Remainders

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Dec 17, 2008 5:03 pm

When the positive integer x is divided by 11, the quotient is y and the remainder is 4. When 2x is divided by 8, the quotient is 3y and the remainder is 2. What is the value of 13y - x ?
A) -4
B) -2
C) 0
D) 2
E) 4

Answer: D

I'd rank this one in the 650 range. It's reasonably complex, and it has the potential to be a time drain if you're not careful. See if you can solve it within 2 minutes.

Brent Hanneson - Creator of GMATPrepNow.com

Source: Beat The GMAT — Problem Solving | Wed Dec 17, 2008 5:03 pm

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Wed Dec 17, 2008 5:08 pm

x=11y+4
2x = 24y+2

Solve y=3
x=37

3y-x = 39-37

=2

D)

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Wed Dec 17, 2008 5:16 pm

Brent,

Beef it up to 700's please. Even if I cant solve I will definitely have some takeaways... I am sure my buddy Logitech will

Thanks for this one by the way! How about 3-5 questions(ps- ds put together) a day, Brent???

dmateer25: Community Manager; Posts: 1049; Joined: Sun Apr 06, 2008 5:15 pmFollowed by: 27 members; Location: Pittsburgh, PA; Thanked: 113 times; GMAT Score:710

by dmateer25 » Wed Dec 17, 2008 5:18 pm

cramya wrote:x=11y+4
2x = 24y+2

Solve y=3
x=37

3y-x = 39-37

=2

D)

I can't even get to the question before you respond!

haha good work cramya.

I worked the problem the exact same way. Took just under 2 mins for me.

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Wed Dec 17, 2008 5:19 pm

Dmateer,
U r good! I have seen some excellent posts from u on this forum. Good luck wiht ur preps!

See a around...

Regards,
CR

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Dec 17, 2008 5:33 pm

Brent,

Beef it up to 700's please. Even if I cant solve I will definitely have some takeaways... I am sure my buddy Logitech will

Thanks for this one by the way! How about 3-5 questions(ps- ds put together) a day, Brent???

That's a pretty tall order. These questions take quite a while to create. I'm probably good for 1 or 2 a day tops.

I'll see what I can do

Brent Hanneson - Creator of GMATPrepNow.com

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Dec 17, 2008 5:41 pm

x=11y+4
2x = 24y+2

Solve y=3
x=37

3y-x = 39-37
=2
D)

There's actually a shortcut here that will save a lot of time.

Once we get to:
x=11y+4
2x = 24y+2

We can rewrite as:
(1) x - 11y = 4
(2) 2x - 24y = 2

We don't need to solve for x and y at this point.
The goal is to find the value of 13y - x

If we subtract (1) - (2), we get 13y - x = 2 --> D

Brent Hanneson - Creator of GMATPrepNow.com

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Wed Dec 17, 2008 5:46 pm

Thanks!

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

by logitech » Wed Dec 17, 2008 5:49 pm

x=11y+4
2x = 24y+2

since the question stem asks 13y...24y and 11 y beg us!! PLEASE SUBSTRACT US FROM EACH OTHER!

-x = -11y-4
2x= 24y+2

+
----------------

x=13y-2

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

vishubn: Legendary Member; Posts: 574; Joined: Sun Jun 01, 2008 8:48 am; Location: Bangalore; Thanked: 28 times

by vishubn » Wed Dec 17, 2008 7:06 pm

X=11Y+4---(1)
2X=24Y+2--(2)

(2)-(1)

X=13Y-2

OA D

53 SECS

VISHU

KILL !! DIE !! or BEAT my FEAR !!! de@D END!!

vittalgmat: Legendary Member; Posts: 621; Joined: Wed Apr 09, 2008 7:13 pmFollowed by: 4 members; Thanked: 33 times

by vittalgmat » Wed Dec 17, 2008 7:44 pm

that was easy.. to solve ..
under 1 min.
I guess this is a 550 level Q ??

Brent: pls give us the tough ones!!..

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