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Manager  Joined: 13 May 2011
Posts: 221
WE 1: IT 1 Yr
WE 2: Supply Chain 5 Yrs
If the three-digit integer x=”abc”, where a, b, and c  [#permalink]

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4
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Difficulty:   25% (medium)

Question Stats: 73% (01:25) correct 27% (01:22) wrong based on 465 sessions

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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
##### Most Helpful Expert Reply
Math Expert V
Joined: 02 Sep 2009
Posts: 55188
Re: If the three-digit integer x=”abc”, where a, b, and c  [#permalink]

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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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Manager  Joined: 28 Jul 2011
Posts: 176
Re: If the three-digit integer x=”abc”, where a, b, and c  [#permalink]

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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)
Manager  Joined: 04 Oct 2013
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Concentration: Finance, Leadership
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Re: If the three-digit integer x=”abc”, where a, b, and c  [#permalink]

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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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Joined: 12 Aug 2015
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GRE 1: Q169 V154 Re: If the three-digit integer x=”abc”, where a, b, and c  [#permalink]

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Nice Question ..!
Here the only value of x possible via combination statement is 931
Smash C
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Manager  B
Joined: 07 Jun 2017
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Re: If the three-digit integer x=”abc”, where a, b, and c  [#permalink]

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I miss the non-zero again.
that's how I got it wrong
Manager  S
Joined: 04 Jun 2018
Posts: 157
GMAT 1: 610 Q48 V25 GMAT 2: 690 Q50 V32 GMAT 3: 710 Q50 V36 Re: If the three-digit integer x=”abc”, where a, b, and c  [#permalink]

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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
chetan2u
Bunuel
gmatbusters
EgmatQuantExpert
@scotttargetprep
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9224
Location: Pune, India
Re: If the three-digit integer x=”abc”, where a, b, and c  [#permalink]

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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
chetan2u
Bunuel
gmatbusters
EgmatQuantExpert
@scotttargetprep

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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Intern  B
Status: when you say,"I can or I can't", Both times you are right!
Joined: 26 Nov 2018
Posts: 31
Location: India
Re: If the three-digit integer x=”abc”, where a, b, and c  [#permalink]

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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
VP  G
Joined: 09 Mar 2018
Posts: 1004
Location: India
Re: If the three-digit integer x=”abc”, where a, b, and c  [#permalink]

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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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Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up. Re: If the three-digit integer x=”abc”, where a, b, and c   [#permalink] 15 Jan 2019, 07:51
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# If the three-digit integer x=”abc”, where a, b, and c

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