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problem solving

by nafiul9090 » Sun May 20, 2012 6:25 am
How many positive integers less than 30 are either a multiple
of 2, an odd multiple of 9, or the sum of a positive multiple of
2 and a positive multiple of 9 ?
(A) 27
(B) 26
(C) 25
(D) 24
(E) 23

i am totally lost in this problem. please someone shed some eco-friendly light :(
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by Brent@GMATPrepNow » Sun May 20, 2012 6:43 am
nafiul9090 wrote:How many positive integers less than 30 are either a multiple
of 2, an odd multiple of 9, or the sum of a positive multiple of
2 and a positive multiple of 9 ?
(A) 27
(B) 26
(C) 25
(D) 24
(E) 23

i am totally lost in this problem. please someone shed some eco-friendly light :(
First check the answer choices. They range from 23 to 27.

Since there are 29 positive integers less than 30, it might be easiest to find the values that don't meet any of the criteria and subtract this value from 29.

Observe
1) Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, . . . 28
2) Odd multiples of 9: 9, 27
3) Sum of a positive multiple of 2 and a positive multiple of 9: By adding an even number to 9 (e.g., 9+2, 9+4, 9+6, etc), we can get every odd number from 11 to 29.

Summarize
The first condition gives us every even number from 2 to 28.
The second condition gives us 9
The third condition gives us every odd number from 11 to 29.

So, it appears that the only numbers that can't be derived are the 4 odd numbers from 1 to 7 (1, 3, 5, and 7)

So, the number of integers that meet the conditions = 29 - 4 = [spoiler]25 = C[/spoiler]

Cheers,
Brent
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by LalaB » Sun May 20, 2012 9:46 pm
Brent@GMATPrepNow wrote:
2) Odd multiples of 9: 9, 27

Summarize

The second condition gives us 9

So, it appears that the only numbers that can't be derived are the 4 odd numbers from 1 to 7 (1, 3, 5, and 7)

Hi Brent,

I didnt get this part of ur post.First you said that we have 9 and 27, but then u summarized that there is only 9.

I also didnt get about 4 numbers. ((

my way of thinking is as following -

integers less than 30

1) a multiple of 2 (28-2)/2+1=14

2)an odd multiple of 9 - 9 and 27 (total 2)

3)the sum of a positive multiple of 2 and a positive multiple of 9 -
for 9 these numbers are from 2 to 16 (total 8)
for 27 this number is 2 (total 1)

total =14+2+8 +1 =25
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by nafiul9090 » Sun May 20, 2012 11:00 pm
LalaB wrote:
Brent@GMATPrepNow wrote:
2) Odd multiples of 9: 9, 27

Summarize

The second condition gives us 9

So, it appears that the only numbers that can't be derived are the 4 odd numbers from 1 to 7 (1, 3, 5, and 7)

Hi Brent,

I didnt get this part of ur post.First you said that we have 9 and 27, but then u summarized that there is only 9.

I also didnt get about 4 numbers. ((

my way of thinking is as following -

integers less than 30

1) a multiple of 2 (28-2)/2+1=14

2)an odd multiple of 9 - 9 and 27 (total 2)

3)the sum of a positive multiple of 2 and a positive multiple of 9 -
for 9 these numbers are from 2 to 16 (total 8)
for 27 this number is 2 (total 1)

total =14+2+8 +1 =25
hi Lala B

i've followed ur process but i have lost in part 3. could you please elaborate it again

regards Nafi
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by LalaB » Sun May 20, 2012 11:57 pm
nafiul9090 wrote:
hi Lala B

i've followed ur process but i have lost in part 3. could you please elaborate it again

regards Nafi
ok, step 3 -
u r asked to find the sum of a positive multiple of 2 and a ODD positive multiple of 9 less than 30 (hm it seems that the word odd is forgotten here)

sum of a positive multiple of 2 are numbers from 2 to 28 (2 4 6 8 10 12 14 16 18...28)


positive odd multiple of 9 - 9 and 27

9+2 ;9+4 ;9+6;...9+16 (total 8 sums)

27+2 (total 1)
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by Brent@GMATPrepNow » Mon May 21, 2012 6:49 am
LalaB wrote:
Brent@GMATPrepNow wrote:
2) Odd multiples of 9: 9, 27

Summarize

The second condition gives us 9

So, it appears that the only numbers that can't be derived are the 4 odd numbers from 1 to 7 (1, 3, 5, and 7)

Hi Brent,

I didnt get this part of ur post.First you said that we have 9 and 27, but then u summarized that there is only 9.

I also didnt get about 4 numbers. ((

my way of thinking is as following -

integers less than 30

1) a multiple of 2 (28-2)/2+1=14

2)an odd multiple of 9 - 9 and 27 (total 2)

3)the sum of a positive multiple of 2 and a positive multiple of 9 -
for 9 these numbers are from 2 to 16 (total 8)
for 27 this number is 2 (total 1)

total =14+2+8 +1 =25
That solution looks great.

Cheers,
Brent
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by nailGmat2012 » Mon Aug 06, 2012 5:44 pm
ok, step 3 -
u r asked to find the sum of a positive multiple of 2 and a ODD positive multiple of 9 less than 30 (hm it seems that the word odd is forgotten here)

sum of a positive multiple of 2 are numbers from 2 to 28 (2 4 6 8 10 12 14 16 18...28)


positive odd multiple of 9 - 9 and 27

9+2 ;9+4 ;9+6;...9+16 (total 8 sums)

27+2 (total 1)
what happened to 9+18 and 9+20 . they are less than 30 too...

doesn't that make total = 27 options - A ?
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by kashishh » Tue Aug 07, 2012 1:55 am
1.)positive multiples of 2 = 14
2.)odd +ve multiples of 9 = 2 (9, 27)
3.)sum of positive multiples of 2,9 = 10
(all multiples of 2 till 20 addeed
with 9 gives <than 30)

1.)+2.)+3.) = 26
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