by bashob September 3, 2016
There are 8 question is this test. Ideally, this test should get completed in 12-15 minutes. Time yourself and find out how well prepared are you in “Number Properties”
GMAT Quant - Set 1
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If the quotient a/b is less than zero, which of the following CANNOT be true?
a > 0
b > 0
ab > 0
a – b > 0
a + b > 0
Question 1 Explanation:
The question indirectly says that a/b is negative. In such a case, either a or b can be negative. In case of ab, it can only be positive if both a and b are negative or both of them are positive.
If a = -0.5, then each of the following must be true EXCEPT.
a < (a^2)
a^3 < a^2
a < a^3
a^2 < a^4
a^3 < a^5
Question 2 Explanation:
Quickly, check the inequalities by substituting the values of a -1/2 < 1/4 (Correct) -1/8 < 1/4 (Correct) -1/2 < -1/8 (Correct) 1/4 < 1/16 (Incorrect) -1/8 < -1/32 (Correct)
In |x – 3/4 | < 9/4, which of the following could be a value of x?
Question 3 Explanation:
Solve the equation. -9/4 < x – 3/4 < 9/4 -6/2 < x < 12/4 or “x” should lie between -1.5 and 3. Only “2” is in this range and hence it is the answer.
If a and b are positive integers and if 1/a + 1/b < 2, which of the following must be true?
a + b > 4
ab > 1
(a/b) + (b/a) < 1
(a – b)^2 > 0
(a + b)^2 < 0
Question 4 Explanation:
Must be true, in general, indicates to an option which must always be true. The given equation can also be written as a + b < 2ab . Now, if you substitute values in the equation you would find that the equation is true only if ab > 1.
If the product of integer m and integer n is odd, then which of the following must be even?
m – n
m + 2n
(m/n) – 1
Question 5 Explanation:
Since, it is given that the product of the two integers is odd, it implies that both m and n are odd. An odd number minus and odd number must be even. You can also substitute arbitrary numbers to find the correct answer.
Sequence S is composed of n integers, where n > 1, whose arithmetic mean is x. If each element of S is multiplied by 3, the arithmetic mean of the resulting integers remains x. Which statement(s) below must be true? I. x = 0 II. The largest and smallest members of S have the same absolute value. III. S contains both positive and negative numbers
I and II only
I, II and III
Question 6 Explanation:
When all the numbers of a set are multiplied by a number, then the mean also gets multiplied by the same number. If the mean remains same, then that implies that mean is equal to 0. Hence, statement I is true. Statement 2 is not necessarily true. For example, an example set can be -3, -2 and 5. The mean of this set is zero, but the absolute values of the largest and smallest number is not the same. Statement 3 is also not true, because it may be possible that the set may contain all zeroes. Hence the correct answer choice is I only.
If r, s and t are consecutive even integers and r < s < t, which of the following must be true? I. t – r = 4 II. (s – r)t is an even integer III. (r + s + t)/3 is an even integer
I and II only
II and III only
I, II and III
Question 7 Explanation:
Substitute any 3 consecutive numbers in this question and solve for the conditions. For example, if our consecutive 3 even numbers are 4, 6, and 8 then condition all three cases are correct. Check for any other three random consecutive even numbers, again all conditions will be satisfied. Hence, answer is all three are correct.
If n is an integer, which of the following cannot be odd?
n + 2
n + 3
Question 8 Explanation:
The mathematical definition of even and odd is that even numbers are divisible by 2, while odd numbers are not divisible by 2. There, we can see that answer choice, 2n cannot be odd. Dividing 2n by 2 will yield n, and we know n is an integer. Therefore, 2n cannot be odd.
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