# GMAT Maths | Number Properties & AP GP

###### GMAT Sample Questions | Number Theory, Sequence & Series Questionbank Page 2

If it has been a while since you did maths, you should start by watching these two GMAT Math lesson videos to help you get better traction when solving the questions given below.

1. What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3?

1. 897
2. 164,850
3. 164,749
4. 149,700
5. 156,720
Approach to solve this arithmetic sequence question

Find the smallest 3-digit number that leaves a remainder of 2 when divided by 3. Find the largest 3-digit number that leaves a remainder of 2 when divided by 3. All the terms of this sequence are in an arithmetic progression. Use the first term and last term to compute the number of terms in the arithmetic sequence. Then compute the sum of the arithmetic sequence using the formula $$frac{n}{2}\\$$first term + last term). A 650 level GMAT sample question in sum of terms of an arithmetic progression.

2. How many 3 digit positive integers exist that when divided by 7 leave a remainder of 5?

1. 128
2. 142
3. 143
4. 141
5. 129
Approach to solve this arithmetic progression question

The approach to solve this arithmetic sequence question is similar to that of the last one. Find the smallest 3-digit number that leaves a remainder of 5 when divided by 7. Find the largest 3-digit number that satisfies this condition. Use the last term = first term + (n - 1)*d formula to compute 'n' - the number of terms in the sequence. The common difference for this arithmetic sequence is 7. A 600 to 650 level GMAT maths question - nth term questions.

3. The average of 5 consecutive integers starting with m as the first integer is n. What is the average of 9 consecutive integers that start with (m + 2)?

1. m + 4
2. n + 6
3. n + 3
4. m + 5
5. n + 4
Hint to solve this GMAT arithmetic progression question

Assume a value for 'm'. Easiest value to assume for 'm' is 1. Compute the average of 9 consecutive integers starting from 3 (If m is 1, m + 2 will be 3). Relate the value that you get for the average in terms of m to find the answer. A sub 600 level GMAT problem solving question.

4. The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 15 terms of the arithmetic progression?

1. 300
2. 120
3. 150
4. 170
5. 270
Approach to solve this arithmetic sequence question

Write the formula to compute the sum of the first 15 terms of the arithmetic progression. Express the information about the sum of the 4th and 12th term of the AP in terms of the first term and common difference. You will be able to use this information to find the required sum. A 650 to 700 level GMAT maths question in sum of arithmetic progressions .

5. If the ratio of the sum of the first 6 terms of a G.P. to the sum of the first 3 terms of the G.P. is 9, what is the common ratio of the G.P?

1. 3
2. $$frac {1} {3}$ 3. 2 4. 9 5. $\frac {1} {9}$ Hint to solve this GMAT geometric sequence question Write the formula to compute the sum of the first 6 terms of a GP. Write the formula to compute the first 3 terms of a GP. The ratio of the two sums is 9 : 1. Solve this equation to find the value of the common ratio of the GP. A 650 to 700 level GMAT question in geometric progressions. 6. Set A contains all the even numbers between 2 and 50 inclusive. Set B contains all the even numbers between 102 and 150 inclusive. What is the difference between the sum of elements of set B and that of set A? 1. 2500 2. 5050 3. 11325 4. 6275 5. 2550 Approach to solve this arithmetic sequence question One way to solve this GMAT sample question in AP is to compute the sum of each of the two arithmetic sequences and compute the difference. A better alternative goes as follows: find the difference between the first term of both the sets. Find the difference between the second term of both the sets and so on and add the differences. A 650 level GMAT question in sum of AP. 7. Data Sufficiency: A set S contains the following elements: {7, 11, 15, 19, 23, x}. What is the value of x? 1. The elements are in arithmetic progression 2. x is prime Hint to solve this number systems and arithmetic sequence DS question Note: Do not assume 'x' to be a number greater than 23 because it is written to the right of 23 in the set. If you could glean that information from the question stem or the statements, only then can you consider x to be greater than 23. Using the information in the statements, list down possible values for 'x'. If you are able to narrow it to a single value, the data is sufficient. A 600 to 650 level GMAT DS question in number systems and arithmetic progression. 8. In the first 1000 natural numbers, how many integers exist such that they leave a remainder 4 when divided by 7, and a remainder 9 when divided by 11? 1. 11 2. 14 3. 12 4. 13 5. 10 Approach to solve this GMAT arithmetic sequence question List down the first 8 to 10 terms of the first AP. List down the first 8 to 10 terms of the second AP. Identify the first number that is common to both the arithmetic sequences. Identify the second number that is common to both the arithmetic sequences. Now, you know the first term and the common difference. Identify the last term that is common to both the arithmetic sequences. Use the AP formula to compute the nth term to find the number of terms. A 650 to 700 level GMAT sample question in arithmetic progressions. 9. Data Sufficiency: What is the 6th term of the Arithmetic sequence? 1. The sum of the 6th to the 12th term of the sequence is 77. 2. The sum of the 2nd to the 10th term of the sequence is 108. Hint to solve this GMAT arithmetic progressions question Express the information in the first statement in terms of the first term and common difference of the AP. Determine whether it will help compute the value of the 6th term of the arithmetic sequence. Repeat the process for the second term. If the statements individually do not give a conclusive answer, combine the statements, solve for the first term and the common difference and arrive at the answer to the DS question. A 600 to 650 level GMAT DS question in arithmetic sequences. 10. Data Sufficiency: What is the value of X, if X and Y are two distinct integers and their product is 30? 1. X is an odd integer 2. X > Y Hint to solve this GMAT DS question in number systems List down all possibile integer values of X and Y such that their product is 30. Use the information in the two statements to determine whether you can compute a unique value of X. A 650 level GMAT data sufficiency question in number systems. 11. Data Sufficiency: Is y an integer? 1. y3 is an integer 2. 3y is an integer 12. Data Sufficiency: Is the positive integer m divisible by 6? 1. m is divisible by 3 2. m is divisible by 4 Hint to solve this GMAT Data Sufficiency Problem A number that is divisible by 6 should be divisible by both 3 and 2. Use the information in the statements to determine whether 'm' is divisible by both 3 and 2. A 600 to 650 level GMAT practice question in number systems. 13. Data Sufficiency: Is ab positive? 1.$a + b)2 < (a-b)2
2. a = b
Hint to solve this number properties data sufficiency question

The product of two numbers is positive either if both the numbers are positive or if both the numbers are negative. Solve the expression in statement 1 to determine whether you get a unique answer to the question. Consider all possible values that 'a' and 'b' can take when determining whether statement 2 is sufficient. Watch out for values that one might tend to overlook. A 650 level GMAT sample question in number properties data sufficiency.

14. Data Sufficiency: When Y is divided by 2, is the remainder 1?

1. (-1)(Y + 2) = -1
2. Y is prime
Hint to solve this GMAT number systems data sufficiency question

If Y is an odd number, you will get a remainder of 1 when 2 divides Y. If Y is an even number, the remainder will be 0 when 2 divides Y. (-1) raised to an odd power is negative. (-1) raised to an even power is positive. Use this property about positive and negative numbers while evaluating statement 1. Do not miss out the obvious when evaluating statement 2. A 600 to 650 level GMAT data sufficiency question in number properties.

15. Data Sufficiency: Is the two digit positive integer P a prime number?

1. (P + 2) and (P - 2) are prime.
2. (P - 4) and (P + 4) are prime.

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