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## Example Questions

### Example Question #1 : Dsq: Solving Linear Equations With One Unknown

Barry left home at am to go to his friend Harry's house. How many miles away is Harry's house from Barry's house?

(1) Barry drove for minutes at mph

(2) Barry stopped at a gas station halfway there and drove an additional miles before reaching Harry's house.

**Possible Answers:**

C: BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient

A: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient

E: Statements (1) and (2) TOGETHER are not sufficient

D: EACH statement ALONE is sufficient

B: Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient

**Correct answer:**

D: EACH statement ALONE is sufficient

Statement 1 gives us the time and the speed so we can derive the distance:

.

Therefore,

Statement 2 tells us that the gas station is halfway betweent the two houses so:

distance between Barry's house and gas station = distance between Harry's house and gas station = 0.5 distance between the two houses

Furthermore, we learn that the distance between the gas station and Harry's house is 20 miles.

Therefore:

distance between Harry's house and gas station = 20 miles = 0.5 distance between the two houses

So the distance = 2 x 20 = 40 miles

So the correct answer is D; each statement alone is sufficient.

### Example Question #2 : Dsq: Solving Linear Equations With One Unknown

Find , a linear equation passing through the point .

I) is parallel to which is given by:

II) has a slope of .

**Possible Answers:**

Each statement alone is enough to solve the question.

Both statements taken together are sufficient to solve the question.

Statement 2 is sufficient to solve the question, but statement 1 is not sufficient to solve the question.

Neither statement is sufficient to solve the question. More information is needed.

Statement 1 is sufficient to solve the question, but statement 2 is not sufficient to solve the question.

**Correct answer:**

Each statement alone is enough to solve the question.

We are given a point and two clues.

Both I and II give us the slope of f(x). It must be 4 because we are told so in II. This holds true from statement I since it must be parallel to g(x), which has a slope of four.

With a slope and a point we can find the equation of f(x) using the point slope form,

.

Therefore either statement alone is enough.

### Example Question #3 : Dsq: Solving Linear Equations With One Unknown

Given:

Find .

I) .

II) and passes through .

**Possible Answers:**

Either statement is sufficient to answer the question.

Both statements are needed to answer the question.

Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.

Neither statement is sufficient to answer the question. More information is needed.

Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.

**Correct answer:**

Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.

To find b, we need a point on k(t).

I) Gives us that point.

II) Gives us some details about a parallel line, which is cool and all, but it doesn't help us find b.

So statement I alone is sufficient to answer the question.

### Example Question #4 : Dsq: Solving Linear Equations With One Unknown

Given:

Find .

I) .

II) crosses the -axis at .

**Possible Answers:**

Either statement is sufficient to answer the question.

Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.

Neither statement is sufficient to answer the question. More information is needed.

Neither statement is sufficient to answer the question. More information is needed.

Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.

**Correct answer:**

Either statement is sufficient to answer the question.

To find m, we need a point on the line.

Both I and II give us points, so we can use either of them to solve for m.

### Example Question #5 : Dsq: Solving Linear Equations With One Unknown

What is ?

(1)

(2)

**Possible Answers:**

Statements 1 and 2 together are sufficient.

Each statement alone is sufficient.

Statement 2 alone is sufficient.

Both statements together are sufficient.

Statement 1 alone is sufficient.

**Correct answer:**

Each statement alone is sufficient.

To answer the question we must know the absolute value of .

Statement 1 tells us the absolute value of , indeed, it is .

Statement 2 also tells us that the absolute value of is 5, since .

Therefore, the final answer is each statement alone is sufficient.

### Example Question #6 : Dsq: Solving Linear Equations With One Unknown

What is ?

(1)

(2)

**Possible Answers:**

Statement 2 alone is sufficient.

Each statement alone is sufficient.

Both statements together are sufficient.

Statements 1 and 2 together are sufficient.

Statement 1 alone is sufficient.

**Correct answer:**

Statement 2 alone is sufficient.

To be able to answer the question, we must have a definitive value for .

Statement 1 tells us that is , in other words could be two values or . This statement gives us two possibilities for and is therefore insufficient.

Statement 2 tells us that the cube of is , therefore must be . This statement gives a single possible value for and therefore is, alone, sufficient.

### Example Question #7 : Dsq: Solving Linear Equations With One Unknown

What is ?

(1)

(2)

**Possible Answers:**

Each statement alone is sufficient.

Statement 2 alone is sufficient.

Both statements together are sufficient.

Statements 1 and 2 together are not sufficient.

Statement 1 alone is sufficient.

**Correct answer:**

Statements 1 and 2 together are not sufficient.

To answer the question, we should be able to find a single value for .

Statement 1 gives us two possible values for . Indeed, or . Hence, the information provided doesn't allow us to find the answer to the problem.

Statement 2 although a complicated equation to calculate, won't prove useful because the power is an even number and therefore, the equation will also have two solutions.

Both statements together are not sufficient because they both give us the value of , which is not sufficient.

Hence, statements 1 and 2 taken together are not sufficient.

### Example Question #8 : Dsq: Solving Linear Equations With One Unknown

, what is if is an integer?

(1)

(2)

**Possible Answers:**

Statement 2 alone is sufficient.

Both statements together are sufficient.

Statement 1 alone is sufficient.

Statements 1 and 2 together are not sufficient.

Each statement alone is sufficient.

**Correct answer:**

Both statements together are sufficient.

To begin with, we should see that information about unknowns or would be useful to answer the problem. We already know that both these unknowns are integers.

Statement 1 gives us information about the upper bound for . However, can still be an infinity of values, therefore this statement alone is insufficient.

Statement 2 gives us information about the lower bound for , just as statement 1, this statement alone doesn't allow us to find a single value for .

Taking these statements together we get that . Since is an integer, can only be . Both statements together are sufficient.

### Example Question #9 : Dsq: Solving Linear Equations With One Unknown

What is ?

(1) is positive

(2)

**Possible Answers:**

Statement 2 alone is sufficient.

Each statement alone is sufficient.

Statements 1 and 2 together are not sufficient.

Statement 1 alone is sufficient.

Both statements together are sufficient.

**Correct answer:**

Statement 2 alone is sufficient.

Firstly, we should try to simplify the equation, to see solutions for . We get . The best west way to simplify quadratic equations is to find the possible factors for the last term in the general quadratic equation and those two factors must add up to . Here for example, and add up to and their products is .

So we have to solutions for the equation and we need to know what we are looking for.

Statement 1 tells us that is positive, however, the two possible solutions are positive and therefore, statement 1 doesn't help us find the correct solution for .

Statement 2 tells us that is smaller than 3. Only one of our solutions is smaller than 3. Therefore statement 2 alone is sufficient.

### Example Question #10 : Dsq: Solving Linear Equations With One Unknown

. What is ?

(1)

(2) is an integer

**Possible Answers:**

Each statement alone is sufficient.

Statements 1 and 2 together are not sufficient.

Statement 2 alone is sufficient.

Statement 1 alone is sufficient.

Both statements together are sufficient.

**Correct answer:**

Statements 1 and 2 together are not sufficient.

First, we should try to simplify the quadratic equation, and we get . This allows to see the two solutions for our equation.

Statement 1 tells us that is between and . But both possible solutions are in this interval. Therefore statement 1 alone is not sufficient.

Statement 2 tells us that is an integer, which we already knew by reducing the equation. Therefore, this statements doesn't help us find a single value for

Statements 1 and 2 together are still insufficient, since none can help us find a single value for .

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