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# Which is greater?

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Senior Manager
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Which is greater? [#permalink]  12 Nov 2017, 01:52
00:00

Question Stats:

20% (01:21) correct 80% (01:09) wrong based on 15 sessions

A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

Kudos for correct solution.

[Reveal] Spoiler:
Attachment:

gqgpp_img11.png [ 627 Bytes | Viewed 897 times ]

Attachment:

gqgpp_img12.png [ 1.32 KiB | Viewed 889 times ]
[Reveal] Spoiler: OA
Manager
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Re: Which is greater? [#permalink]  12 Nov 2017, 04:34
Bunuel wrote:

A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

Kudos for correct solution.

[Reveal] Spoiler:
Attachment:
gqgpp_img11.png

Attachment:
gqgpp_img12.png

Don't know how it works; can anyone give explanation?
Director
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Re: Which is greater? [#permalink]  12 Nov 2017, 10:15
1
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Let's start from the fact that $$\frac{AB}{AC}=\frac{AC}{BC}$$, then given AB = AC+BC, we can rewrite the equality as $$\frac{AC+BC}{AC}=1+\frac{BC}{AC}=\frac{AC}{BC}$$. Then, given that BC is smaller than AC, BC/AC is smaller than 1 so that summed to 1 is surely less than 3. Quantity B is greater.

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Re: Which is greater? [#permalink]  12 Nov 2017, 18:16
1
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IlCreatore wrote:
Let's start from the fact that $$\frac{AB}{AC}=\frac{AC}{BC}$$, then given AB = AC+BC, we can rewrite the equality as $$\frac{AC+BC}{AC}=1+\frac{BC}{AC}=\frac{AC}{BC}$$. Then, given that BC is smaller than AC, BC/AC is smaller than 1 so that summed to 1 is surely less than 3. Quantity B is greater.

thank you for the info: but how do you make sure that BC is smaller than AC given that the picture might not be drawn to scale?
Manager
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Re: Which is greater? [#permalink]  07 Dec 2017, 19:47
IlCreatore wrote:
Let's start from the fact that $$\frac{AB}{AC}=\frac{AC}{BC}$$, then given AB = AC+BC, we can rewrite the equality as $$\frac{AC+BC}{AC}=1+\frac{BC}{AC}=\frac{AC}{BC}$$. Then, given that BC is smaller than AC, BC/AC is smaller than 1 so that summed to 1 is surely less than 3. Quantity B is greater.

how do you get the part 1+\frac{BC}{AC} ?
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Re: Which is greater? [#permalink]  07 Dec 2017, 23:03
2
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Peter wrote:
IlCreatore wrote:
Let's start from the fact that $$\frac{AB}{AC}=\frac{AC}{BC}$$, then given AB = AC+BC, we can rewrite the equality as $$\frac{AC+BC}{AC}=1+\frac{BC}{AC}=\frac{AC}{BC}$$. Then, given that BC is smaller than AC, BC/AC is smaller than 1 so that summed to 1 is surely less than 3. Quantity B is greater.

thank you for the info: but how do you make sure that BC is smaller than AC given that the picture might not be drawn to scale?

Good question,

But you can try putting the some values,

But remember it should satisfy the equation $$\frac{AB}{AC}=\frac{AC}{BC}$$

Let AB =12
AC= 6
BC = 3

These values satisfy the above equation , and $$\frac{AC}{BC}= 2$$ which is less than 3
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Director
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Re: Which is greater? [#permalink]  07 Dec 2017, 23:07
2
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wongpcla wrote:
IlCreatore wrote:
Let's start from the fact that $$\frac{AB}{AC}=\frac{AC}{BC}$$, then given AB = AC+BC, we can rewrite the equality as $$\frac{AC+BC}{AC}=1+\frac{BC}{AC}=\frac{AC}{BC}$$. Then, given that BC is smaller than AC, BC/AC is smaller than 1 so that summed to 1 is surely less than 3. Quantity B is greater.

how do you get the part 1+\frac{BC}{AC} ?

Because AB = AC + BC

Now
$$\frac{AB}{AC}$$ can be written as

$$\frac{(AC +BC)}{AC} = \frac{AC}{AC} + \frac{BC}{AC}$$

= $$1 + \frac{BC}{AC}$$
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Re: Which is greater? [#permalink]  24 Jan 2018, 07:00
1
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pranab01 wrote:
Peter wrote:
IlCreatore wrote:
Let's start from the fact that $$\frac{AB}{AC}=\frac{AC}{BC}$$, then given AB = AC+BC, we can rewrite the equality as $$\frac{AC+BC}{AC}=1+\frac{BC}{AC}=\frac{AC}{BC}$$. Then, given that BC is smaller than AC, BC/AC is smaller than 1 so that summed to 1 is surely less than 3. Quantity B is greater.

thank you for the info: but how do you make sure that BC is smaller than AC given that the picture might not be drawn to scale?

Good question,

But you can try putting the some values,

But remember it should satisfy the equation $$\frac{AB}{AC}=\frac{AC}{BC}$$

Let AB =12
AC= 6
BC = 3

These values satisfy the above equation , and $$\frac{AC}{BC}= 2$$ which is less than 3

I think if AB=12 and AC = 6 then BC must equal to 6 and not 3 as BC = AB-AC
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This is my response to the question and may be incorrect. Feel free to rectify any mistakes

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Re: Which is greater? [#permalink]  24 Jan 2018, 10:44
Peter wrote:
IlCreatore wrote:
Let's start from the fact that $$\frac{AB}{AC}=\frac{AC}{BC}$$, then given AB = AC+BC, we can rewrite the equality as $$\frac{AC+BC}{AC}=1+\frac{BC}{AC}=\frac{AC}{BC}$$. Then, given that BC is smaller than AC, BC/AC is smaller than 1 so that summed to 1 is surely less than 3. Quantity B is greater.

thank you for the info: but how do you make sure that BC is smaller than AC given that the picture might not be drawn to scale?

BC must be smaller, otherwise the equation in the question cannot hold.
Try to plug in numbers (with BC > AC) and you'll see
Re: Which is greater?   [#permalink] 24 Jan 2018, 10:44
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