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Sequences GMAT

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Sequences GMAT

by abhi75 » Fri May 02, 2008 11:11 am
If the sequence x1, x2, x3, …, xn, … is such that x1 = 3 and xn+1 = 2xn – 1 for n = 1, then x20 – x19 =
A. 2^19
B. 2^20
C. 2^21
D. 2^20 - 1
E. 2^21 - 1

Can someone please mention which is best prep material for Sequences Series question. Is anyone using MGMAT techniques to solve the sequences problem. The Kaplan series also have either very limited or no coverage for Sequences problems. Can someone please point out any good material for understanding and solving Sequences problems.

Thanks.
Abhi
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by VP_RedSoxFan » Fri May 02, 2008 1:32 pm
Sometimes, depending on time, I like to take a look at a few examples of the sequence to get a better handle on it. For instance:

X1=3
X2=2(3)-1=5
X3=2(5)-1=9
X4=2(9)-1=17

That took like 20 seconds to do quickly and I can see from these sequences and, **by quickly surveying the answer choices** that there is something going on with powers of 2. I notice that the increases from Xn to Xn+1 move by a power of two related to Xn. The sequence can be written as:

Xn = Xn-1 + 2^(n-1) (you can quickly check that that works as well starting at X1)

So, to solve the problem X20 - X19, I'll use that formula to solve

X20 = X19 + 2^19 and then subtract X19 without having to expand it gives me:

ANS = X19 + 2^19 - X19 = 2^19 [A]

Hope that helps!
Ryan S.
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by abhi75 » Sat May 03, 2008 5:42 am
Thanks for showing the smart way to solve this kind of problem.
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GMAT decimals DS

by abhi75 » Sat May 03, 2008 6:16 am
In the decimal representation of x, where 0 < x < 1, is the tenths digit if x nonzero?
(1) 16x is an integer.
(2) 8x is an integer.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

According to me the answer is D but the OA is B.

Now the range of x is 0 < x < 1
From 1) 16x is an integer. The only possible value of x is 0.5 and therefore I pick D.

Is there something i am missing or the OA might be wrong ;-).

Thanks.
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Re: GMAT decimals DS

by f00kie » Sat May 03, 2008 3:16 pm
B is correct; here's why:

Let's go step by step and take 16x first. Since 0 < x < 1, in order for 16x to be an integer, x can be 1/16, 2/16, ... 15/16. 1/16 is < 0.1, therefore the tenth's digit is 0, but 15/16 is > 0.1, therefore the tenth digit is not 0; insufficient.

Now, loot at 8x. Same thing applies; x = 1/8, 2/8, ... 7/8. All of these produce a tenths digit that is non-zero, which is sufficient.
abhi75 wrote:In the decimal representation of x, where 0 < x < 1, is the tenths digit if x nonzero?
(1) 16x is an integer.
(2) 8x is an integer.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

According to me the answer is D but the OA is B.

Now the range of x is 0 < x < 1
From 1) 16x is an integer. The only possible value of x is 0.5 and therefore I pick D.

Is there something i am missing or the OA might be wrong ;-).

Thanks.
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by henryjejo » Tue Sep 11, 2012 7:28 pm
X1=3
X2=2.3-1= 5
X3=2.5-1=9
X4=2.9-1=17
X5 = 2.17-1=33

In the above sequence, we find the X2 and X1 differs by 2, X3-X2 = 4, X4-X3 = 8

=> XN - X(N-1)= 2^(N-1)
X20-X19 => 2^19
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