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Is mn<10?

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Is mn<10?  [#permalink]

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New post 11 Oct 2015, 00:23
1
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Difficulty:

  75% (hard)

Question Stats:

48% (01:03) correct 52% (00:36) wrong based on 341 sessions

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Is mn < 10?

(1) m < 5 and n < 2
(2) 1 < m < 3 and n^2<25
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Director
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Re: Is mn<10?  [#permalink]

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New post 27 Jan 2017, 05:43
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Top Contributor
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Hi Srav,

The best thing to do while solving questions of this type is to make use of the Max/Min Concept of Inequalities.

If we are given two ranges say -11 < x < 9 and -9 < y < 2 and the question asks us to find the max and min values of x * y then we can place the ranges one below the other and find the values for x * y for the 4 extreme values i.e. -11, 9, -9 and 2.

The four extreme values of x * y are 99, 18, -22 and -81. So -81 < xy < 99.

To apply the max min concept we need to keep in mind that the inequalities of the two ranges are the same. If they are not then we manipulate the numbers or use the properties of inequalities to make them the same. This same procedure can also be used to find the extreme values of x + y and x - y.

So where do we use the max min concept?

Whenever we have been given two ranges, one for x and the other for y (with the same inequality sign) and the question asks us to find the value of x + y, x - y and x * y.


Now coming to the question given

Is mn < 10?

(1) m < 5 and n < 2
(2) 1 < m < 3 and n^2 < 25


Statement 1 : Clearly insufficient as m can be 4 and n can be 1, which gives us a YES for mn < 10 or m can be -5 and n can be -2 which gives us a NO for mn < 10.

Statement 2 : 1 < m < 3 and n^2 < 25

Now here we can apply the max min concept, since 1 < m < 3 and -5 < n < 5. Multiplying the extreme values we get -5, 5, 15 and -15. So the range here is -15 < mn < 15. Insufficient.

Combining statements 1 and 2 : The range for m is 1 < m < 3 and the range for n is -5 < n < 2.

Again applying the max min concept we get -15 < mn < 6. Since mn here will always be less than 10. Sufficient.

Hope this helps!

For some more strategies on Inequalities, you can download a free Inequality eBook from the link given below

http://gmat.crackverbal.com/free-resources/ebook-library/

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Re: Is mn<10?  [#permalink]

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New post 11 Oct 2015, 04:21
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Srav wrote:
Q. Is mn < 10?

(1) m < 5 and n < 2
(2) 1 < m < 3 and n^2<25


The question asks mn<10 ?

Per statement 1, m<5 and n<2 ---> no if m=-10, n = -5 but yes if m=1 and n =1 . Not sufficient

Per statement 2, 1<m<3 and \(n^2<25\) ----> 1<m<3 and -5<n<5. Again you get 2 different answers for (m,n)=(2.9,4) or (1.5,-1). Thus not sufficient.

Combining the 2 statements you get, 1<m<3 and -5<n<2, giving you -15<mn<6 and thus you get an unambiguous "no" and hence C is the correct answer.
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Re: Is mn<10?  [#permalink]

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New post 25 Jan 2017, 01:09
unless it is stated that m, n are integers shouldnt the answer be E?

m=2.99 n=4 mn> 10,
so shouldnt the answer be E?
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Re: Is mn<10?  [#permalink]

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New post 25 Jan 2017, 04:02
krisnaren2010 wrote:
unless it is stated that m, n are integers shouldnt the answer be E?

m=2.99 n=4 mn> 10,
so shouldnt the answer be E?


Hi krisnaren2010,

By combining statement 1 and 2 we have following:

1<m<3 and -5<n<2 .

So, you can't take n = 4.

Hope it helps.
Thanks.
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Is mn<10?  [#permalink]

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New post 15 Apr 2017, 18:24
Srav wrote:
Is mn < 10?

(1) m < 5 and n < 2
(2) 1 < m < 3 and n^2<25


Statement 1
m < 5 and n < 2

m could be (-7) and n could be (-6) which would result in a number greater than ten; however,
m could be (-7) and n could be (1) which would result in a number less than ten.

Insufficient.

Statement 2

1<2.7<3 and (4)^2 equals a number greater than ten

1<2<3 and (4)^2 equals a number less than ten

Statement 1 and Statement 2


1<m<4 subsumes a value less than five

(-4)<n<2 contains a number that when squared is less than 25 and less than 2

The product of each and every combination that can be formed from both sets is less than ten (e.g the product of 2.7 and 1 is less than 10)

Sufficient.
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Re: Is mn<10?  [#permalink]

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New post 22 Apr 2017, 08:12
Srav wrote:
Is mn < 10?

(1) m < 5 and n < 2
(2) 1 < m < 3 and n^2<25



What is the source? Good question.
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Re: Is mn<10?  [#permalink]

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New post 22 Apr 2017, 09:03
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Re: Is mn<10?  [#permalink]

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New post 19 Jul 2017, 08:21
Srav wrote:
Is mn < 10?

(1) m < 5 and n < 2
(2) 1 < m < 3 and n^2<25


(1) \(m < 5\) and \(n < 2\)

Lets try some numbers.

\(m = 4; n = 1\)
\(mn = (4*1) = 4 < 10\)

\(m = -6; n = -2\)
\(mn = (-6*-2) = 12 > 10\)

Hence I is Not Sufficient.

(2) \(1 < m < 3\) and \(n^2<25\)

\(m = 2; n = 4\)
\(mn = (2*4) = 8 < 10\)

\(m = 2.9; n = 4\)
\(mn = (2.9*4) = 11.6 > 10\)

Hence II is Not Sufficient.

Combining I and II

Value of \(m\) is between \(=> 1 < m < 3\)

\(n^2 < 25\)
\(-5 < n < +5\)
From (1) \(n < 2\)
Therefore; Value of \(n\) is between \(=> -5 < n < 2\)

Checking minimum and maximum value of \(mn\);

Minimum value of \(mn > (3*-5) = -15\)
Maximum value of \(mn < (3*2) = 6\)
\(-15<mn<6\)

Therefore \(mn<10\)

Answer (C)...
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Re: Is mn<10?  [#permalink]

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New post 10 Dec 2017, 14:38
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Hi All,

We're asked if (M)(N) is less than 10. This is a YES/NO question. We can solve it by TESTing VALUES.

1) M < 5 and N < 2

IF.....
M=4 and N=1 then the product is 4 and the answer to the question is YES.
M= -6 and N= -2 then the product is 12 and the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) 1 < M < 3 and N^2 <25

IF.....
M=2 and N=1 then the product is 2 and the answer to the question is YES.
M= 2.9999 and N=4.9999 then the product is really close to 15 and the answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, the various inequalities 'limit' us down to:
1 < M < 3
-5 < N < 2
At MOST, the product (M)(N) would get really close to 6 - but no higher. Thus, the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

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Re: Is mn<10? &nbs [#permalink] 10 Dec 2017, 14:38
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