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# a × c and b × d

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a × c and b × d [#permalink]  30 Aug 2018, 16:38
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Question Stats:

58% (00:28) correct 41% (01:04) wrong based on 63 sessions
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 Quantity A Quantity B $$a \times c$$ $$b \times d$$

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.
[Reveal] Spoiler: OA

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Re: a × c and b × d [#permalink]  30 Aug 2018, 18:20
How can the Answe be B if the values of a,b,c,d is not provided. It should be D
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Re: a × c and b × d [#permalink]  31 Aug 2018, 06:28
Expert's post
mathurmudit1003 wrote:
How can the Answe be B if the values of a,b,c,d is not provided. It should be D

Sorry abut that fixed it!
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Re: a × c and b × d [#permalink]  31 Aug 2018, 21:20
Answer is D as the values of a,b,c,d are not specified .
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Re: a × c and b × d [#permalink]  01 Sep 2018, 07:04
sandy wrote:
mathurmudit1003 wrote:
How can the Answe be B if the values of a,b,c,d is not provided. It should be D

Sorry abut that fixed it!

It has not been fixed and how is the answer D when all the numbers are right to the 0 and choice B is further to the right than choice A.
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Re: a × c and b × d [#permalink]  01 Sep 2018, 09:31
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IshanGre wrote:
sandy wrote:
mathurmudit1003 wrote:
How can the Answe be B if the values of a,b,c,d is not provided. It should be D

Sorry abut that fixed it!

It has not been fixed and how is the answer D when all the numbers are right to the 0 and choice B is further to the right than choice A.

If you observe the image, a,b,c,d are all greater than zero

Now there is no specification about a,b,c,d being Integers or fraction but we have following information

0<a<b<c<d

we have to compare axc and bxd

Assuming axc = Z

Now we know that b is greater than a and d is greater than c

So any value of b will be greater than a and any value of d will be greater than c

So if axc = Z then bxd will always be greater than Z.

You can try doing this assuming values as well. but based on the above calculation, axc = Z < bxd

Hence the Answer is B

Hope it helps.

Regards,
Mudit
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Re: a × c and b × d [#permalink]  21 Jun 2020, 07:23
That's a tricky example.
Test at least three scenarios for more accuracy:

For example if:
1) a=1 b=2 c=3 d=4
2) a=0,5 b=0,6 c=0,8 d=0,9
3) a=0,5 b=0,6 c=0,8 d=1

Now:
1) A=1*3=3 and B=2*4=8
2) A=0.5*0.8=0.4 and B=0.6*0.9=0.54
3) A=0.5*0.8=0.4 and B=0.6*1=0.6

In every case B is more than A
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Re: a × c and b × d [#permalink]  23 Jun 2020, 17:59
It was a simple one.
consider a=1, b=2, c=3, d=4
in this case quantity B is bigger

now consider decimals a=0.1, b=0.2, c=0.3, d=0.4
again quantity B is bigger

The key concept is number line i.e. numbers are greater than zero and in ascending order
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Re: a × c and b × d [#permalink]  25 Jun 2020, 08:01
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Expert's post
sandy wrote:
Attachment:
Capture.PNG

 Quantity A Quantity B $$a \times c$$ $$b \times d$$

We can also solve this question using matching operations (my favorite QC strategy)

Given: 0 < a < b < c < d

Given:
QUANTITY A: ac
QUANTITY B: bd

Since a is POSITIVE, we can safely divide both quantities by a to get:
QUANTITY A: c
QUANTITY B: bd/a

Since b is POSITIVE, we can safely divide both quantities by b to get:
QUANTITY A: c/b
QUANTITY B: d/a

Since d is the biggest number, and a is the smallest number, we know that d/a > c/b

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Re: a × c and b × d   [#permalink] 25 Jun 2020, 08:01
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