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19 Mar 2020, 22:24
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A number M is the product of seven negative numbers, and the number N is the product of six negative numbers and one positive number. Which of the following holds true for all possible values of M and N ?
I. M * N < 0
II. M - N < 0
III. N + M < 0
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III
I. M * N < 0
II. M - N < 0
III. N + M < 0
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III
20 Mar 2020, 00:17
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SajjadAhmad
A number M is the product of seven negative numbers, and the number N is the product of six negative numbers and one positive number. Which of the following holds true for all possible values of M and N ?
I. M * N < 0
II. M - N < 0
III. N + M < 0
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III
I. M * N < 0
II. M - N < 0
III. N + M < 0
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III
- • M is a product of 7 negative numbers.
- o That means M is a negative number.
- o That means N is a positive number.
Thus,
- • M * N = negative * positive = negative.
- o Thus M * N < 0
- o For example, M = -3 and N = 2, then M – N = -3 – 2 = -5
- Thus, M – N < 0
- o For example, M = -3 and N = 2, then N + M = -1 OR
o M = -2 and N = 3, them N + M = 1
- Thus, we cannot be sure if N + M < 0 or > 0
Hence, only statement I and II are true and the correct answer is Option C
27 Mar 2020, 05:09
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This is a must be true question. Based on the conditions given, we are to evaluate which statements are always true/definitely true. Typically, the best way to solve these questions is to use simple cases to prove the statements false once and then whatever is left HAS to be the correct answer. However, in this question, analyzing the question stem seems like a better approach.
If M is the product of seven negative integers, M HAS to be negative since we have odd number of negative values.
Note that the product of odd number of negative values will be negative, whereas the product of even number of negative values will be positive. For example, if we multiply 3 negative numbers with each other, the product will be negative, whereas the product of 2 negative numbers is positive.
From the above discussion, we know that M IS negative.
N is the product of six negative integers and one positive integer. Based on the examples discussed above, we can infer that N IS positive.
Let us now look at the statements.
Statement I says M*N<0. This is always true since the product of one negative and one positive value is always negative. We don’t even have to worry about the actual values of M and N here. Statement I is definitely true. So, we can eliminate answer options B and D since they do not say that statement I is definitely true.
Statement II says, M-N<0. This means, M<N. This is also true since a negative value will always be smaller than a positive value. Statement II is definitely true. Answer option A can be eliminated since it doesn’t say that statement II is definitely true.
Statement III says N + M < 0 which means N < - M.
If M = \((-1)^7\), M = -1 and hence -M = 1.
If N = \((-2)^6\) * 1, N = 64.
Clearly N is not less than -M.
Statement III is not always true since we were able to prove it false by just taking a very simple case. Statement III is not definitely true.
Answer option E can now be eliminated. The correct answer option has to be C.
Hope that helps!
If M is the product of seven negative integers, M HAS to be negative since we have odd number of negative values.
Note that the product of odd number of negative values will be negative, whereas the product of even number of negative values will be positive. For example, if we multiply 3 negative numbers with each other, the product will be negative, whereas the product of 2 negative numbers is positive.
From the above discussion, we know that M IS negative.
N is the product of six negative integers and one positive integer. Based on the examples discussed above, we can infer that N IS positive.
Let us now look at the statements.
Statement I says M*N<0. This is always true since the product of one negative and one positive value is always negative. We don’t even have to worry about the actual values of M and N here. Statement I is definitely true. So, we can eliminate answer options B and D since they do not say that statement I is definitely true.
Statement II says, M-N<0. This means, M<N. This is also true since a negative value will always be smaller than a positive value. Statement II is definitely true. Answer option A can be eliminated since it doesn’t say that statement II is definitely true.
Statement III says N + M < 0 which means N < - M.
If M = \((-1)^7\), M = -1 and hence -M = 1.
If N = \((-2)^6\) * 1, N = 64.
Clearly N is not less than -M.
Statement III is not always true since we were able to prove it false by just taking a very simple case. Statement III is not definitely true.
Answer option E can now be eliminated. The correct answer option has to be C.
Hope that helps!
