What is the value of x?

Question

(1) The average (arithmetic mean) of 5, x^2, 2, 10x, and 3 is -3
(2) The median of 109, -32, -30, 208, -15, x, 10, -43, 7 is -5

KarishmaB · Answer

1) The average (arithmetic mean) of 5, x^2, 2, 10x, and 3 is -3

This means:

\frac{(5 + x^2 + 2 + 10x + 3)}{5} = -3 
Notice that you will get a quadratic. You need to solve it to see whether you get 1 or 2 acceptable values.

x^2 + 10x + 25 = 0

(x + 5)^2 = 0

x = -5

This statement is sufficient alone

2) The median of 109, -32, -30, 208, -15, x, 10, -43, 7 is -5

Notice that the given list of numbers has 9 numbers. So median must be the 5th number when all numbers are arranged in increasing order. Median is -5 but none of the numbers are -5. Hence x must be -5. Sufficient alone.

Answer (D)

mau5 · Answer

From F.S 1, we know that \frac{(5+x^2+2+10x+3)}{5}= -3

or x^2+10x = -15-10

or  x^2+10x+25=0 --> (x+5)^2 = 0 ; x = -5. Sufficient.

From F.S 2, the number of terms in the given series is ODD. Thus the median would be a distinct value.As -5 is not present in the given list, the only value x can take is -5. Sufficient.

D.

unceldolan · Answer

short question here:

If I have the stmt that the median of the given numbers is -5, but -5 doesn't appear in the given numbers (which include x), isn't it directly clear that x = -5? or am I getting this wrong?

Thanks for your help

Bunuel · Answer

Yes, since the number of elements in the set is odd, then the median must be one of the element of the set (the middle one). Both solutions above follow the same logic.

unceldolan · Answer

Ok, then I got it right. What if stmt 2 would have another number, e.g. -10, then it would be IS? Because then x could be anything?

Bunuel · Answer

No, in this case x=-10: {-43, -32, -30, -15,  x=-10 , 7, 10, 109, 208}

But if we were told that the median is 7, then the statement would be unsufficient: {-43, -32, -30, -15,  7 , 10, 109, 208, x} -->  x\geq{7} .

unceldolan · Answer

Thanks for your answer, this makes it clear.

Another question: What if the count would be even? Say -43, -32, -30, -15, 7, 10, 109, 208, 400 and somewhere x. Would be IS right?

Priyank38939 · Answer

What is the value of x?

(1) The average (arithmetic mean) of 5, x2, 2, 10x, and 3 is -3.
(2) The median of 109, -32, -30, 208, -15, x, 10, -43, 7 is -5.

Bunuel · Answer

Merging topics.

Please refer to the discussion above.

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What is the value of x?

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