Explanation of answer to GMAT Practice Test 1 math problem:

Question

I just realized that there are no explanations to the answers on the official MBA.com practice tests. (BUMMER!) I want to make sure I learn everything I have gotten wrong fully, so that I will be at ease if I see the problems come test day.

The correct answer is (C) by the way. Can anyone help to explain why this is so?

A little about me: I'm just starting out on my studying for the test. This was my first practice test and I scored a 560. I plan to bring this up above 700 in the next two months.

Thanks in advance!

WhiteWNNoise · Answer

Explanation:

t1 = 23
t2 = t1 - 3 = 20
t3 = t2 - 3 = 17 and so on....

t(n) can also be represented as t1+(n-1)d ................ from Arithmetic Progression basics where last term = first term + (n-1)th times the common difference

where d is the common difference and in this case d = -3 (since the values are reducing)

Therefore,
t(n) = t1 + (n-1)d
t(n) = 23 + (n-1)(-3) = 23 - (3n-3) = 23 - 3n + 3
t(n) = 26 - 3n

Since t(n) = -4,
-4 = 26 - 3n
Hence, 3n = 30 and n = 10.

Correct Answer: 10 (option C)

Anurag@Gurome · Answer

T(1) = 23 and T(n) = T(n - 1) - 3 for each n > 1

Hence, the series is an arithmetic progression with first term, a = 23 and common difference, d = -3.

Hence, T(n) = a + (n - 1)d = 23 + (n - 1)*(-3) = 23 - 3n + 3 = 26 - 3n

Given that, T(n) = -4
(26 - 3n) = -4
3n = 30
n = 10

The correct answer is C.
[/spoiler]

GMATGuruNY · Answer

ejazzy wrote:I just realized that there are no explanations to the answers on the official MBA.com practice tests. (BUMMER!) I want to make sure I learn everything I have gotten wrong fully, so that I will be at ease if I see the problems come test day.

The correct answer is (C) by the way. Can anyone help to explain why this is so?

A little about me: I'm just starting out on my studying for the test. This was my first practice test and I scored a 560. I plan to bring this up above 700 in the next two months.

Thanks in advance!

The formula indicates that the distance between one term and the next -- the INTERVAL -- is 3.
The result is a sequence of EVENLY SPACED INTEGERS.
To count evenly spaced integers:
Total number of integers = (biggest - smallest)/interval + 1.

In the problem at hand:
Biggest = 23
Smallest = -4
Interval = 3
Total number of integers = (23 - (-4))/3 + 1 = 10.
Thus, t(n) is the 10th integer in the sequence.

The correct answer is D.

We also should know how to determine the SUM of evenly spaced integers. Check my post here:

https://www.beatthegmat.com/for-any-posi ... tml#361604

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