Interger

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cartera: Senior | Next Rank: 100 Posts; Posts: 59; Joined: Tue Jun 10, 2008 6:49 pm; Thanked: 2 times

by cartera » Sun Nov 23, 2008 7:52 am

How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3 ?

A. 15

B. 16

C. 17

D. 18

E. 19

OA
C [spoiler][(49 - 1)/3]+1=17[/spoiler]

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Source: Beat The GMAT — Problem Solving | Sun Nov 23, 2008 7:52 am

orel: Master | Next Rank: 500 Posts; Posts: 247; Joined: Sun Jul 27, 2008 1:39 am; Thanked: 2 times; GMAT Score:660

by orel » Sun Nov 23, 2008 8:07 am

isn't it 16?

0<=3n+1<=50
n<=16

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4meonly: Legendary Member; Posts: 891; Joined: Sat Aug 16, 2008 4:21 amFollowed by: 1 member; Thanked: 27 times; GMAT Score:660(

by 4meonly » Sun Nov 23, 2008 8:07 am

the least integer that will satisfy given options is 1
the greates - 49
49-1 /3 = 16
do not forget to add 1
16+1 = 17

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orel: Master | Next Rank: 500 Posts; Posts: 247; Joined: Sun Jul 27, 2008 1:39 am; Thanked: 2 times; GMAT Score:660

by orel » Sun Nov 23, 2008 8:40 am

4meonly wrote:the least integer that will satisfy given options is 1
the greates - 49
49-1 /3 = 16
do not forget to add 1
16+1 = 17

hi!

how the remainder can be 1 when 1 is devided by 3? so, the least integer satisfying the option is 4.
but even if we count one by one, the integers satisfying the option are:

4, 7,10,13,16,19,22,25,28,31,34,37,40,43,46,49
so, 16
am i missing smth???
please, explain!!!

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4meonly: Legendary Member; Posts: 891; Joined: Sat Aug 16, 2008 4:21 amFollowed by: 1 member; Thanked: 27 times; GMAT Score:660(

by 4meonly » Sun Nov 23, 2008 11:41 am

Yes, u still miss 1
How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3 ?

n=3q+1
where n - your integer
3 - factor
Q- quotent
1 - remainder
you should find the number of n that are 0<n<50

4=3*1 +1
7=3*2 +1
10 = 3*3 +1

and 1 = 3*0 +1

OK?

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logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members; Thanked: 237 times; GMAT Score:730

by logitech » Sun Nov 23, 2008 2:05 pm

if you divide X with Y

and

X < Y

The remainder is X itself.

Ex:

3 is divided by 4

the remainder is 3

1 is divided by 3

the remainder is 1

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

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orel: Master | Next Rank: 500 Posts; Posts: 247; Joined: Sun Jul 27, 2008 1:39 am; Thanked: 2 times; GMAT Score:660

by orel » Mon Nov 24, 2008 12:25 am

now it makes sense to me!

thanks guys!

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GMATCHPOINT: Senior | Next Rank: 100 Posts; Posts: 51; Joined: Wed Oct 08, 2008 12:50 pm

by GMATCHPOINT » Mon Nov 24, 2008 1:21 pm

Logitech,
If one day you decide to share your flashcards, I would love to hv a copy. hehehe.

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