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GMATPrep Test 1 questions - help please

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GMATPrep Test 1 questions - help please

by JP » Thu Sep 06, 2007 7:26 am
Hi,
I tried to search the answers to below questions in the forum but could not find. I am not sure if my search criteria are an issue. So posting my questions below from GMAT Prep test 1. There are multiple questions, so I will post one after another.

Can you please suggest the most effective way to solve the below problem?

For every integer K from 1 to 10 inclusive, the kth term of a certain sequence is given by ((-1)^(k+1)) * (1/2^k) . If T is the sum of the first 10 terms in the sequence, then T is

A. greater than 2
B. between 1 and 2
C. between 1/2 and 1
D. between 1/4 and 1/2 (CORRECT)
E. less than 1/4

I tried the below method. If you substitute 1 to 10, you get
= ((-1)^1+1) * (1/2) + ((-1)^2+1) * (1/4) + ((-1)^3+1) * (1/ 8 ) and so on

= 1/2 -1/4 + 1/8 - 1/16 + 1/32 - 1/64....

So D makes sense as after 1/2 and 1/4, all the other numbers are very small to make any difference. But this would still be a guess. Is there any effective way to solve it?

Thanks in advance.
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by ri2007 » Thu Sep 06, 2007 7:32 am
https://www.beatthegmat.com/viewtopic.php?t=4896
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GMAT Prep - Question 2

by JP » Thu Sep 06, 2007 7:33 am
In the figure shown, what is the value of x? (Figure is in the attached file).

1. The length of line segment QR is equal to the length of line segment RS
2. The length of line segment ST is equal to the length of line segment TU
Attachments
GMATPrep Test 1 Q7 - DS Geometry.GIF
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by ri2007 » Thu Sep 06, 2007 7:37 am
check the forum - I have already solved this one as well - not sure if I posted the ans but the ans is def there on the forum
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Thanks for the quick reply - but can you please explain

by JP » Thu Sep 06, 2007 7:39 am
The answer states
The series you have mentioned is correct and is GP
T = [1/2(1-(-1/2)^10]/(1-(-1/2))
Solving this gives 1/3 - (1/3)*(1/2^10)
Since the sum is less than 1/3 answers 1, 2 and 3 are eliminated
Now, the second term in above equation is smaller that 1/12 (difference of 1/3 and 1/4) so total will NOT be less than 1/4

WHAT IS GP and WHAT IS GP's formula?

Thanks
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In the figure shown, what is the value of x?

by JP » Thu Sep 06, 2007 7:50 am
Found the explanation for this question. It was embedded in image file and hence the search was not returning anything.
Thanks again.
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by kajcha » Thu Sep 06, 2007 9:43 am
Jp, can you please post the link where DS question is discussed
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by gabriel » Thu Sep 06, 2007 9:54 am
.. Hi JP .. Welcome to BTG ..

..Couple of things you should note .. post only 1 question per thread .. and DO NOT post DS questions on the problem solving thread ..

Thanks
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by samirpandeyit62 » Thu Sep 06, 2007 10:48 pm
Hi All,
I would like to present the way I solved JP's first problem, i.e. the GP one

Here we can find all the individual 10 terms of the sequence using the Common difference i.e. -1/2

so we can say that each term is negative half of the term before it and first term is 1/2

i.e we need to cut 1/2 in 1/2 10 times and adding the minus sign alternatively

here the complexity lies in adding the 10 terms and not finding them
because we will need to work with decimals/fractions

we can exploit this strength of the problem by taking an interger value which can be cut into half 10 times.

now the easilest one will be be 2 ^ 10

where 2 ^ 10 = 1024 (very common with IT guys) corresponds to 1/2 in the problem.

then we have the sequence as

1024 - 512 + 256 -128 + 64.....

solving upto ..+64 we get value as 704 now stop here as we dont need to find exact value but only the range.

now we have 704 with us, now only small nos like 32, 16 etc will get added/subtracted from this figure, In no way these can add to 1024, or subtract down to 512 as between 704 and these terms is huge.

so we can conclude that our original value will lie between 512 & 1024

now coming back to original problem here

1024 corresponds to 1/2 of org problem & 512 corresponds to 1/4

so answer must be D between 1/4 & 1/2

( this would be valid as both the GP's have the same common diff hence their sums or basically any operation on 1 can be directly correlated to the other)

Thanks & Sorry again for the lengthy explanation

Pls let me know if u find any problems with my approach

Samir
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by mtg123 » Fri Sep 07, 2007 1:28 pm
JP, Could you please send the link of the solution to the geometry question
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DS Geometry question link

by JP » Sat Sep 08, 2007 1:40 am
Hi,

The DS geometry question link is

https://www.beatthegmat.com/viewtopic.ph ... 4438c6b3eb
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Thanks to all for your help in understanding

by JP » Sat Sep 08, 2007 1:44 am
Hi,

Thanks Samir for providing the detailed explanation of GP.
Gabriel,
I will post only one question from now on and would take care to post it under appropriate forum :)
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by mtg123 » Sat Sep 08, 2007 4:33 am
Thankx JP
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Re: Thanks to all for your help in understanding

by gabriel » Sat Sep 08, 2007 5:32 am
JP wrote:Hi,

Thanks Samir for providing the detailed explanation of GP.
Gabriel,
I will post only one question from now on and would take care to post it under appropriate forum :)
Thanx :) :) ..
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