comparison of slopes

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LevelOne: Senior | Next Rank: 100 Posts; Posts: 69; Joined: Fri Jun 19, 2009 11:46 am; Location: London; Thanked: 1 times

comparison of slopes

by LevelOne » Sat Jul 04, 2009 10:46 am

1) Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p?

(1) lines n and p intersect at the point (5,1)
(2) the y-intercept of line n is greater than the y-intercept of line p

I'm trying to figure out how an equation would look like to solve this question. Any ideas?

2) What is the hundredths digit of the decimal z?

(1) the tenths digit of 100z is 2.
(2) the units digit of 1,000z is 2.

Slightly lost here...

thanks

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Source: Beat The GMAT — Data Sufficiency | Sat Jul 04, 2009 10:46 am

GMATQuantCoach: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Sun Jun 28, 2009 8:58 am; Location: Online; Thanked: 13 times; GMAT Score:51

by GMATQuantCoach » Sat Jul 04, 2009 9:27 pm

Question 1.

This is a data sufficiency coordinate question. Most of the time you can solve this type of question by drawing some lines and examining different cases.

(1) Mark point (5, 1). Draw any 2 lines that pass through that point. You can mark the first line as n and the second line as p, or vice versa. Insufficient.

(2) Pick any 2 points on the y axis. n must pass through the top point on the y axis. Simply draw 2 parallel lines. Change the slope of one of the lines. Insufficient.

When combined, try to draw scenarios satisfying both statements. You will find that you cannot draw a case where the slope of n is greater than the slope of p.

C is your answer.

Let me know if this graphing technique makes sense or not.

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GMATQuantCoach: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Sun Jun 28, 2009 8:58 am; Location: Online; Thanked: 13 times; GMAT Score:51

by GMATQuantCoach » Sat Jul 04, 2009 9:38 pm

Question 2

Let's give each digit a variable. Let z = abc.ef
f is what you're looking for.

(1) 100 * z = abcdef. Insufficient.

(2)1000 * z = abcdef0. Insufficient

E is the answer.

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amitsahdev: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Fri Jun 26, 2009 8:03 pm; Thanked: 1 times

by amitsahdev » Sat Jul 04, 2009 10:03 pm

2) What is the hundredths digit of the decimal z?
(1) the tenths digit of 100z is 2.
(2) the units digit of 1,000z is 2.

B. Only the second statement is sufficient. If z=0.012 then 1000x0.012=12 with units digit being a two. Same will be true for z=0.022, 0.032 etc...
Statement 1, for tents digit to be 2, z==1.2, 100x1.2=120 ie the tenths digit is a 2 and same will be true for 2.2,3.2 etc but this does NOT give you the hundredths digit for z. Thus, only statement 2 is sufficient with answer choice B :)