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555-605 Level|   Algebra|      
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Bunuel
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In the sequence w, x, y, 30, adding any one of the first three terms Updated on: 30 Dec 2023, 13:49
Originally posted by Bunuel on 28 May 2017, 03:18.
Last edited by Bunuel on 30 Dec 2023, 13:49, edited 2 times in total.
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A
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35% (medium)

Question Stats:

72% (02:13) correct 28% (02:06) wrong based on 127 sessions

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In the sequence w, x, y, 30, adding any one of the first three terms to the term immediately following it yields w/2. What is the value of w ?

(A) –60
(B) –30
(C) 0
(D) 5
(E) 25
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A
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In the sequence w, x, y, 30, adding any one of the first three terms 28 May 2017, 03:23
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Placing W just before 30 ..on substitution of answers -60 is the correct choice...hence A


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In the sequence w, x, y, 30, adding any one of the first three terms 28 May 2017, 06:12
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Since there is a sequence of numbers, the difference between them must be constant.
Lets evaluate the answer options available.

If w=-60, the difference between the numbers are 30
So the sequence is -60,-30,0,30
Since the sum of any one of the first three numbers with the term immediately following it is w/2
-30 + 0 = -60/2(w/2)

Hence we have our answer. Option A
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In the sequence w, x, y, 30, adding any one of the first three terms 29 May 2017, 05:43
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Bunuel
In the sequence w, x, y, 30, adding any one of the first three terms to the term immediately following it yields w/2. What is the value of w ?

(A) –60
(B) –30
(C) 0
(D) 5
(E) 25

So, we can say, y + 30 = w/2 or w = 2y + 60.
Similarly, x + y = w/2 or w = 2x + 2y. Substitute w, we get 2y + 60 = 2x + 2y or x = 30.
Now, w + x = w/2 or 2w + 2x = w or w = -2x. Which gives w = -60.

I am doing a calculation error I think. Can someone help with above calculation?
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In the sequence w, x, y, 30, adding any one of the first three terms 29 May 2017, 06:42
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as per the question , below equations can be formed:

1: w + x = \(\frac{w}{2}\)
2: x + y = \(\frac{w}{2}\)
3: y + 30 = \(\frac{w}{2}\)

adding equation 1 & 3 and subtracting the result by equation 2

w + 30 = \(\frac{w}{2}\)

w = -60 ( A)
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In the sequence w, x, y, 30, adding any one of the first three terms 30 Dec 2023, 11:37
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Bunuel can you please explain the answer
If W is -60 and x is -30 than how adding both will result in w/2 i.e -30? Similarly adding y and 30 i.e 0 + 30 ≠ w/2 i.e -30.

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In the sequence w, x, y, 30, adding any one of the first three terms 30 Dec 2023, 14:01
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gupta.vinit
Bunuel can you please explain the answer
If W is -60 and x is -30 than how adding both will result in w/2 i.e -30? Similarly adding y and 30 i.e 0 + 30 ≠ w/2 i.e -30.

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In the sequence w, x, y, 30, adding any one of the first three terms to the term immediately following it yields w/2. What is the value of w ?

(A) –60
(B) –30
(C) 0
(D) 5
(E) 25

Since adding any one of the first three terms to the term immediately following it yields w/2, we get:

    w + x = w/2

    x + y = w/2

    y + 30 = w/2

The first two give w + x = x + y, which yields w = y. Substituting this into the third equation, gives w + 30 = w/2, which yields w = -60.

Thus, w = y = -60, and x = 30.

Answer: A.
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