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# If g and h are integers and g/h > 1, which of the following could

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If g and h are integers and g/h > 1, which of the following could  [#permalink]

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14 Jul 2017, 00:58
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79% (00:58) correct 21% (00:58) wrong based on 76 sessions

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If g and h are integers and g/h > 1, which of the following could illustrate the position of g and h on the number line?

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2017-07-14_1156.png [ 15.15 KiB | Viewed 944 times ]

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Re: If g and h are integers and g/h > 1, which of the following could  [#permalink]

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14 Jul 2017, 01:13
Bunuel wrote:
If g and h are integers and g/h > 1, which of the following could illustrate the position of g and h on the number line?

Attachment:
2017-07-14_1156.png

Only A suffices

we know g and h will have same sign (g/h>1) hence C & D are rejected

Now if g & h both are positive

then g>h

and if both are negative then

h>g

Only A is compatible
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If g and h are integers and g/h > 1, which of the following could  [#permalink]

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14 Jul 2017, 10:19
Bunuel wrote:
If g and h are integers and g/h > 1, which of the following could illustrate the position of g and h on the number line?

Attachment:
2017-07-14_1156.png

Method I - Choose numbers

1. Pick an integer quotient greater than 1. Use 2.
Let g = 4, so h must = 2.

The answer choices should signal scenario two:
g = -4, in which case h must = -2.

So g = 4 and h = 2, OR g = -4 and h = -2

Chosen values are +/+ and -/-, i.e., same sign, and must be that way. 4/-2, e.g., equals -2. Our quotient is positive.

2. Eliminate C and D; opposite signs won't work.

3. Answers B and E have the variables in the wrong order.

For B, 4 is not less than 2.
For E, -4 is not greater than -2.

Eliminate B and E.

3. Check variables' placement in A. -4 is less than -2. Correct.

Method II - Mostly algebra

1. We need two positive or two negative values.
If $$\frac{g}{h}$$ > 1, either both are positive or both are negative because their quotient is positive.

2. Determine relative size of variables.

When both are positive:

$$\frac{+g}{+h}$$ > 1, multiply by h

g > h

When both are negative:

$$\frac{-g}{-h}$$ > 1, multiply by h and reverse the sign

-g < -h

(When dealing with variables, it's easy to get this one wrong. That's what trap answer E is for. So: g is more negative than h, farther left on number line).

3. Eliminate C and D; g and h have different signs.

4. B, both variables positive, says g < h. From above, false. When positive, g > h. Eliminate B.

5. A or E? In both choices, both variables are negative.

E is backwards, says -g > - h (g is not, as it should be, farther left on number line). Eliminate E.

A says -g < - h. (g is farther left than h on number line.) Correct.

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If g and h are integers and g/h > 1, which of the following could  [#permalink]

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15 Jul 2017, 21:55
Option A.
Given g/h > 1
So we need to check
1. if g and h are positive, then g > h
2. if g and h are negative, then g < h

A - correct.
B - g and h are positive but g < h, eliminate.
C & D - has one positive and another negative, eliminate.
E - g and h are negative but g > h, eliminate.
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Re: If g and h are integers and g/h > 1, which of the following could  [#permalink]

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16 Jul 2017, 02:21
(A) I believe. C and D have different signs. B and E gives ratio<0.
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Re: If g and h are integers and g/h > 1, which of the following could  [#permalink]

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16 Jul 2017, 17:44
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Bunuel wrote:
If g and h are integers and g/h > 1, which of the following could illustrate the position of g and h on the number line?

Attachment:
2017-07-14_1156.png

We are given that g/h > 1; so, g and h must be the same sign. That is, g and h must be either both positive or both negative. If g and h are both positive, then g > h, and if g and h are both negative, then g < h. Looking at our answer choices, we see that answer choice A accurately depicts that g and h are negative and g < h.

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Re: If g and h are integers and g/h > 1, which of the following could   [#permalink] 16 Jul 2017, 17:44
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