The Product of Two Negative Numbers is 160.

Question: The product of two negative numbers is 160. If the lesser of the two numbers is 4 less than twice the greater, what is the greater number?

A) -20
B) -16
C) -10
D) -8
E) -4

“The product of two negative numbers is 160. If the lesser of the two numbers is 4 less than twice the greater, what is the greater number?” - this is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Approach 1

The problem statement says:
The product of two negative numbers is 160 and that the lesser of the two numbers is 4 less than twice the greater.

Let us consider the larger number as x and the smaller number as y.
We can create the following equations:
(x)(y) = 160
and
y = 2x - 4
Now, we will be substituting (2x - 4) for y in the first equation yields:
x(2x - 4) = 160
2x^2 + 4x = 160
x^2 - 2x - 80 = 0
(x - 10)(x + 8) = 0
x = 10 or x = -8
Since x is negative, x = -8 and y = 2(-8) -4 = -20.
Thus, the greater number is -8.

Hence, D is the correct answer.

Approach 2

The problem statement says:
The product of two negative numbers is 160 and that the lesser of the two numbers is 4 less than twice the greater.

We will use the options in this approach.

The options that gives us the greater number. Let us start from the middle option.

(C) - 10
Twice of -10 is -20 and 4 less is -24.
-24 * -10 = 240 (Not correct)

We need lower product (of 160) so let us try option (D).

(D) - 8
Twice of -8 is -16 and 4 less is -20.
-20 * -8 = 160

Hence, D is the correct answer.

Approach 3

In this approach, we will use the options. The options will give us the greater number. Let us start from the middle option.

(C) - 10
Twice of -10 is -20 and 4 less is -24.
-24 * -10 = 240
Hence, this is Not correct

We need lower product (of 160)
We will try option D.

(D) - 8
Twice of -8 is -16 and 4 less is -20.
-20 * -8 = 160

Hence, this is the correct answer.

Correct Answer: D

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