Does 'constant' also mean integer?

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wayofjungle: Senior | Next Rank: 100 Posts; Posts: 77; Joined: Fri Mar 11, 2011 8:55 am; Thanked: 12 times

Does 'constant' also mean integer?

by wayofjungle » Sun Apr 17, 2011 1:13 pm

OG assumes this is true, although I thought a constant is defined as any number and not a variable. In the following DS question assuming 'r' is a constant makes both statements sufficient, otherwise assuming 'r' can be a fraction makes them both insufficient (I think).

If r is a constant and a(n) = rn for all positive integers n, for how many values of n is a(n) < 100?
1.) a(50) = 500
2.) a(100) + a(105) = 2050

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Source: Beat The GMAT — Quantitative Reasoning | Sun Apr 17, 2011 1:13 pm

ldoolitt: Master | Next Rank: 500 Posts; Posts: 184; Joined: Sat Apr 14, 2007 9:23 am; Location: Madison, WI; Thanked: 17 times

by ldoolitt » Sun Apr 17, 2011 2:16 pm

wayofjungle wrote:OG assumes this is true, although I thought a constant is defined as any number and not a variable. In the following DS question assuming 'r' is a constant makes both statements sufficient, otherwise assuming 'r' can be a fraction makes them both insufficient (I think).

If r is a constant and a(n) = rn for all positive integers n, for how many values of n is a(n) < 100?
1.) a(50) = 500
2.) a(100) + a(105) = 2050

Hey wayofjungle,

Could you explain the rationale behind your statement "otherwise assuming 'r' can be a fraction makes them both insufficient (I think)" in this instance? How are you approaching this problem? Just wanted a little additional insight so I might be able to help.

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wayofjungle: Senior | Next Rank: 100 Posts; Posts: 77; Joined: Fri Mar 11, 2011 8:55 am; Thanked: 12 times

by wayofjungle » Sun Apr 17, 2011 2:51 pm

Sorry, I confused the properties of r and n after solving for r.

Each statement gives us information to find that r=10, so using this information to restate the question we have:

how many values are there for n that 10*n < 100

because n is defined as an integer there are limited values, 9 in fact.

I dont think GMAT confuses definitions like this on purpose, but even though this question is no longer a good example is it safe to assume a variable labeled 'constant' can signify any single numerical value, integer or fraction?

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ldoolitt: Master | Next Rank: 500 Posts; Posts: 184; Joined: Sat Apr 14, 2007 9:23 am; Location: Madison, WI; Thanked: 17 times

by ldoolitt » Sun Apr 17, 2011 2:56 pm

wayofjungle wrote:...is it safe to assume a variable labeled 'constant' can signify any single numerical value, integer or fraction?

I believe that 'constant' belongs to the set of reals. It doesn't necessarily have to be an integer or fraction (it could be pi or sqrt(2) for example).

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

by Stuart@KaplanGMAT » Sun Apr 17, 2011 7:30 pm

wayofjungle wrote:OG assumes this is true, although I thought a constant is defined as any number and not a variable.

Hi,

"constant" is simply the opposite of "variable"; since the GMAT only deals with the set of real numbers, for GMAT purposes a constant is any fixed real number (an integer, fraction, positive, negative, 0, irrational number like pi, etc...).