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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
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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Nice Question ..!
Here the only value of x possible via combination statement is 931
Smash C
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I miss the non-zero again.
that's how I got it wrong
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BDSunDevil
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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nitesh50
BDSunDevil
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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BDSunDevil
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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