It is currently 16 Dec 2017, 01:26

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# For an added challenge, time yourself to 4 minutes tops to

Author Message
Director
Joined: 31 Mar 2007
Posts: 574

Kudos [?]: 82 [0], given: 0

For an added challenge, time yourself to 4 minutes tops to [#permalink]

### Show Tags

04 Oct 2007, 17:56
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

For an added challenge, time yourself to 4 minutes tops to do these questions.

Does anyone have a fast way to do these? Brutal
Attachments

quant-q-8.JPG [ 67.11 KiB | Viewed 780 times ]

quant-q-2.jpg [ 69.96 KiB | Viewed 782 times ]

Kudos [?]: 82 [0], given: 0

Director
Joined: 17 Sep 2005
Posts: 901

Kudos [?]: 118 [0], given: 0

### Show Tags

04 Oct 2007, 18:23
For 1st Question, I am getting D.

ST1 gives r = 2
ST2 gives r = 5

- Brajesh

Kudos [?]: 118 [0], given: 0

Director
Joined: 17 Sep 2005
Posts: 901

Kudos [?]: 118 [0], given: 0

### Show Tags

04 Oct 2007, 18:28
For Question2, I am getting C.

You need to quickly draw combination of lines.
Concept is "One Line should go upward and other Line should go downward" then the product of their slope will be negative.

- Brajesh

Kudos [?]: 118 [0], given: 0

Intern
Joined: 05 Sep 2007
Posts: 41

Kudos [?]: 21 [0], given: 0

### Show Tags

04 Oct 2007, 19:57
1. D?
2. B? (B because x value of l and k we know from the question itself - the value is x=4 for both l and k - am not sure if this logic is correct).

Kudos [?]: 21 [0], given: 0

GMAT Instructor
Joined: 04 Jul 2006
Posts: 1259

Kudos [?]: 345 [0], given: 0

### Show Tags

05 Oct 2007, 05:20
For the first question, it is helpful to factor, as it is for most questions involving number properties

Kudos [?]: 345 [0], given: 0

Senior Manager
Joined: 04 Jun 2007
Posts: 363

Kudos [?]: 114 [0], given: 0

### Show Tags

05 Oct 2007, 10:11
First question

ST. 1
7n+6= t
let n=2
t= 20
then t^2+5t+6= 506 which yields remainder of 2 when divided by 7

try with n=3, remainder will be 2 again
SUFF

ST. 2
7n+1= t^2
let n= 5
then t= 6
and t^2+5t+6= 72 which leaves remainder of 2 when divided by 7
SUFF

D

Kudos [?]: 114 [0], given: 0

Director
Joined: 31 Mar 2007
Posts: 574

Kudos [?]: 82 [0], given: 0

### Show Tags

05 Oct 2007, 13:25
Wrong.

I said D as well.

OA is A.

Like I said, Hard Quant Q's

Kudos [?]: 82 [0], given: 0

Manager
Joined: 01 Oct 2007
Posts: 86

Kudos [?]: 29 [0], given: 0

### Show Tags

05 Oct 2007, 14:16
First question:

I. Factor t^2+5t+6 into (t +3)(t + 2). If t/7 has remainder 6, then t = k*7+6, where k is an integer. So t+3 = k*7 + 9 = (k+1)*7 + 2.
t+2 = (k+1)*7 + 1. Multiplying them gives you:

(k*7)^2*49 + (k+1)*21 + 2. Whatever t is, the remainder when t^2+5t + 6 is divided by 7 will be 2. SUFF.

II. t^2/7 has a remainder of 1. Then t^2+6 is divisible by 7. So the value of r is the remainder when 5t is divided by 7. We don't have enough information to know. Since t^2/7 has a remainder of 1, t could be 6 (36-1 = 35), in which case r = 2. (30/7). Or t could be 8 (64- 1 = 63), in which case r = 5 (40/7).

So it's A.

Kudos [?]: 29 [0], given: 0

Director
Joined: 31 Mar 2007
Posts: 574

Kudos [?]: 82 [0], given: 0

### Show Tags

05 Oct 2007, 16:15
John, fantastic explanation. I understand how to do the question now. Thanks I have to brush up on my remainder arithmetic.

Kudos [?]: 82 [0], given: 0

Senior Manager
Joined: 02 Aug 2007
Posts: 346

Kudos [?]: 54 [0], given: 0

Location: Greater New York City area
Schools: Tuck, Ross (R1), Duke, Tepper, ISB (R2), Kenan Flagler (R2)

### Show Tags

14 Oct 2007, 14:28
I think the explanation provided by r019h was correct for first statement.

But for the second statement, the remainder is not 2, when some other number is considered, for e.g. when n = 9, in statement 2, the remainder is not 2. So the answer is not D, but it is A.

Honestly, I think the approach taken by r019h was much more straightforward and can be quick.

Kudos [?]: 54 [0], given: 0

Current Student
Joined: 28 Dec 2004
Posts: 3345

Kudos [?]: 325 [0], given: 2

Location: New York City
Schools: Wharton'11 HBS'12

### Show Tags

15 Oct 2007, 07:54
I dont think this is that hard...

asks what is r if (t+3)(t+2) is divided by 7!

1) says t=7N+6

so (t+3)=7N+9 => 7(N+1)+2
(t+2) => 7N+8 => 7(N+1)+1

so you will notice that r will always be 2... for any value of N...

sufficient

2) t^2=7N+1

t=6 then in that case (9)(8)/7 gives remainder 2...

t can also be 8... in that case (10)(11)/7 gives remainder 5..insuff

A it is..

Kudos [?]: 325 [0], given: 2

Director
Joined: 03 May 2007
Posts: 867

Kudos [?]: 279 [0], given: 7

Schools: University of Chicago, Wharton School

### Show Tags

15 Oct 2007, 08:25
fresinha12 wrote:
I dont think this is that hard...

asks what is r if (t+3)(t+2) is divided by 7!

1) says t=7N+6

so (t+3)=7N+9 => 7(N+1)+2
(t+2) => 7N+8 => 7(N+1)+1

so you will notice that r will always be 2... for any value of N...

sufficient

2) t^2=7N+1

t=6 then in that case (9)(8)/7 gives remainder 2...

t can also be 8... in that case (10)(11)/7 gives remainder 5..insuff

A it is..

excellent approach..

agree with A.

can be done this way as well:

1: since t has 6 reminder if t is divided by 7, t = 7k +6.

= t^2 + 5t + 6
= (7k+6)(7k+6) + 5 (7k+6) + 6
= 49k^2 + 42k + 42k + 36 + 35k + 30 + 6
= 49k^2 + 119k + 72

in the above expression, 49k^2 and 119k are evenly divided by 7. so remains 72 which as 2 as reminder when it is divided by 7.

so suff...

2: t^2 has 1 reminder if t^2 is divided by 7.

t could be 6 or 8 or 15 each has 1 as reminder so the reminder of the expression t^2 + 5t + 6 is different with t values. nsf.

A.

Kudos [?]: 279 [0], given: 7

Manager
Joined: 02 Feb 2007
Posts: 117

Kudos [?]: 13 [0], given: 0

### Show Tags

15 Oct 2007, 10:31
All these are great explanations guys!!! Greatly appreciated.

If i may add my thoughts...i thought the best way to solve it, since i am nowhere near as advanced as all of you are is to plug in nuymbers.

I tried different ones, but only 13 diveded by 7 gave the reminder 6. All other numbers will divide and give reminders but not 6. Since t is 13 if we do the brutal multiplications and divisions we could find the reminder of the main quadratic equation. Therefore SUFF.

The second one states that t*2 divided by 2, reminder is 1. Now off the top of my head i know that t can be either positive or negative, there may be differentmunbers giving the same remainder 1, thefore i ignore it and call INSUFF.
Thereofre i would go with A

Kudos [?]: 13 [0], given: 0

Manager
Joined: 10 Jan 2005
Posts: 63

Kudos [?]: 4 [0], given: 0

### Show Tags

15 Oct 2007, 13:48
Fistail wrote:
fresinha12 wrote:
I dont think this is that hard...

asks what is r if (t+3)(t+2) is divided by 7!

1) says t=7N+6

so (t+3)=7N+9 => 7(N+1)+2
(t+2) => 7N+8 => 7(N+1)+1

so you will notice that r will always be 2... for any value of N...

sufficient

2) t^2=7N+1

t=6 then in that case (9)(8)/7 gives remainder 2...

t can also be 8... in that case (10)(11)/7 gives remainder 5..insuff

A it is..

excellent approach..

agree with A.

can be done this way as well:

1: since t has 6 reminder if t is divided by 7, t = 7k +6.

= t^2 + 5t + 6
= (7k+6)(7k+6) + 5 (7k+6) + 6
= 49k^2 + 42k + 42k + 36 + 35k + 30 + 6
= 49k^2 + 119k + 72

in the above expression, 49k^2 and 119k are evenly divided by 7. so remains 72 which as 2 as reminder when it is divided by 7.

so suff...

2: t^2 has 1 reminder if t^2 is divided by 7.

t could be 6 or 8 or 15 each has 1 as reminder so the reminder of the expression t^2 + 5t + 6 is different with t values. nsf.

A.

I think these approaches are too time consuming. I just finished my GMAT today and I saw a problem VERY VERY similar to this question. The general idea/concept was the same, but the quadratic and divisor was different. Here's my take on how to approach (1):

The quadratic factors to: (t + 2)(t +3)

hmm...what pattern have we consistently seen involving divisors and quadratics? I'm thinking consecutive integers.

(1) Provides info on t so add to this consecutive integer string: t, t + 1, t + 2, t + 3

we know t has a remainder 6 when divided by 7 so t + 1 MUST be divisible by 7 which means t + 2 will have a remainder of 1 when divided by 7 and t + 3 will have a remainder of 2 when divided by 7. How do I know this? Simple: remainders increase from 0 to x - 1 as you iterate over consecutive integers and reset back to 0 once you reach a number that divides evenly. 7%7 = 0, 8%7 = 1, 9%7 = 2 etc etc where % is the modulus function (gives the remainder).

So now pick two values for t + 2 and t + 3 which have remainders 1 and 2, respectively.
8 and 9: 8*9 = 72; 72%7 = 2
15 and 16: 15*16 = 240%7 = 2
etc etc

SUFF. This method is simple, easy to understand and just involves picking numbers - no long winded quadratic calculations necessary.

(2) I'm not going to discuss because I just wanted to mention how I solved for (1)

Kudos [?]: 4 [0], given: 0

15 Oct 2007, 13:48
Display posts from previous: Sort by

# For an added challenge, time yourself to 4 minutes tops to

Moderator: chetan2u

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.