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a × c and b × d

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a × c and b × d [#permalink] New post 30 Aug 2018, 16:38
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57% (00:28) correct 42% (01:01) wrong based on 66 sessions
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Capture.PNG [ 25.08 KiB | Viewed 1361 times ]


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] New post 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] New post 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] New post 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] New post 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] New post 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.

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

Answer: B

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