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Math Expert V
Joined: 02 Sep 2009
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How many two-digit whole numbers yield a remainder of 3 when divided  [#permalink]

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10 00:00

Difficulty:   35% (medium)

Question Stats: 69% (01:35) correct 31% (01:48) wrong based on 292 sessions

### HideShow timer Statistics Tough and Tricky questions: Geometry.

How many two-digit whole numbers yield a remainder of 3 when divided by 10 and also yield a remainder of 3 when divided by 4?

A) One
B) Two
C) Three
D) Four
E) Five

Kudos for a correct solution.

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Re: How many two-digit whole numbers yield a remainder of 3 when divided  [#permalink]

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1
A whole number is essentially an integer and a two digit whole number is 10-99, inclusive. I'm not sure whether we consider positive and negative or just positive. Let's stick to just positives for now.

All positive two-digit integers that leave a remainder of 3 when divided by 10 are: 13, 23, 33, 43, 53, 63, 73, 83 and 93. Of these only the numbers with an even tens digit leave a remainder of 3 when divided by 4--23, 43, 63 and 83. Answer is 4. I guess that means we don't consider negatives.

Choice D
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Re: How many two-digit whole numbers yield a remainder of 3 when divided  [#permalink]

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3
Numbers yield a remainder of 3 when divided by 10. Let x be the number.
x= 10m+3 ......... 1

Numbers yield a remainder of 3 when divided by 4.
x= 4n+3 .......... 2

combining 1 and 2,
x= 20p+3 ....... (20 is the LCM of 10 and 4 and 3 is the first term in the series that satisfies both equations)
p can take value of 1,2,3 and 4 to keep x a two digit number.
so total numbers = 4

Ans - D

Originally posted by desaichinmay22 on 04 Dec 2014, 11:20.
Last edited by desaichinmay22 on 05 Dec 2014, 00:28, edited 1 time in total.
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Re: How many two-digit whole numbers yield a remainder of 3 when divided  [#permalink]

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Numbers giving remainder 3 when divided by 10 = 13, 23, 33, 43, 53, 63, 73, 83, 93

Numbers giving remainder 3 when divided by 4 = Alternate numbers (coloured in red) = 4
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Re: How many two-digit whole numbers yield a remainder of 3 when divided  [#permalink]

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1
desaichinmay22 wrote:
Numbers yield a remainder of 3 when divided by 10. Let x be the number.
x= 10m+3 ......... 1

Numbers yield a remainder of 3 when divided by 4.
x= 4n+3 .......... 2

combining 1 and 2,
x= 20p+3 ....... (20 is the LCM of 10 and 4 and 3 is the first term in the series that satisfies both equations)
p can take value of 0,1,2,3 and 4 to keep x a two digit number.
so total numbers = 5

Ans - E

If we place p = 0, it will return x = 3 (Single digit number)
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Re: How many two-digit whole numbers yield a remainder of 3 when divided  [#permalink]

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PareshGmat wrote:
desaichinmay22 wrote:
Numbers yield a remainder of 3 when divided by 10. Let x be the number.
x= 10m+3 ......... 1

Numbers yield a remainder of 3 when divided by 4.
x= 4n+3 .......... 2

combining 1 and 2,
x= 20p+3 ....... (20 is the LCM of 10 and 4 and 3 is the first term in the series that satisfies both equations)
p can take value of 0,1,2,3 and 4 to keep x a two digit number.
so total numbers = 5

Ans - E

If we place p = 0, it will return x = 3 (Single digit number)

Yes.. missed on that... I have corrected the solution
Math Expert V
Joined: 02 Sep 2009
Posts: 56300
Re: How many two-digit whole numbers yield a remainder of 3 when divided  [#permalink]

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Bunuel wrote:

Tough and Tricky questions: Geometry.

How many two-digit whole numbers yield a remainder of 3 when divided by 10 and also yield a remainder of 3 when divided by 4?

A) One
B) Two
C) Three
D) Four
E) Five

Kudos for a correct solution.

Source: Chili Hot GMAT

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Re: How many two-digit whole numbers yield a remainder of 3 when divided  [#permalink]

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First Of all we could arrange every 2 digit number when we divide by 10 give us reminder 3 . It Is obvious that the number will have 3 in its unit digit

so we will have the list of numbers as follows : 13 , 23, 33, 43, 53, 63, 73, 83, and 93......

in this stage we should divide each number by 4 and see which of them yields reminder 3 after dividing by 4

we see here the first number (13) gives us reminder 1 so it is out the second number( 23) gives us reminder 3 so it is OK

the third number gives reminder 1 so out and if we continue this action we see the pattern will be repeat again one by one so the even members will give us reminder 3

if we count the even number we see here we have 23 , 43, 63, and 83 so we have 4 number and Option D is fit ... VP  P
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How many two-digit whole numbers yield a remainder of 3 when divided  [#permalink]

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How many two-digit whole numbers yield a remainder of 3 when divided by 10 and also yield a remainder of 3 when divided by 4?

A) One
B) Two
C) Three
D) Four
E) Five

lowest value of n=3
interval between possible values of n=lcm of divisors=20
let x=number of two-digit values of n
3+20x<100
20x<97
x<4.9
x=4
D
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Re: How many two-digit whole numbers yield a remainder of 3 when divided  [#permalink]

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Bunuel wrote:

Tough and Tricky questions: Geometry.

How many two-digit whole numbers yield a remainder of 3 when divided by 10 and also yield a remainder of 3 when divided by 4?

A) One
B) Two
C) Three
D) Four
E) Five

We need to determine how many two-digit whole numbers yield a remainder of 3 when divided by 10 and also yield a remainder of 3 when divided by 4. Let’s list out the numbers that have a remainder of 3 when divided by 10.

Remainder of 3 when divided by 10:

13, 23, 33, 43, 53, 63, 73, 83, 93

Of those numbers, only 23, 43, 63, and 83 leave a remainder of 3 when divided by 4.

Alternate Solution:

Note that for a number to yield a remainder of 3 when divided by 10, the unit digit must be 3. Note also that for a number to yield a remainder of 3 when divided by 4, three less than that number must be divisible by 4. Combining these two pieces of information, we need to look for two-digit numbers that are divisible by 4 and that have a units digit of zero. These numbers are 20, 40, 60, and 80. Therefore, 23, 43, 63, and 83 are the only two-digit numbers that yield a remainder of 3 when divided by 4 and by 10.

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Re: How many two-digit whole numbers yield a remainder of 3 when divided  [#permalink]

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LCM of 10 and 4 is 20. The only 2-digit multiples of 20 are 20,40,60,80. The 2 digit numbers which when divided by 4 and 10 have remainder 3 are thus: 23, 43, 63, 83.

4 in all.

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Re: How many two-digit whole numbers yield a remainder of 3 when divided  [#permalink]

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1
take the lcm of 4 and 10. which is 20.

now take the first common number from both the patters 10k+3 and 4q+3, which is 3.

now common series is 20n+3 and we will get 0,23,43,63 and 83.

since we have been asked only 2 digit numbers, the answer is 4.

option D is the correct asnwer.
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Re: How many two-digit whole numbers yield a remainder of 3 when divided  [#permalink]

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_________________ Re: How many two-digit whole numbers yield a remainder of 3 when divided   [#permalink] 17 Aug 2018, 11:04
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