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# Does the product jkmn equals 1?

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Does the product jkmn equals 1?  [#permalink]

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Updated on: 31 Mar 2014, 01:29
00:00

Difficulty:

45% (medium)

Question Stats:

63% (01:01) correct 37% (01:02) wrong based on 210 sessions

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Does the product jkmn equals 1?

(1) $$\frac{jk}{mn} = 1$$

(2) $$mn>7$$

Why statement 1 is not sufficient please? In any situation ( +ve on -ve) I think statement 1 is sufficient to answer the question but that's not the answer. Can someone please help?

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Originally posted by enigma123 on 30 Mar 2014, 15:44.
Last edited by Bunuel on 31 Mar 2014, 01:29, edited 1 time in total.
Edited the question.
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Re: Does the product jkmn equals 1  [#permalink]

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30 Mar 2014, 20:37
1
First statement suggests that jk=mn
but value of jk or mn is not known Not sufficient

second statement is mn>7 but value of jk is not known
if jk is 1/7.. jkmn will equal 1

together since jk = mn, so if mn=8 then jk=8
jkmn cannot be 1
so C
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Re: Does the product jkmn equals 1?  [#permalink]

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31 Mar 2014, 01:43
enigma123 wrote:
Does the product jkmn equals 1?

(1) $$\frac{jk}{mn} = 1$$

(2) $$mn>7$$

Why statement 1 is not sufficient please? In any situation ( +ve on -ve) I think statement 1 is sufficient to answer the question but that's not the answer. Can someone please help?

Does the product jkmn equals 1?

(1) $$\frac{jk}{mn} = 1$$ --> $$jk=mn$$. The question becomes: does $$(mn)^2=1$$. We don't know that. Not sufficient.

(2) $$mn>7$$. If $$mn=8$$ and $$jk=\frac{1}{8}$$, then $$jkmn=1$$ but if $$mn=8$$ and $$jk \neq{\frac{1}{8}}$$, then $$jkmn\neq{1}$$. Not sufficient.

(1)+(2) Since from (1) $$jk=mn$$ and from (2) $$mn>7$$, then $$jk>7$$ too. Now, the product of two multiples (jk and mn) each of which is greater than 7 cannot equal to 1. Sufficient.

Answer: C.

Similar question to practice: does-the-product-jkmn-24606.html

Hope it helps.
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Re: Does the product jkmn equals 1?  [#permalink]

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30 Sep 2018, 04:18
1- Jk=mn
which states that they both are equal. here comes two cases: 1st case- Both JK and mn = 1 then there multiplication will be 1 but if they are =2 then there multiplication will be 4. hence Not sufficient.

2- mn>7 not sufficient does not tells anything about J.k which can be 1/7 or an integer.

1+2- 2nd statement makes sure M.N is greater than 7 and 1st statement states that J.K is equal to M.N. so there multiplication cant be 1.

Please comment if I am wrong at something.
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Re: Does the product jkmn equals 1?  [#permalink]

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30 Sep 2018, 08:59
enigma123 wrote:
Does the product jkmn equals 1?

(1) $$\frac{jk}{mn} = 1$$

(2) $$mn>7$$

$$jkmn\,\,\mathop = \limits^? \,\,1$$

$$\left( 1 \right)\,\,\,{{jk} \over {mn}} = 1\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {j,k,m,n} \right) = \left( {1,1,1,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr \,{\rm{Take}}\,\,\left( {j,k,m,n} \right) = \left( {2,2,2,2} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr} \right.$$

$$\left( 2 \right)\,\,\,mn > 7\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {j,k,m,n} \right) = \left( {1,8,1,8} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr \,{\rm{Take}}\,\,\left( {j,k,m,n} \right) = \left( {{1 \over 8},1,1,8} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.$$

$$\left( {1 + 2} \right)\,\,\,\,\,?\,\,\,:\,\,\,jkmn\,\, = \,\,\left( {jk} \right)\left( {mn} \right)\,\,\,\mathop = \limits^{\left( 1 \right)} \,\,\,{\left( {mn} \right)^2}\,\,\,\mathop > \limits^{\left( 2 \right)} \,\,\,{7^{\,2}}\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Fabio Skilnik :: http://www.GMATH.net (Math for the GMAT)
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Re: Does the product jkmn equals 1? &nbs [#permalink] 30 Sep 2018, 08:59
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# Does the product jkmn equals 1?

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