### All GMAT Math Resources

## Example Questions

### Example Question #51 : Data Sufficiency Questions

Jake invests $5000 at 10% simple annual interest and another amount of money at percent simple interest. What amount of money did Jake invests at percent interest?

(1) The total amount of interest earned on all investments at the end of one year is $800.

(2) .

**Possible Answers:**

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.

Statements (1) and (2) TOGETHER are not sufficient.

Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient.

Each Statement ALONE is sufficient.

Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

**Correct answer:**

Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

(1) The total amount of interest earned on all investments at the end of one year is $800.

Let A be the amount of money invested at x percent. The total interest earned on both investments is:

We cannot calculate A because x is also unknown. Statement (1) Alone is not sufficient then.

(2) x=6%

Statement (2) Alone is not sufficient.

Combining both statements, we have:

Both Statements together are sufficient but neither statement alone is sufficient.

### Example Question #1 : Dsq: Calculating Compound Interest

Jenna needs years from today to start a business. After talking to an investment banker, Jenna is assured to gain an annually compounded interest of *.*

What amount of money does Jenna need to invest today?

(1)

(2)

**Possible Answers:**

Each statement ALONE is sufficient

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient

Both statements TOGETHER are not sufficient.

Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient

Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient

**Correct answer:**

Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient

Using statement (1), the value of i cannot be determined because t is not specified.

Therefore Statement (1) ALONE is not sufficient.

Using statement (2), the value of i can be determined:

We can then set the following equation with X being the amount of money Jenna has to invest today:

We calculate X as follows:

### Example Question #1 : Dsq: Calculating Compound Interest

Tyler invests $20,000 in a certificate of deposit that draws compound interest. How frequently is the interest compounded - monthly, bimonthly, or quarterly?

Statement 1: The certificate draws 3.15% annual compound interest.

Statement 2: The certificate draws $638.33 the first year.

**Possible Answers:**

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

**Correct answer:**

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

The compound interest equation is

where is the value at the end of the period in question, is the principal, or initial investment, is the interest rate in decimal form, is the number of times the interest is compounded per year, and is the number of years.

We know from the main body of the problem. It is known that only if Statement 1 is knwon, and it is known that only if Statement 2 is known. Also, can only be deduced from Statement 2:

Therefore, neither statement alone is sufficient. If both statements are assumed true, the equation becomes

or, dividing both sides by 20,000,

The question can be answered by substituting 4 (quarterly), 6 (bimonthly), and 12 (monthly) in turn and seeing which one makes the above statement true.

### Example Question #2161 : Gmat Quantitative Reasoning

Joe invests $4,000 in a certificate of deposit that accrues interest that is compounded monthly. What is the annual interest rate?

Statement 1: During the first month, the certificate drew $7.83 in interest.

Statement 2: During the second month, Joe drew $7.85 in interest.

**Possible Answers:**

EITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

**Correct answer:**

EITHER statement ALONE is sufficient to answer the question.

Assume Statement 1 alone is true.

If is the *annual *interest rate, in its decimal form, of a $4,000 CD that draws $7.83 interest in the first month, then

This is a linear equation in one variable that can be solved for .

Assume Statement 2 is true. Then the equation becomes

This is a quadratic equation in one variable that can be solved for .

Either way, the annual interest rate can be found, so either statement alone is sufficient.

### Example Question #51 : Data Sufficiency Questions

Quincy invests $30,000 in a certificate of deposit that draws compound interest. How frequently is the interest compounded - monthly, bimonthly, or quarterly?

Statement 1: The first interest payment is 0.964% of the principal.

Statement 2: The first interest payment is $289.20

**Possible Answers:**

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

**Correct answer:**

BOTH statements TOGETHER are insufficient to answer the question.

The two statements are equivalent, since 0.964% of $30,000 is

Therefore, it can be determined that the interest rate 0.964% is per compounding period. However, no clue is given as to how many compounding periods there are - for example, the annual interest rate is unknown. The two statements together provide insufficient information.

### Example Question #11 : Interest Problems

At the beginning of January of 2015, Olga invested one half of the money she earned in December of 2014 in a certificate of deposit that pays 3.15% annual interest, compounded monthly. At the end of six years, how much will that certificate of deposit be worth?

Statement 1: Olga earned $63,000 in 2014.

Stateent 2: Olga earned the same amount of money each month in 2013.

**Possible Answers:**

BOTH statements TOGETHER are insufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

**Correct answer:**

BOTH statements TOGETHER are insufficient to answer the question.

In order to know how much money is in an account after compound interest is accrued, one thing that must be known is the principal, or amount invested.

Statement 2 is unhelpful, since information from 2013 is not relevant to information for 2014.

From Statement 1 we only know her 2014 earnings, not her December earnings (it is not given that she earned the same per month in 2014). Therefore, the two statements together provide insufficient information.

### Example Question #51 : Data Sufficiency Questions

Natasha decides to invest her entire Christmas bonus in a certificate of deposit that pays 2.15% annual interest, compounded monthly. At the end of five years, how much will that certificate of deposit be worth?

Statement 1: Natasha was given a $3,000 Christmas bonus.

Stateent 2: Natasha earns an annual salary of $54,000.

**Possible Answers:**

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

**Correct answer:**

In order to know how much money is in an account after compound interest is accrued, the following must be known:

The amount of principal, which is given as $3,000 (Natasha's Christmas bonus) *only* in Statement 1;

The amount of time over which interest is accrued, which is stated to be five years in the main body of the problem;

The frequency with which the interest is compounded, which is given as monthly in the main body of the problem; and,

The rate of interest, which is given as 2.15% in the main body of the problem.

Statement 1 alone provides sufficient information to allow the answer to be calculated. Statement 2 is irrelevant, since it provides no information about Natasha's Christmas bonus.

### Example Question #2171 : Gmat Quantitative Reasoning

Mitchell deposits an amount of money in a savings account that pays compound interest. He does not deposit or withdraw during that time. How much money does he have at the end of five years?

Statement 1: Mitchell deposited $10,000.

Statement 2: The savings account draws annual interest of 2.12%, compounded quarterly.

**Possible Answers:**

BOTH statements TOGETHER are insufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

**Correct answer:**

In order to know how much money is in an account after compound interest is accrued, the following must be known:

The amount of principal, which is given as $10,000 *only* in Statement 1;

The amount of time over which interest is accrued, which is stated to be five years in the main body of the problem;

The frequency with which the interest is compounded, which is given as quarterly *only* in Statement 2; and,

The rate of interest, which is given as 2.12% *only* in Statement 2.

Therefore, both statements together are necessary and sufficient to answer the question.

### Example Question #1 : Dsq: Calculating Compound Interest

John deposits an amount of money in a savings account that pays compound interest. He does not deposit or withdraw during that time. How much money does he have at the end of five years?

Statement 1: John deposited $5,000.

Statement 2: The interest is compounded monthly.

**Possible Answers:**

BOTH statements TOGETHER are insufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

**Correct answer:**

BOTH statements TOGETHER are insufficient to answer the question.

Assume both statements are known.

In order to know how much money is in an account after compound interest is accrued, the following must be known:

The amount of principal, which is stated to be $5,000 in Statement 1;

The amount of time over which interest is accrued, which is stated to be five years in the main body of the problem;

The frequency with which the interest is compounded, which is given to be monthly in Statement 2; and,

The rate of interest, which is not given anywhere.

Insufficient information is given.

### Example Question #1 : Dsq: Calculating Probability

A *fair *coin is tossed a given number of times. What is the probability that three or more of the tosses will come up heads?

1) The number of times the coin is tossed is four.

2) The previous day, the coin was tossed ten times, and heads came up eight times.

**Possible Answers:**

BOTH statements TOGETHER are not sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is not sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is not sufficient to answer the question.

**Correct answer:**

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is not sufficient to answer the question.

This is a binomial probability experiment.

The probability that a fair coin will come up heads in any single toss is .

If the coin is tossed four times, then the probability that heads will appear three times is:

The probability that heads will appear four times is:

So the probability that heads will appear* at least* three times is

The second statement is irrelevant; the result of a previous trial has no influence on that of the current trial. It has already been established in the problem that the coin is fair.

The answer is that Statement 1 alone is sufficient to answer the question, but not Statement 2.

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