In the equation \(\frac{1}{4}|\frac{3}{5}*x+\frac{2}{3}|−\frac{1}{2}=\frac{5}{8}\), x could equal which value?

A. –12

B. –10

C. −155/18

D. −92/24

E. 46/7

lets simplify\(\frac{1}{4}|\frac{3}{5}*x+\frac{2}{3}|−\frac{1}{2}=\frac{5}{8}\) ........

\(\frac{1}{4}|\frac{3}{5}*x+\frac{2}{3}|=\frac{5}{8}+\frac{1}{2}=\frac{9}{8}\) ..

\(|\frac{3}{5}*x+\frac{2}{3}|=\frac{9}{8}*4=\frac{9}{2}\) .

since values are mostly in -ive, let me open the mod such that the answer is -ive..

\(-(\frac{3}{5}*x+\frac{2}{3})=\frac{9}{2}\) .

\( -(\frac{3}{5}*x)=\frac{9}{2}+\frac{2}{3}=\frac{31}{6} \)

...

]]>

In the equation \(\frac{1}{4}|\frac{3}{5}*x+\frac{2}{3}|−\frac{1}{2}=\frac{5}{8}\), x could equal which value?

A. –12

B. –10

C. −155/18

D. −92/24

E. 46/7

lets simplify\(\frac{1}{4}|\frac{3}{5}*x+\frac{2}{3}|−\frac{1}{2}=\frac{5}{8}\) ........

\(\frac{1}{4}|\frac{3}{5}*x+\frac{2}{3}|=\frac{5}{8}+\frac{1}{2}=\frac{9}{8}\) ..

\(|\frac{3}{5}*x+\frac{2}{3}|=\frac{9}{8}*4=\frac{9}{2}\) .

since values are mostly in -ive, let me open the mod such that the answer is -ive..

\(-(\frac{3}{5}*x+\frac{2}{3})=\frac{9}{2}\) .

\( -(\frac{3}{5}*x)=\frac{9}{2}+\frac{2}{3}=\frac{31}{6} \)

...]]>

If x and y are positive integers, is the greatest common factor (GCF) of x and y equal to 1?

(1) x – y > 1

(2) |x| – |y| > 1

Answer is E as suggested by Vyshak.

one point here, question already says x and y are positive, so what is statement 2 trying to say ?, how does mode matters here. In my opinion both statements are same.

Bunuel, any comment.

]]>

If x and y are positive integers, is the greatest common factor (GCF) of x and y equal to 1?

(1) x – y > 1

(2) |x| – |y| > 1

Answer is E as suggested by Vyshak.

one point here, question already says x and y are positive, so what is statement 2 trying to say ?, how does mode matters here. In my opinion both statements are same.

Bunuel, any comment.]]>

In the equation |6x+9| = |3x+25|, what is the sum of all possible values of x?

A. 4/9

B. 4/5

C. 14/9

D. 15/7

E. 17/3

since it is MOD on both sides we can square both sides..

thereafter we get the two terms on ONE side and we will have a QUADRATIC equation..

In a Quadratic equation, the value of sum of roots /x is\(-\frac{(coeff of x}{coeff of x^2)}\)..

so lets concentrate ONLY on x^2 and x values..

\(|6x+9| = |3x+25|\) ..

\((6x+9)^2 = (3x+25)^2\) .

\(36x^2 +108 x+ 9^2 = 9x^2+150x +25^2\) .

\( (36-9)x^2\)

...

]]>

In the equation |6x+9| = |3x+25|, what is the sum of all possible values of x?

A. 4/9

B. 4/5

C. 14/9

D. 15/7

E. 17/3

since it is MOD on both sides we can square both sides..

thereafter we get the two terms on ONE side and we will have a QUADRATIC equation..

In a Quadratic equation, the value of sum of roots /x is\(-\frac{(coeff of x}{coeff of x^2)}\)..

so lets concentrate ONLY on x^2 and x values..

\(|6x+9| = |3x+25|\) ..

\((6x+9)^2 = (3x+25)^2\) .

\(36x^2 +108 x+ 9^2 = 9x^2+150x +25^2\) .

\( (36-9)x^2\)

...]]>

11*10^n+1<1

try solution for n :

n= 0 => 11 x 10 ^1 = 110 >1

n=-1 => 11 x 10^0 = 11 > 1

n=-2 => 11 x 10^-1 = 11/10 > 1

n=-3 => 11 x 10^-2 = 11/100 < 1

So answer choice -3, B

]]>

11*10^n+1<1

try solution for n :

n= 0 => 11 x 10 ^1 = 110 >1

n=-1 => 11 x 10^0 = 11 > 1

n=-2 => 11 x 10^-1 = 11/10 > 1

n=-3 => 11 x 10^-2 = 11/100 < 1

So answer choice -3, B]]>

Question: Is |x| > y ?

St1: x - y = -1

x = -3; y = -2 --> |x| > y

x = 1; y = 2 --> |x| < y

Not Sufficient

St2: x < 0 --> Clearly insufficient as we do not know anything about y.

Combining St1 and St2: x is negative and x - y = -1

x = -1; y = 0

x = -2; y = -1

y numerically lags behind x by 1 unit and hence |x| is always greater than y

Sufficient

Answer: C

Small correction: the question asks whether |x|>|y|

...

]]>

Question: Is |x| > y ?

St1: x - y = -1

x = -3; y = -2 --> |x| > y

x = 1; y = 2 --> |x| < y

Not Sufficient

St2: x < 0 --> Clearly insufficient as we do not know anything about y.

Combining St1 and St2: x is negative and x - y = -1

x = -1; y = 0

x = -2; y = -1

y numerically lags behind x by 1 unit and hence |x| is always greater than y

Sufficient

Answer: C

Small correction: the question asks whether |x|>|y|

...]]>

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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]]>

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.]]>

2. a > c > b > d > e

3. c > a > b > d > e

c > e is the only must be true statement.

Answer: E

]]>

2. a > c > b > d > e

3. c > a > b > d > e

c > e is the only must be true statement.

Answer: E]]>

Let a, b, c and d be nonzero real numbers. If the quadratic equation ax(cx+d)=-b(cx+d) is solved for x, which of the following is a possible ration of the 2 solutions?

A. -ab/(cd)

B. -ac/(bd)

C. -ad/(bc)

D. ab/(cd)

E. ad/(bc)

Actually, I dont understand why do we have a quadratic equation. Isn't it the same as ax=-b ? Then we would have only 1 solution

I appreciate your suggestions.

Thank you in advance!

No, you cannot cancel (cx+d) from both the sides. Because (cx+d) can be 0 too and you cannot

...

]]>

Let a, b, c and d be nonzero real numbers. If the quadratic equation ax(cx+d)=-b(cx+d) is solved for x, which of the following is a possible ration of the 2 solutions?

A. -ab/(cd)

B. -ac/(bd)

C. -ad/(bc)

D. ab/(cd)

E. ad/(bc)

Actually, I dont understand why do we have a quadratic equation. Isn't it the same as ax=-b ? Then we would have only 1 solution

I appreciate your suggestions.

Thank you in advance!

No, you cannot cancel (cx+d) from both the sides. Because (cx+d) can be 0 too and you cannot

...]]>

Great wayOptimusPrepJanielle

Here is something parallel to OptimusPrepJanielle'sway

Jeneli is taking product of each row as 4 to arrive at the product of units digit.

However I feel it can also be done simply by taking columns ( As there will be only 4 columns )

Posting the approach , plz feel free to revert in case of any question , bothOptimusPrepJanielle & I will be more than happy to discuss further on this issue...

...

]]>

Great wayOptimusPrepJanielle

Here is something parallel to OptimusPrepJanielle'sway

Jeneli is taking product of each row as 4 to arrive at the product of units digit.

However I feel it can also be done simply by taking columns ( As there will be only 4 columns )

Posting the approach , plz feel free to revert in case of any question , bothOptimusPrepJanielle & I will be more than happy to discuss further on this issue...

...]]>

I tried to do in this way:

think first considering all integers with all different algorithms, odd and even.

For the first digit we have: 8 or 9 = two possibilities.

For the second, we can have all numbers between 0 and 9, except the "8" or "9" digit chosen so: 10-1=nine.

For the third: the same reasoning except the two previous digit already taken: 10-2=eight.

two*nine*eight=144. We divide it per two to consider only the odd numbers: 144/2=72.

obs:We could have

...

]]>

I tried to do in this way:

think first considering all integers with all different algorithms, odd and even.

For the first digit we have: 8 or 9 = two possibilities.

For the second, we can have all numbers between 0 and 9, except the "8" or "9" digit chosen so: 10-1=nine.

For the third: the same reasoning except the two previous digit already taken: 10-2=eight.

two*nine*eight=144. We divide it per two to consider only the odd numbers: 144/2=72.

obs:We could have

...]]>

sabxu1 wrote:

Bunuel wrote:

If the positive integer N is a perfect square, which of the following must be true?

I. The number of distinct factors of N is odd.

II. The sum of the distinct factors of N is odd.

III. The number of distinct prime factors of N is even.

Yes, your understanding of III is right. Prime factor of 4 is 2 and prime factor of 9 is 3. So III is not alway true: a perfect square can have any number of primefactors.

Tips about the perfect square :

1. Thenumber of distinct factors of

I. The number of distinct factors of N is odd.

II. The sum of the distinct factors of N is odd.

III. The number of distinct prime factors of N is even.

Yes, your understanding of III is right. Prime factor of 4 is 2 and prime factor of 9 is 3. So III is not alway true: a perfect square can have any number of primefactors.

Tips about the perfect square :

1. Thenumber of distinct factors of

...

]]>

sabxu1 wrote:

Bunuel wrote:

If the positive integer N is a perfect square, which of the following must be true?

I. The number of distinct factors of N is odd.

II. The sum of the distinct factors of N is odd.

III. The number of distinct prime factors of N is even.

Yes, your understanding of III is right. Prime factor of 4 is 2 and prime factor of 9 is 3. So III is not alway true: a perfect square can have any number of primefactors.

Tips about the perfect square :

1. Thenumber of distinct factors of

I. The number of distinct factors of N is odd.

II. The sum of the distinct factors of N is odd.

III. The number of distinct prime factors of N is even.

Yes, your understanding of III is right. Prime factor of 4 is 2 and prime factor of 9 is 3. So III is not alway true: a perfect square can have any number of primefactors.

Tips about the perfect square :

1. Thenumber of distinct factors of

...]]>

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

]]>

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.]]>

\(\sqrt{3\sqrt{80}+\frac{3}{9+4\sqrt{5}}} =\)

A) \(2\sqrt{3\sqrt{5}}\)

B) \(3\)

C) \(3\sqrt{3}\)

D) \(9+4\sqrt{5}\)

E) \(3+2\sqrt{5}\)

You can simplify this question by changing\(\sqrt{80}\) to\(\sqrt{81}\)

\(4\sqrt{5}\) is actually\(\sqrt{80}\) , change it also...

\(\sqrt{81}\) is 9

so approximately the equation produce\(\sqrt{27}\)

=\(3\sqrt{3}\)

...

]]>

\(\sqrt{3\sqrt{80}+\frac{3}{9+4\sqrt{5}}} =\)

A) \(2\sqrt{3\sqrt{5}}\)

B) \(3\)

C) \(3\sqrt{3}\)

D) \(9+4\sqrt{5}\)

E) \(3+2\sqrt{5}\)

You can simplify this question by changing\(\sqrt{80}\) to\(\sqrt{81}\)

\(4\sqrt{5}\) is actually\(\sqrt{80}\) , change it also...

\(\sqrt{81}\) is 9

so approximately the equation produce\(\sqrt{27}\)

=\(3\sqrt{3}\)

...]]>

A dishonest person wants to make a profit on the selling of milk. He would like to mix water (costing nothing) with milk costing 33 $ per litre so as to make a profit of 20% on cost when he sells the resulting milk and water mixture for 36$. In what ratio should he mix the water and milk?

(A)1:20

(B) 1:10

(C) 1:8

(D)1:4

(E)1:2

Similar questions to practice:

a-dishonest-milkman-sells-a-40-liter-mixture-of-milk-and-water-that-co-192299.htmla-dishonest-milkman-sells-a-40-liter-mixture-of-milk-and-water-that-co-192299.htmlhttp://magoosh.com/gmat/2013/difficult-

...

]]>

Hi Bunuel

Actually i did not see clear explanation for the OA.

please help to start from.

Dearhatemnag ,

I'm happy to respond. I'm going answer in the place of the genius Bunuel because I am the author of this particular question. It is question #2 on this blog:

...]]>

13!12! x 183

13!12! x 3 x 61

]]>

13!12! x 183

13!12! x 3 x 61]]>

7 -2 + 6 - 1 = 10

]]>

7 -2 + 6 - 1 = 10]]>

prime factors of \(728\) =\(2^{3}\) * \(7\) * \(13\)

greatest prime factor is 13

Correct answer - D

]]>

prime factors of \(728\) =\(2^{3}\) * \(7\) * \(13\)

greatest prime factor is 13

Correct answer - D]]>

prime factors of \(4095\) = \(3^2\) *\(5\) * \(7\) * \(13\)

greatest prime factor is 13

Correct answer - A

]]>

prime factors of \(4095\) = \(3^2\) *\(5\) * \(7\) * \(13\)

greatest prime factor is 13

Correct answer - A]]>

-2 < x < 10

30 < y < 48

So greatest value for x y = 9 x 47 = 423

Answer choice A

]]>

-2 < x < 10

30 < y < 48

So greatest value for x y = 9 x 47 = 423

Answer choice A]]>

I think this the explanation isn't clear enough, please elaborate. Can this answer be elaborated?

Please refer to the discussion above.

Hope it helps.

]]>

I think this the explanation isn't clear enough, please elaborate. Can this answer be elaborated?

Please refer to the discussion above.

Hope it helps.]]>

So 6, answer choice A

]]>

So 6, answer choice A]]>