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If the three-digit integer x=”abc”, where a, b, and c

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If the three-digit integer x=”abc”, where a, b, and c  [#permalink]

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New post 04 May 2012, 07:21
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If the three-digit integer x=”abc”, where a, b, and c represent nonzero digits of x, what is the value of x?

(1) a>= 3b
(2) b>= 3c
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Re: If the three-digit integer x=”abc”, where a, b, and c  [#permalink]

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New post 04 May 2012, 08:55
6
3
If the three-digit integer x=”abc”, where a, b, and c represent nonzero digits of x, what is the value of x?

(1) a>= 3b. Not sufficient, since no info about c.
(2) b>= 3c. Not sufficient, since no info about a.

(1)+(2) We have that a>= 3b and b>= 3c. Now, since each represent a nonzero single digit then c can only be 1, b can only be 3 and a can only be 9. Because if c=2 (or more) then the least value of b is 6 and in this case the least value of a is 18, so it's no more a single digit. Sufficient.

Answer: C.

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Hope it helps.
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Re: If the three-digit integer x=”abc”, where a, b, and c  [#permalink]

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New post 06 May 2012, 16:20
Will vote for C

(A) a >= 3b

if (b = 1)

a = {3,4,5 ...}

not sufficient

(B) b >= 3c


if (c = 1)
b = {3,4,5 ....}

(C)

if (c = 1)

b = 3 and a = 3b = 3 * 3 = 9

and therefore sufficient

b cannot be > 3, if b = 4 then a will be 12 (not a digit)
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Re: If the three-digit integer x=”abc”, where a, b, and c  [#permalink]

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New post 21 Jan 2014, 15:22
1
If the three-digit integer x=”abc”, where a, b, and c represent nonzero digits of x, what is the value of x?

(1) a>= 3b
Insufficient. a<= 9
(2) b>= 3c
Insufficient b<= 9

1+2) If we combine both inequalities together we end up with a/3>=b>=3c, thus the only values a can assume are 3 and 9, if a=3 the inequality does not hold true. Pick a=9 at this point we must minimize c, which will be 1, and b will be 3. Thus the value of abc is 931.

Otherwise you can solve it by plugging in numbers.

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Re: If the three-digit integer x=”abc”, where a, b, and c  [#permalink]

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New post 11 Aug 2016, 07:49
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Re: If the three-digit integer x=”abc”, where a, b, and c  [#permalink]

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New post 24 Aug 2017, 21:25
I miss the non-zero again.
that's how I got it wrong
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Re: If the three-digit integer x=”abc”, where a, b, and c  [#permalink]

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New post 29 Dec 2018, 00:01
BDSunDevil wrote:
If the three-digit integer x=”abc”, where a, b, and c represent nonzero digits of x, what is the value of x?

(1) a>= 3b
(2) b>= 3c



HI

Can any expert please explain my doubt?

So I tried solving this question using inequalities.

If a>=3b
and B>=3c
If we add them up
A+B>=3b+3c

A>=2b+3c

Now in this case why do have to follow the original constrains?
Can't we just say that all the values which will satisfy the above resultant inequality will satisfy the original constrains?

For Eg:
If c=1 b=2 A= 8,9

I know there is a big conceptual gap here. Would really be grateful if someone can take up this doubt in detail.
Thank you.

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Re: If the three-digit integer x=”abc”, where a, b, and c  [#permalink]

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New post 01 Jan 2019, 06:10
nitesh50 wrote:
BDSunDevil wrote:
If the three-digit integer x=”abc”, where a, b, and c represent nonzero digits of x, what is the value of x?

(1) a>= 3b
(2) b>= 3c



HI

Can any expert please explain my doubt?

So I tried solving this question using inequalities.

If a>=3b
and B>=3c
If we add them up
A+B>=3b+3c

A>=2b+3c

Now in this case why do have to follow the original constrains?
Can't we just say that all the values which will satisfy the above resultant inequality will satisfy the original constrains?

For Eg:
If c=1 b=2 A= 8,9

I know there is a big conceptual gap here. Would really be grateful if someone can take up this doubt in detail.
Thank you.

VeritasKarishma
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When you derive a relation between a, b and c, you lose the relation between b and c and the relation between a and b individually.

e.g.
a > b
c > d

a + c > b + d
-> In this inequality, c doesn't need to be greater than d. Just that sum of a and c needs to be greater than the sum of b and d. a could be much greater making up for b and d on its own such that c is very small e.g.
100 + 2 > 24 + 39

But originally c needs to be greater than d and such a set up would not be acceptable.
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Re: If the three-digit integer x=”abc”, where a, b, and c  [#permalink]

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New post 15 Jan 2019, 07:33
Hello Bunuel,

Please help me out!

if we combine both equations

a>=3b>=9c

case: 1 (taken positive value of c) only 1 is possible for a,b ,and c.

Case: 2 (taken -ve value of c)
if we take c = -1
b could be -2,-1,1,and2

Please help me out to rectify this...Perhaps I'm overthinking
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Re: If the three-digit integer x=”abc”, where a, b, and c  [#permalink]

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New post 15 Jan 2019, 07:51
BDSunDevil wrote:
If the three-digit integer x=”abc”, where a, b, and c represent nonzero digits of x, what is the value of x?

(1) a>= 3b
(2) b>= 3c


From Statement 1 and Statement 2, we dont the values of c and a respectively.

After combining you get to know that the value can be 931
making it sufficient to give a unique value

Answer C.
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Re: If the three-digit integer x=”abc”, where a, b, and c   [#permalink] 15 Jan 2019, 07:51
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