Problem Solving

Joy Shaha wrote:Q. If the sum of the consecutive integers from -22 to x, inclusive 72, what is the Value of x?
a. 23 b. 25. c. 50 d.75 e. 94

We know that (-22) + (-21) + (-20) + . . . 0 . . . + 20 + 21 + 22 will equal zero, since (-22) + 22 = 0, (-21) + 21 = 0, (-20) + 20 = 0, etc.

So, let's start at 23 and keep going up until we reach a sum of 72

23 + 24 = 47 (not yet)
23 + 24 + 25 = 72 BINGO

x = 25
Answer: B

Cheers,
Brent

Hi Joy Shaha,

This question can be solved by TESTing THE ANSWERS.

We're told that that sum of the INTEGERS from -22 to X (inclusive) is 72. We're asked for the value of X.

When TESTing THE ANSWERS, you will typically start with either Answer B or Answer D. Looking at the 5 answer choices, Answer B looks like the 'easier' option, so we'll start there.

Answer B: 25

IF... X = 25, then what is the sum of the integers from -22 to +25?

Each of the negative integers will be 'cancelled out' by the equivalent positive integers (re: -22 and +22 = 0, -21 and +21 = 0, etc.), so we'd be left with a short series of positive integers that don't get cancelled out: 23, 24 and 25.

23+24+25 = 72

This matches what we were told so this MUST be the answer.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

Joy Shaha wrote:Q. If the sum of the consecutive integers from -22 to x, inclusive 72, what is the Value of x?
a. 23 b. 25. c. 50 d.75 e. 94

The quantity is x - (-22) + 1 = x + 23.

The average is (-22 + x)/2 = (x - 22)/2.

Since sum = average x quantity:

72 = (x + 23)(x - 22)/2

144 = x^2 + x - 506

x^2 + x - 650 = 0

(x + 26)(x - 25) = 0

x = - 26 or x = 25

Since x can't be negative (otherwise all the integers will be negative and the sum won't be positive), x = 25.

Alternate Solution:

Note that the sum of all the consecutive integers from -22 to 22 is 0. Therefore, the question really asks for the number n such that 23 + 24 + ... + n = 73. We notice that 23 + 24 + 25 = 73; thus, n = 25.

Answer: B