Doubt: MGMAT Algebra Guide (Inequalities Problem Set)

[NabanitaG536]

Hello Experts,
I have doubts in 2 questions from the MGMAT Algebra Guide.

Q7. If d> a and L<a, which of the following cannot be true?
(A) d + L = 14 (B) d-L = 7 (C) d-L = 1 (D )a -d = 9 (E)a + d = 9

The Solution says:
7. (D): Simplify the inequalities, so that all the inequality symbols point in the same direction. Then, line up the inequalities as shown. Finally, combine the inequalities.
L<a , a<d -----► L<a<d
Since d is a larger number than a> a — d cannot be positive. Therefore, (D) cannot be true

My Question : Shouldn't (C) be considered too? If we assume L, a & d to be consecutive integers, d-L=1 cannot be true. Am I mistaken here?


Q9. If 4x - 12 >= x + 9, which of the following must be true?
(A) x > 6 (B) x < 7 (C) x > 7 (D)x> 8 (E) x<8

The Solution says : (A)
4x - 12 >= x + 9
3x >=21
x >=7

You were asked to pick the answer that must be true. If x is greater than or equal to 7, then x could be 7, 7.3, 8, 9.2, and so on. Which of the five answers contains an expression that covers all possible values of x? Most people will immediately look at answer (C) x > 7, but be careful! Does x have to be greater than 7? No; x could be 7 itself, in which case answer (C) is inaccurate. Similarly, answers (D) and (E) cover some of the possible values for x, but not all of them. Answer (B) doesn’t share anything in common with x > 7, so it’s wrong. You’re left with answer (A). Why must it be true that x is greater than 6? Because x could be 7, 7.3, 8, 9.2 and so on. All of those possible values for x are greater than 6.

My Question : What about values such as 6.1,6.2 until 6.99, wont they also come in the cohort if we choose option A, and they are also not greater than 7. Then why is option A the answer?

Please let me know your thoughts and correct me if I have misunderstood anything in the answer explanations.

Thanks a tonne.

Regards,
Nab

[RonPurewal]

My Question : Shouldn't (C) be considered too? If we assume L, a & d to be consecutive integers, d-L=1 cannot be true. Am I mistaken here?

ok, but why would you ever assume that?
you can't just make up facts/restrictions at random!

[RonPurewal]

My Question : What about values such as 6.1,6.2 until 6.99, wont they also come in the cohort if we choose option A, and they are also not greater than 7. Then why is option A the answer?

if you have a bunch of people who are all over 40 years old, then it must be true that they're all over 30 years old.
same thing here.

the question just says 'which of these must be true?'
it does NOT say 'what is the exact range of possible answers?'


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to be honest, though, this isn't something you'll have to worry about on test day. this question is 'tricky', and the gmat DOES NOT contain 'trick' questions.
in fact, for that reason i'll recommend that the problem be removed from future editions of the book.

[NabanitaG536]

ok, but why would you ever assume that?
you can't just make up facts/restrictions at random!

Thanks Ron for the reply. Yes I realize I shouldn't make assumptions.
I missed considering non-integer values that satisfy the equation L<a<d , if L=-1, a=-0.5 and d=0, then (d-L)=1.
Will be careful from next time.

Thanks again

[NabanitaG536]

Thank you so much Ron for the clarification! Indeed the problem was a little confusing.

[tim]

Let us know if there are any further questions.

[RonPurewal]

Thank you so much Ron for the clarification! Indeed the problem was a little confusing.

you're welcome.