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M22-35

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M22-35  [#permalink]

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New post 16 Sep 2014, 01:17
1
7
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

46% (01:31) correct 54% (01:20) wrong based on 138 sessions

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M22-35  [#permalink]

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New post 16 Sep 2014, 01:17
Official Solution:

If \(a=0.xyz\), where \(x\), \(y\) and \(z\) are digits from 0 to 9, inclusive, is \(a \gt \frac{2}{3}\)?

First of all \(\frac{2}{3}\) is a recurring decimal 0.666...

(1) \(x+y \gt 13\). The least value of x is \(5 (5+9=14 \gt 13)\), so in this case \(x=0.59z \lt 0.66(6)\) but \(x=7\) and \(y=9\) is also possible, and in this case \(x=0.79z \gt 0.66(6)\). Not sufficient.

(2) \(x+z \gt 14\). The least value of \(x\) is \(6 (6+9=15 \gt 14)\), but we don't know the value of \(y\). Not sufficient.

(1)+(2) The least value of \(x\) is 6 and in this case from (1) the least value of \(y\) is \(8 (6+8=14 \gt 13)\), hence the least value of \(a\) is \(0.68z \gt 0.66(6)\). Sufficient.


Answer: C
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Re: M22-35  [#permalink]

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New post 24 Mar 2015, 09:17
Bunuel wrote:
Official Solution:


First of all \(\frac{2}{3}\) is a recurring decimal 0.666...

(1) \(x+y \gt 13\). The least value of x is \(5 (5+9=14 \gt 13)\), so in this case \(x=0.59z \lt 0.66(6)\) but \(x=7\) and \(y=9\) is also possible, and in this case \(x=0.79z \gt 0.66(6)\). Not sufficient.

(2) \(x+z \gt 14\). The least value of \(x\) is \(6 (6+9=15 \gt 14)\), but we don't know the value of \(y\). Not sufficient.

(1)+(2) The least value of \(x\) is 6 and in this case from (1) the least value of \(y\) is \(8 (6+8=14 \gt 13)\), hence the least value of \(a\) is \(0.68z \gt 0.66(6)\). Sufficient.


Answer: C



Hi Bunuel

When combining, why cant I ADD the inequalities, which gives

2x + y + z > 27

least value can be 28

2 (6) + 7 + 9 = 28 ........ Here I get 0.679 ---> Yes
2 (5) + 9 + 9 = 28 ........ Here I get 0.599 ----> No

Hence (E) is the ans

Where am I going wrong?

Thanks
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M22-35  [#permalink]

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New post 24 Mar 2015, 09:46
1
buddyisraelgmat wrote:
Bunuel wrote:
Official Solution:


First of all \(\frac{2}{3}\) is a recurring decimal 0.666...

(1) \(x+y \gt 13\). The least value of x is \(5 (5+9=14 \gt 13)\), so in this case \(x=0.59z \lt 0.66(6)\) but \(x=7\) and \(y=9\) is also possible, and in this case \(x=0.79z \gt 0.66(6)\). Not sufficient.

(2) \(x+z \gt 14\). The least value of \(x\) is \(6 (6+9=15 \gt 14)\), but we don't know the value of \(y\). Not sufficient.

(1)+(2) The least value of \(x\) is 6 and in this case from (1) the least value of \(y\) is \(8 (6+8=14 \gt 13)\), hence the least value of \(a\) is \(0.68z \gt 0.66(6)\). Sufficient.


Answer: C



Hi Bunuel

When combining, why cant I ADD the inequalities, which gives

2x + y + z > 27

least value can be 28

2 (6) + 7 + 9 = 28 ........ Here I get 0.679 ---> Yes
2 (5) + 9 + 9 = 28 ........ Here I get 0.599 ----> No

Hence (E) is the ans

Where am I going wrong?

Thanks


You can add but numbers you choose should still fit the statements and your numbers do not.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M22-35  [#permalink]

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New post 24 Mar 2015, 09:52
Bunuel wrote:
buddyisraelgmat wrote:
Bunuel wrote:
Official Solution:


First of all \(\frac{2}{3}\) is a recurring decimal 0.666...

(1) \(x+y \gt 13\). The least value of x is \(5 (5+9=14 \gt 13)\), so in this case \(x=0.59z \lt 0.66(6)\) but \(x=7\) and \(y=9\) is also possible, and in this case \(x=0.79z \gt 0.66(6)\). Not sufficient.

(2) \(x+z \gt 14\). The least value of \(x\) is \(6 (6+9=15 \gt 14)\), but we don't know the value of \(y\). Not sufficient.

(1)+(2) The least value of \(x\) is 6 and in this case from (1) the least value of \(y\) is \(8 (6+8=14 \gt 13)\), hence the least value of \(a\) is \(0.68z \gt 0.66(6)\). Sufficient.


Answer: C



Hi Bunuel

When combining, why cant I ADD the inequalities, which gives

2x + y + z > 27

least value can be 28

2 (6) + 7 + 9 = 28 ........ Here I get 0.679 ---> Yes
2 (5) + 9 + 9 = 28 ........ Here I get 0.599 ----> No

Hence (E) is the ans

Where am I going wrong?

Thanks


You can add but numbers you choose should still fit the statements and your numbers do not.



Oh I get it - wow this is really tricky !! Thanks a ton! +1 Kudos
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Re: M22-35  [#permalink]

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New post 13 Dec 2016, 08:52
I am not able to understand the exact question stem (If a=0.xyz)
Is this equation means a = 0*x*y*z ?
Please explain?
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Re: M22-35  [#permalink]

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New post 13 Dec 2016, 10:19
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Re: M22-35  [#permalink]

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New post 20 Jul 2018, 21:12
Bunuel wrote:
Official Solution:

If \(a=0.xyz\), where \(x\), \(y\) and \(z\) are digits from 0 to 9, inclusive, is \(a \gt \frac{2}{3}\)?

First of all \(\frac{2}{3}\) is a recurring decimal 0.666...

(1) \(x+y \gt 13\). The least value of x is \(5 (5+9=14 \gt 13)\), so in this case \(x=0.59z \lt 0.66(6)\) but \(x=7\) and \(y=9\) is also possible, and in this case \(x=0.79z \gt 0.66(6)\). Not sufficient.

(2) \(x+z \gt 14\). The least value of \(x\) is \(6 (6+9=15 \gt 14)\), but we don't know the value of \(y\). Not sufficient.

(1)+(2) The least value of \(x\) is 6 and in this case from (1) the least value of \(y\) is \(8 (6+8=14 \gt 13)\), hence the least value of \(a\) is \(0.68z \gt 0.66(6)\). Sufficient.


Answer: C


Hi Bunuel,

Here in S1 the value of x and y has been taken as 5,9 and 7,9.
and in S2 the value of x and z has been taken as 6,9.

Then how have we arrived at the conclusion that the lowest value of x is 6? I am not able to understand the logic, may you pl elaborate on it. Also why cant the value assumed in both the statements be reversed, after all there is nothing in the question stem that suggests that x is greater/smaller than y or z.

Regards
Re: M22-35 &nbs [#permalink] 20 Jul 2018, 21:12
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