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505-555 Level|   Algebra|                  
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Bunuel
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What is the value of x/(yz) ?

(1) x = y/2 and z = 2x/5
(2) x/z = 5/2 and 1/y = 1/10

Sol: St 1---> x=2y and z=2x/5 or 4y/5
Thus we have 2y/(y*4y/5) or 10y/4y^2---> 10/4y but we don't the value of y so not sufficient

St 2: x=5/2z and y=10
Subsituting we get (5z/2)/10*z or 5z/20z or 1/4
Ans B
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Option B:
From S1: replacing y=2x and z=2x/5 does not give a value for x/(yz)
Not sufficient

From S2: x/z * 1/y are both given
So value=1/4
Sufficient
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Bunuel
SOLUTION

What is the value of x/(yz) ?

(1) \(x = \frac{y}{2}\) and \(z = \frac{2x}{5}\). If \(y=10\), then \(x=5\), \(z=2\) and in this case \(\frac{x}{yz}=\frac{5}{20}=\frac{1}{4}\) BUT if \(y=20\), then \(x=10\), \(z=4\) and in this case \(\frac{x}{yz}=\frac{10}{80}=\frac{1}{8}\). Not sufficient.

(2) \(\frac{x}{z} = \frac{5}{2}\) and \(\frac{1}{y} = \frac{1}{10}\). Multiply these two equations: \(\frac{x}{yz}=\frac{5}{20}\). Sufficient.

Answer: B.


In statement 1.......I tried to solve it through algebra. y= 2x and z=2x/5 so if we pick up expression given in question and replace y and z with 2x and 2x/5 respectively......the entire expression would only have one variable(x).....by a little calculation all x in expressions would be cancelled with each others and we will get 4/5 as answer of expression. Than why sttment 1 is insufficient? can you please guide me? :cry:
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Bunuel
SOLUTION

What is the value of x/(yz) ?

(1) \(x = \frac{y}{2}\) and \(z = \frac{2x}{5}\). If \(y=10\), then \(x=5\), \(z=2\) and in this case \(\frac{x}{yz}=\frac{5}{20}=\frac{1}{4}\) BUT if \(y=20\), then \(x=10\), \(z=4\) and in this case \(\frac{x}{yz}=\frac{10}{80}=\frac{1}{8}\). Not sufficient.

(2) \(\frac{x}{z} = \frac{5}{2}\) and \(\frac{1}{y} = \frac{1}{10}\). Multiply these two equations: \(\frac{x}{yz}=\frac{5}{20}\). Sufficient.

Answer: B.


In statement 1.......I tried to solve it through algebra. y= 2x and z=2x/5 so if we pick up expression given in question and replace y and z with 2x and 2x/5 respectively......the entire expression would only have one variable(x).....by a little calculation all x in expressions would be cancelled with each others and we will get 4/5 as answer of expression. Than why sttment 1 is insufficient? can you please guide me? :cry:

When you substitute y = 2x and z = 2x/5 into x/(yz) you get 5/(4x). Without knowing the value of x we cannot get the value of 5/(4x).

Hope it's clear.
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What is the value of \(\frac{x}{yz}\)?

(1) \(x = \frac{y}{2}\) and \(z = \frac{2x}{5}\)

(2) \(\frac{x}{z} = \frac{5}{2}\) and \(\frac{1}{y} = \frac{1}{10}\)

We'll try to simplify and rearrange our data to create x/yz.
This is a Precise approach.

(1) we have x = y/2 --> x/y = 1/2. Multiplying by z = 2x/5 gives xz/y = (2x^2)/(5y), which can have many different values.
Insufficient.

(2) multiplying x/z = 5/2 by 1/y = 1/10 gives x/yz = 5/20, a unique value.
Sufficient.

(B) is our answer.
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financeguy25
What is the value of \(\frac{x}{yz}\)?


(1) \(x = \frac{y}{2}\) and \(z = \frac{2x}{5}\)

(2) \(\frac{x}{z} = \frac{5}{2}\) and \(\frac{1}{y} = \frac{1}{10}\)

DS86602.01

Target question: What is the value of x/yz?

Statement 1: x = y/2 and z = 2x/5
Take x = y/2 and multiply both sides by 2 to get: 2x = y
Also given: z = 2x/5

This allows us to take our target expression, x/yz, and replace y and z to get: x/yz = x/[(2x)(2x/5)]
= x/(4x²/5)
= (x)(5/4x²)
= 5x/4x²
= 5/4x
Since x can be any value, we can see that we cannot answer the target question with certainty
Statement 1 is NOT SUFFICIENT

Statement 2: x/z = 5/2 and 1/y = 1/10[
Important: we are trying to find the value of x/yz
Notice that we can take x/yz and rewrite it as (x/z)(1/y), which works nicely with our given information.
We get: x/yz = (x/z)(1/y) = (5/2)(1/10) = 5/20 = 1/4
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent
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What is the value of \(\frac{x}{yz}\)?


(1) \(x = \frac{y}{2}\) and \(z = \frac{2x}{5}\)

(2) \(\frac{x}{z} = \frac{5}{2}\) and \(\frac{1}{y} = \frac{1}{10}\)

DS86602.01

Statement - I (Insufficient)
1. \(x = \frac{y}{2}\) can be written as \(\frac{x}{y} = \frac{1}{2}\)

2. Substituting \(\frac{x}{y} = \frac{1}{2}\) and \(z = \frac{2x}{5}\) in \(\frac{x}{yz}\) we get \(\frac{1}{2} * \frac{5}{2x}\)

3. As we see, one variable is remains uncancelled and hence we cannot arrive at the final answer

Statement - II (Sufficient)
Substituting \(\frac{x}{z} = \frac{5}{2}\) and \(\frac{1}{y} = \frac{1}{10}\) in \(\frac{x}{yz}\) we get \(\frac{5}{2}*\frac{1}{10} = \frac{1}{4}\)

Ans. B
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What is the value of x/yz?

(1) x=y/2 and z=2x/5
(2) x/z=5/2 and 1/y=1/10

Statement 1:
substituting value of x:1/2z
substituting value of z: 5/4x

Statement 2:
substituting value of x:5/2y
substituting value of y: 25


Statement 2 thus B
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KanikaJain
What is the value of x/yz?

(1) x=y/2 and z=2x/5
(2) x/z=5/2 and 1/y=1/10

Statement 1:
substituting value of x:1/2z
substituting value of z: 5/4x

Statement 2:
substituting value of x:5/2y
substituting value of y: 25


Statement 2 thus B
Pure algebraic questions are no longer a part of the DS syllabus of the GMAT.

DS questions in GMAT Focus encompass various types of word problems, such as:

  • Word Problems
  • Work Problems
  • Distance Problems
  • Mixture Problems
  • Percent and Interest Problems
  • Overlapping Sets Problems
  • Statistics Problems
  • Combination and Probability Problems

While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won’t encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."

Check GMAT Syllabus for Focus Edition

You can also visit the Data Sufficiency forum and filter questions by OG 2024-2025, GMAT Prep (Focus), and Data Insights Review 2024-2025 sources to see the types of questions currently tested on the GMAT.

So, you can ignore this and similar questions.

Hope it helps.
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