 because 3,305 * 3 is less than 5 digits.

Since the ones digit is 5 that means x has to be an odd integer greater than 4. These are 5,7, and 9.

Now we are concerned with hundreds digit.

We can take 300 * 5 = 1,500

300 * 7 = 2,100

and 300 * 9 = 2,700

So we get 1,5, and 7

Answer choice D

stne · Answer

Dear Moderator, This same question seems to have been duplicated in the link below, you may wish to merge the same, Thank you. https://gmatclub.com/forum/the-product- ... l#p1859424

Bunuel · Answer

Topics merged. Thank you.

legendinthewomb · Answer

Crazy sum! Can't believe it's still in the 600 range.

3305*x= _ _ y _ 5
1. ends with 5: only odd numbers multiplied with 5 end with 5, x must be odd. This doesn't help eliminate any of the answer choices, so let's look for another one. 
2. it's a 5 digit number. x needs to be more than 3. So, let's eliminate A, B, and C.

Amongst D and E, we have to multiply and since the first part (Set A) is the same, we save some time. 
3305*5=_ _525
3305*7=_ _135, so far so good. 
3305*9=_ _745

If you're out of time, skip the last two calculations. eg 3305*9=_ _7_ _

MHIKER · Answer

Single-digit numbers are  0,1,2,3,4,5,6,7,8,9  but according to condition we can't take  0,1,2,3,4,6 , and  3305*3  will end up with unit digit  5  but the number will a four digits number again, so  3   is out.

Now, we have  5,7,9  as set  A  so, options are narrowed down to  D  and  E  as set  A 
 3305*9= 29 7 45 Option E does not has 7

So, D is the answer.

egmat · Answer

Let's break down what we're looking for:

We need to find all single-digit values of x where $3305 × x$ gives us:

A 5-digit number (between 10,000 and 99,999)
With units digit = 5
Then collect all possible hundreds digits from these products

Step 1: Apply the 5-digit constraint

For the product to be exactly 5 digits, we need $10,000 ≤ 3305x ≤ 99,999$

Let's find the boundary:

$10,000 ÷ 3305 ≈ 3.02$
So we need $x ≥ 4$ to get a 5-digit number

Let me verify: $3305 × 3 = 9,915$ (only 4 digits - doesn't work!)

So x must be at least 4. Since x is a single digit, possible values are: 4, 5, 6, 7, 8, 9

Step 2: Apply the units digit constraint

Now here's the key insight: Since 3305 ends in 5, we need to find which digits, when multiplied by 5, give a units digit of 5.

Think about the pattern:

$1 × 5 = 5$ (units digit is 5 ✓)
$2 × 5 = 10$ (units digit is 0 ✗)
$3 × 5 = 15$ (units digit is 5 ✓)
$4 × 5 = 20$ (units digit is 0 ✗)
$5 × 5 = 25$ (units digit is 5 ✓)

Notice the pattern? The units digit is 5 only when x is odd: 1, 3, 5, 7, 9

Step 3: Combine both constraints

From Step 1: $x ≥ 4$ (to get 5 digits)
From Step 2: x must be odd (to get units digit 5)

Combining these: x can only be 5, 7, or 9

Therefore, Set A = {5, 7, 9}

Step 4: Find the hundreds digits

Now let's calculate each product and identify the hundreds digit:

$3305 × 5 = 16,525$ → The hundreds digit is 5
$3305 × 7 = 23,135$ → The hundreds digit is 1
$3305 × 9 = 29,745$ → The hundreds digit is 7

Therefore, Set B = {1, 5, 7}

Answer: (D) {5, 7, 9}----------{1, 5, 7}

The most common mistake? Students often include x = 1 and x = 3 in Set A because they correctly identify that odd numbers give a units digit of 5, but they forget to check that these values don't produce 5-digit numbers!

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