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# If both A and B are 2-digit even numbers, what is the value of A?

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Math Expert
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If both A and B are 2-digit even numbers, what is the value of A?  [#permalink]

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27 Jul 2018, 22:04
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If both A and B are 2-digit positive even numbers, what is the value of A?

(1) Ratio of A to B is 1:9
(2) B-A=80

New question!!!..

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If both A and B are 2-digit even numbers, what is the value of A?  [#permalink]

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27 Jul 2018, 22:22
1
Update: My analysis for this question is wrong. Please check out other explanations.

To find the value of A

A and B are 2-digit even numbers

Statement 1

Ratio of A to B is 1:9

=> $$\frac{A}{B} = \frac{x}{9x}$$

=> A can be 10 and B can be 90 satisfying that A and B are both even numbers and $$\frac{A}{B} = \frac{1}{9}$$

=> A can be 20 and B can be 180 satisfying that A and B are both even numbers and $$\frac{A}{B} = \frac{1}{9}$$

Statement 1 is not sufficient

Statement 2

B-A=80

=> A can be 10 and B can be 90 satisfying that A and B are both even numbers

=> A can be 20 and B can be 100 satisfying that A and B are both even numbers

Statement 2 is not sufficient

Combining statements 1 and 2

A = x and B = 9x and A-B = 9x - x = 8x = 80

=> x = 10

=> A = x = 10 and B = 9x = 90

Statements 1 and 2 together are sufficient

Hence option C
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Re: If both A and B are 2-digit even numbers, what is the value of A?  [#permalink]

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27 Jul 2018, 22:26
workout wrote:

Hence option C

workout, A cannot be 2 as it is 2-digit number.
you may have to relook in the statement I

Given info A and B are 2-digit even numebrs

1) A:B=1:9
so if A is 10, B is 90
if A is 11, B is 99
and when A = 12, B=12*9=108.... NOT possible as B is 2-digit number
So A can be 10 or 11, but A is EVEN, so A=10
suff

2) B-A=80
A can be 10,12,14,16 or 18
insuff

A
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Re: If both A and B are 2-digit even numbers, what is the value of A?  [#permalink]

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27 Jul 2018, 22:34
chetan2u wrote:

workout, A cannot be 2 as it is 2-digit number.
you may have to relook in the statement I

Thanks chetan2u for catching that. Careless mistake on my part. I have updated the example cases.
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Re: If both A and B are 2-digit even numbers, what is the value of A?  [#permalink]

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27 Jul 2018, 22:37
workout wrote:
chetan2u wrote:

workout, A cannot be 2 as it is 2-digit number.
you may have to relook in the statement I

Thanks chetan2u for catching that. Careless mistake on my part. I have updated the example cases.

another careless mistake.. B cannot be 3-digit number
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Re: If both A and B are 2-digit even numbers, what is the value of A?  [#permalink]

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27 Jul 2018, 22:38
1
chetan2u wrote:
If both A and B are 2-digit even numbers, what is the value of A?
(1) Ratio of A to B is 1:9
(2) B-A=80

New question!!!..

OA: A
Given:A and B are 2-digit even numbers, what is the value of A
(1) Ratio of A to B is 1:9
Take A as 10 (lowest 2 digit even number) then B = 90
Now take A as 12 , then B =108 which is not possible as per question stem
So A= 10
Statement 1 alone is sufficient

(2) B-A=80
Let us take B= 98(greatest/highest two-digit even number) then A =18
Taking B=96, A =16
Similarly,B can be 98,96,94,92 or 90, and A can be 18,16,14,12 or 10
There is no unique value of A as per statement 2.
So Statement 2 alone is not sufficient
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Re: If both A and B are 2-digit even numbers, what is the value of A?  [#permalink]

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27 Jul 2018, 22:38
1
chetan2u wrote:
If both A and B are 2-digit even numbers, what is the value of A?
(1) Ratio of A to B is 1:9
(2) B-A=80

New question!!!..

Is it A?

Given: A : B = 1 : 9
Also given: A & B are both 2-digit even numbers. So, the smallest 2-digit even number is 10, which would make B = 90. The next even number is 12 but that would make B = 108. So, Statement 1 is sufficient to uniquely identify the value of A.

Statement B is insufficient because there is more than one possible value of A that would satisfy the condition (10,90; 12,92; ... 18,98)
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Re: If both A and B are 2-digit even numbers, what is the value of A?  [#permalink]

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27 Jul 2018, 22:39
1
chetan2u wrote:
If both A and B are 2-digit even numbers, what is the value of A?
(1) Ratio of A to B is 1:9
(2) B-A=80

New question!!!..

1. Ratio of A to B is 1:9
Since both A and B are 2 digit even numbers with ratio 1:9,
If A = 10(first two-digit even number) B = 90
Let A = 12, then B = 108(which is a 3-digit number)
We are able to uniquely determine the value of A (Sufficient)

2. B - A = 80
Since the difference of B and A is 80,
If B = 90, then A = 10
Similarly, if B = 92, then A = 12
We are not able to determine an unique value of A (Insufficient)(Option A)
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Re: If both A and B are 2-digit even numbers, what is the value of A?  [#permalink]

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27 Jul 2018, 22:46
1
chetan2u wrote:
workout wrote:
chetan2u wrote:

workout, A cannot be 2 as it is 2-digit number.
you may have to relook in the statement I

Thanks chetan2u for catching that. Careless mistake on my part. I have updated the example cases.

another careless mistake.. B cannot be 3-digit number

Looks like I need more caffeine in. Thanks for these wonderful questions. I am just gonna keep my post the same (no editing) so that others can learn from my mistake.
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Re: If both A and B are 2-digit even numbers, what is the value of A?  [#permalink]

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27 Jul 2018, 22:47
1
If both A and B are 2-digit even numbers, what is the value of A?
(1) Ratio of A to B is 1:9
(2) B-A=80

Given :- A & B are 2 digit even number , so Smallest/Largest value each can take is 10/98.
To Find A = ?

Statement (1)
A/B = 1/9

Let me assume A to be smallest value, i.e A = 10
10/B = 1/9
B = 9*10 = 90

Let me assume A to be second smallest even number, i.e A = 12
12/B = 1/9
B = 12*9
B = 108
Discarded, as B is a 2 digit even number !!!

So we have unique values of A & B , 10 & 90 respectively .

Statement (1) is sufficient.

Statement(2) :-
B-A=80
A can take values from :- 10 to 18
B can take values from :- 90 to 98

90 - 10 = 80 , 92 - 12 = 80 , etc etc

So no unique values for A & B pair, hence
Statement (2) is not sufficient.

Correct answer:- (A)

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Re: If both A and B are 2-digit even numbers, what is the value of A?  [#permalink]

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27 Jul 2018, 22:56
chetan2u wrote:
If both A and B are 2-digit even numbers, what is the value of A?
(1) Ratio of A to B is 1:9
(2) B-A=80

New question!!!..

Let $$A = xy, B = cd$$

Statement I:

$$cd = 9*xy$$, which means $$xy = 10/12$$.... Sufficient.

Statement II:

$$10(c-x) + (d-y) = 80$$, which means $$c-x = 8$$ and $$d= y.$$
c = 9, x = 1. Again, Insufficient as xy = 10/12 & cd = 90/92.

Hence, A.
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Re: If both A and B are 2-digit even numbers, what is the value of A?  [#permalink]

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29 Jul 2018, 05:37
pushpitkc chetan2u

But why? 1/9 could also be -10/-90 in which case the value of A would be -10
Or it could be 10/90 then the value of A could be 10

So I think therefore answer is C because nowhere it is mentioned that both are positive even two digit no.s
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Re: If both A and B are 2-digit even numbers, what is the value of A?  [#permalink]

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29 Jul 2018, 06:09
BigUD94 wrote:
pushpitkc chetan2u

But why? 1/9 could also be -10/-90 in which case the value of A would be -10
Or it could be 10/90 then the value of A could be 10

So I think therefore answer is C because nowhere it is mentioned that both are positive even two digit no.s

Hi...

Yes in most cases I have seen on OG they mention that positive 2-digit integers or 2-digit positive integers. But once in a while they have skipped it too.
But I am yet to see a question which meant a 2-digit number to mean a negative number too..
If they have wanted to create a trap, they generally write X is an integer with 2 digits..

Also if I write a ratio as 1:9 it means the second is 9 times more than the first but -90 is not exactly 9 times more than -10, it is 9times lesser..

But would follow what OG follows most of the time, so editing and thank you..
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Re: If both A and B are 2-digit even numbers, what is the value of A?  [#permalink]

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29 Jul 2018, 08:51
A and B are two 2-digit positive even numbers.
Statement 1
A/B= 1/9
There are two options are here.
10/90 or 11/99
as both numbers are even so 10/90 is ok.
Sufficient.

take statement 2
B-A= 10
90-10= 80
92-82= 80
Not sufficient.

A is answer.
Re: If both A and B are 2-digit even numbers, what is the value of A? &nbs [#permalink] 29 Jul 2018, 08:51
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