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# Is n > m ? (1) 7n > 9m (2) |n/m| > 1

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Re: Is n > m ? (1) 7n > 9m (2) |n/m| > 1 [#permalink]
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mikemcgarry wrote:
PrepTap wrote:
Is n > m, where n and m are real numbers?

1. 7n > 9m
2. mod (n/m) > 1

Dear PrepTap,

My friends, if I may offer some constructive feedback, I don't believe "mod" as you are using it is well-defined in most mathematical literature concerning the GMAT, including, for example, the Math Review in the OG. In general, students are not expected to know symbols and functions that are not discussed in the OG Math Review.

Do you mean the function that Americans call the absolute value? If so, you probably should use the notation for that, as the "mod" notation is ambiguous.
(2) |m/n| > 1

Best of luck,
Mike

I'd also add that no official source uses the term "natural number". You should change it to integer or non-negative integer.
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Re: Is n > m ? (1) 7n > 9m (2) |n/m| > 1 [#permalink]
Bunuel wrote:
mikemcgarry wrote:
PrepTap wrote:
Is n > m, where n and m are real numbers?

1. 7n > 9m
2. mod (n/m) > 1

Dear PrepTap,

My friends, if I may offer some constructive feedback, I don't believe "mod" as you are using it is well-defined in most mathematical literature concerning the GMAT, including, for example, the Math Review in the OG. In general, students are not expected to know symbols and functions that are not discussed in the OG Math Review.

Do you mean the function that Americans call the absolute value? If so, you probably should use the notation for that, as the "mod" notation is ambiguous.
(2) |m/n| > 1

Best of luck,
Mike

I'd also add that no official source uses the term "natural number". You should change it to integer or non-negative integer.

Thanks but we are only saying "real numbers" not "natural numbers".
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Re: Is n > m ? (1) 7n > 9m (2) |n/m| > 1 [#permalink]
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PrepTap wrote:
Thanks but we are only saying "real numbers" not "natural numbers".

Yes, sorry.

But the same applies to "real numbers": numbers on the GMAT are restricted to real numbers by default, so no official question uses the term "real number" in them.
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Re: Is n > m ? (1) 7n > 9m (2) |n/m| > 1 [#permalink]
Bunuel wrote:
But the same applies to "real numbers": numbers on the GMAT are restricted to real numbers by default, so no official question uses the term "real number" in them.

Yes, you are right. Using the term 'real numbers' isn't adding anything to the question. Have removed it now.
Thanks for pointing it out.

Originally posted by PrepTap on 29 Apr 2015, 04:28.
Last edited by PrepTap on 07 May 2015, 00:03, edited 1 time in total.
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Re: Is n > m ? (1) 7n > 9m (2) |n/m| > 1 [#permalink]
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Hi, I am getting the answer to be A.
My solution:
1) 7n>9m
Using Negative values
using n=-1 and m=-2
-7>-18
n>m-True
using decimals, for the above to be true, let n=0.3 m=0.2
7n=2.1 9m=1.8
n>m-true
using positive integers 7n>9m if n>m So A is sufficient
2) |n/m|>1
considering the above values, it holds true for decimals but not for negative values
so B is insufficient.

Correct me if I am wrong.
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Re: Is n > m ? (1) 7n > 9m (2) |n/m| > 1 [#permalink]
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You should consider another scenario – if n = 3 and m = 10 ---- is 7n>9m?

21 > 90 – FALSE

So with Statement A we cannot be sure. Hence insufficient

Similarly – for Statement B –

|n/m|>1

As we don’t know if n and m are positive or negative – we cannot be sure of statement B too.

Example: n = -10 m= -2 |10/2| = 5 which satisfies the statement and we can discern that n is not greater than m

Lets take another set of numbers : n = 10 m = 5 --> n is greater than m

As no definitive answer can be found – B is insufficient too

E is the correct option.

aks456 wrote:
Hi, I am getting the answer to be A.
My solution:
1) 7n>9m
Using Negative values
using n=-1 and m=-2
-7>-18
n>m-True
using decimals, for the above to be true, let n=0.3 m=0.2
7n=2.1 9m=1.8
n>m-true
using positive integers 7n>9m if n>m So A is sufficient
2) |n/m|>1
considering the above values, it holds true for decimals but not for negative values
so B is insufficient.

Correct me if I am wrong.
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Re: Is n > m ? (1) 7n > 9m (2) |n/m| > 1 [#permalink]
aks456 wrote:
Hi, I am getting the answer to be A.
My solution:
1) 7n>9m
Using Negative values
using n=-1 and m=-2
-7>-18
n>m-True
using decimals, for the above to be true, let n=0.3 m=0.2
7n=2.1 9m=1.8
n>m-true
using positive integers 7n>9m if n>m So A is sufficient
2) |n/m|>1
considering the above values, it holds true for decimals but not for negative values
so B is insufficient.

Correct me if I am wrong.

A is not sufficient.
For explanation look at this post:
solving-complex-problems-using-number-line-197045.html#p1521230

Originally posted by PrepTap on 30 Apr 2015, 05:20.
Last edited by PrepTap on 07 May 2015, 00:13, edited 1 time in total.
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Re: Is n > m ? (1) 7n > 9m (2) |n/m| > 1 [#permalink]
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aks456 wrote:
Hi, I am getting the answer to be A.
My solution:
1) 7n>9m
Using Negative values
using n=-1 and m=-2
-7>-18
n>m-True

Consider even smaller numbers in negatives

Statement (1)
7n>9m

n= -5 and m = -4
7n>9m
-35 > -36
n < m

n = 5 and m = -4
7n>9m
35 > -36
n > m
Not Sufficient

Statement (2)
$$|\frac{n}{m}|$$ >1
n=-5 and m = -4
$$|\frac{-5}{-4}|$$ >1
n < m

n= 5 and m = -4
$$|\frac{5}{-4}|$$ >1
n > m

Not Sufficient

from (1) and (2)
both the cases are same for both statements

Answer E
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Re: Is n > m ? (1) 7n > 9m (2) |n/m| > 1 [#permalink]
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Why E? Why not C? With both statements, can't we answer?
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dina98 wrote:
Why E? Why not C? With both statements, can't we answer?

Dear dina98,

I'm happy to respond. I don't know whether you read the other posts in this thread: it may be that somewhere else on this page is already the answer to your question. In the future, I would recommend this blog article:
https://magoosh.com/gmat/2014/asking-exc ... questions/

I don't know whether, in thinking about possible numbers, whether you considered all categories of numbers --- positive & negative, integers & fractions.

It's clear that, if n is considerably bigger than m, that both statements would be true. Thus, it would be easy to pick example numbers, such as n = 100 and m = 3, that satisfy each statement and give a "yes" answer to the prompt.

The question, then, is whether it is possible to pick two values that are totally consistent with both statement but which would give a "no" answer to the prompt --- in other words, two numbers such that n < m.

The second statement guarantees that n has a larger absolute value, so if both values are positive, then n > m. What if both are negative.

If m = -1 and n = -2, then $$|\frac{n}{m}|$$>1, but m > n ---- because a less negative number to the right, on the number line, of a more negative number. Another way to say it: if I have $200 in my bank account, I am richer than if I have$100, but if I have no balance and a credit card debt, then if I have a debt of $100 I am richer than if I have a debt of$200.

Now, 7m = -7, and 9n = -18, and once again, -7 > -18, so 7m > 9n.

The pair (m = -1, n = -2) is a set that is consistent with both statements but produces a "no" response to the prompt question.

Thus, even if both statements are true, we can pick numbers that give either a "yes" or "no" answer to the prompt question. Even with both statements, we do not have sufficient information to give a single definitive answer to the prompt. Together, both statements are insufficient. OA = (E)

You may also find this blog article helpful:
https://magoosh.com/gmat/2013/gmat-data- ... ency-tips/

Does all this make sense?
Mike
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Re: Is n > m ? (1) 7n > 9m (2) |n/m| > 1 [#permalink]
mikemcgarry wrote:

If m = -1 and n = -2, then $$|\frac{n}{m}|$$>1, but m > n ---- because a less negative number to the right, on the number line, of a more negative number. Another way to say it: if I have $200 in my bank account, I am richer than if I have$100, but if I have no balance and a credit card debt, then if I have a debt of $100 I am richer than if I have a debt of$200.

Now, 7m = -7, and 9n = -18, and once again, -7 > -18, so 7m > 9n.

The pair (m = -1, n = -2) is a set that is consistent with both statements but produces a "no" response to the prompt question.

Thus, even if both statements are true, we can pick numbers that give either a "yes" or "no" answer to the prompt question. Even with both statements, we do not have sufficient information to give a single definitive answer to the prompt. Together, both statements are insufficient. OA = (E)

You may also find this blog article helpful:
https://magoosh.com/gmat/2013/gmat-data- ... ency-tips/

Does all this make sense?
Mike

THanks, yes missed out in this particular scenario. Kept thinking both statements satisfy.
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Re: Is n > m ? (1) 7n > 9m (2) |n/m| > 1 [#permalink]
Expert Reply
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is n > m ?

(1) 7n>9m
(2) |nm |>1

There are 2 variables (m,n) and 2 equations are given from the 2 conditions, so there is high chance (C) will be our answer.
Looking at the conditions together, the answer is 'yes' for n=2, m=1, but 'no' for n=-5, m=-4, so the answer becomes (E).

For cases where we need 2 more equation, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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