GMAT Algebra Questions With Answers
Algebra questions constitute a major portion of the Quant section of the GMAT. These questions can come under both Problem Solving and Data Sufficiency types. Algebra has a number of topics in it. In this article, we will be looking into –
- GMAT Algebra Topics
- GMAT Algebra Questions with Answers
- 5 tips that can help you ace these questions.
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GMAT Algebra Topics
In the GMAT, Algebra constitutes a number of topics. They are as follows (this list is in accordance with the GMAT Official Guide):
- Simplifying Algebraic Expressions
- Equations
- Linear Equations
- Quadratic Equations
- Exponents
- Inequalities
- Absolute value or modulus
- Functions
Examples – GMAT Algebra Questions
Question 1:
Is xy < 6 ?
Statement 1: x< 2, y<3
Statement 2: x and y are non-negative
Approach:
Let us consider Statement 1. If x < 2 and y < 3, then xy < 6. But this is only possible if we do not consider the sign.
Imagine that one of them turns out to be negative, then irrespective of the other value, xy < 6.
However, if both turn out to be negative, then xy can take any value as large as possible.
Hence, Statement 1 is not sufficient.
Statement 2 is again not sufficient since x and y can take any value.
When we combine these statements, we know that x and y are either positive or zero. If any one or both are zero, xy < 6
When none of them is zero, they are still less than 6.
Hence, option C stating that both together are sufficient, however, none of them individually are sufficient is right.
Question 2:
For how many integer values of x does the following inequality hold true?
(x-2)(x-4)(x-6)(x-8) < 0
Approach:
In these questions, we take the boundary points. In this case, they are
2, 4, 6, 8
Now we start with one region.
Let’s say the region where x > 8, the expression is positive.
Now, we can change signs at boundaries if the power of the term (x – a) where a is the point of the boundary is odd, else we retain the sign.
Hence, from 6 to 8, it is negative.
Again from 4 to 6, it is positive.
From 2 to 4, it is negative.
For x < 2, it is positive.
Hence, for a total of 2 values – 3 and 7 – the inequality holds true.
Question 3:
A function f(x) is defined for all natural numbers such that
f(x) = x + 1 [x is even]
f(x) = x – 1 [x is odd]
The range of values of f(x) does not include how many natural numbers?
Approach:
f(1) = 0
f(2) = 3
f(3) = 2
f(4) = 5
f(5) = 4
…..
…..
This way, all the natural numbers are covered except for 1.
Hence, only 1 is not present in the range of values that represent the range of f(x).
Note:
Though these examples provide a good sense of what type of GMAT Algebra questions you can expect, in no way do they represent the exhaustive list of concepts required for the Quantitative section of GMAT.
Tips to keep in mind:
- Try to take some time out from the Problem-Solving Algebra questions so that you can use that time to solve the tricky Data Sufficiency Algebra questions.
- Do not get stuck in a question for long. If you find yourself trapped in a question for long, take a guess and move on.
- Read the signs carefully.
- Look out for negation words. For example: Which of the following are NOT possible values of x?
- Some questions can be solved faster by the use of options. Make sure you don’t solve these questions in a conventional way.
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Hope this article was helpful. Wish you all the best for the GMAT.
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