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# If a and b are positive, what is the value of a+b

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VP
Joined: 09 Mar 2018
Posts: 1007
Location: India
If a and b are positive, what is the value of a+b  [#permalink]

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01 Jan 2019, 20:38
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75% (hard)

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24% (00:59) correct 76% (01:12) wrong based on 35 sessions

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If a and b, are positive, what is the value of a+b ?

(1) $$(3^a) (3^b)$$=81
(2) $$(3^a) (5^b)$$=225

_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

RC Moderator
Joined: 24 Aug 2016
Posts: 743
Concentration: Entrepreneurship, Operations
GMAT 1: 630 Q48 V28
GMAT 2: 540 Q49 V16
If a and b are positive, what is the value of a+b  [#permalink]

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01 Jan 2019, 21:01
1
(1) $$(3^a) (3^b)$$=81 - Sufficient- as $$(3^a) (3^b)$$=$$3^{a+b}$$=$$3^4$$ ==>a+b=4
(2) $$(3^a) (5^b)$$=225 - Not Sufficient - remember the cond is only positive not positive integer.
One way to think of the proof is :
225= 3.3.5.5 = 5.45
Case 1: $$3^2$$ * $$5^2$$ ==>a=2 & b=2.Hence a+b=4
Case 2:one component is 5 so b=1
Now 45 could be $$3^a$$ ==>a=log45/log3 = 3.465 ( $$3^{3.465}$$ almost=45). Hence a+b=4.465

Hence Ans is A.
_________________

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Intern
Joined: 08 Sep 2018
Posts: 20
Location: United States
GMAT 1: 640 Q44 V33
If a and b are positive, what is the value of a+b  [#permalink]

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01 Jan 2019, 22:24
u1983 wrote:
(1) $$(3^a) (3^b)$$=81 - Sufficient- as $$(3^a) (3^b)$$=$$3^{a+b}$$=$$3^4$$ ==>a+b=4
(2) $$(3^a) (5^b)$$=225 - Not Sufficient - remember the cond is only positive not positive integer.
One way to think of the proof is :
225= 3.3.5.5 = 5.45
Case 1: $$3^2$$ * $$5^2$$ ==>a=2 & b=2.Hence a+b=4
Case 2:one component is 5 so b=1
Now 45 could be $$3^a$$ ==>a=log45/log3 = 3.465 ( $$3^{3.465}$$ almost=45). Hence a+b=4.465

Hence Ans is A.

GMAT will not give false information between the two facts so if

1.) A+B = 4, then

2.) A+B = 4 as well. and in your explanation A+B = 4.465.

Wouldn't the correct solution be D?

2.) A = 2, B = 2?
RC Moderator
Joined: 24 Aug 2016
Posts: 743
Concentration: Entrepreneurship, Operations
GMAT 1: 630 Q48 V28
GMAT 2: 540 Q49 V16
Re: If a and b are positive, what is the value of a+b  [#permalink]

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02 Jan 2019, 01:07
soloyolodolo wrote:
u1983 wrote:
(1) $$(3^a) (3^b)$$=81 - Sufficient- as $$(3^a) (3^b)$$=$$3^{a+b}$$=$$3^4$$ ==>a+b=4
(2) $$(3^a) (5^b)$$=225 - Not Sufficient - remember the cond is only positive not positive integer.
One way to think of the proof is :
225= 3.3.5.5 = 5.45
Case 1: $$3^2$$ * $$5^2$$ ==>a=2 & b=2.Hence a+b=4
Case 2:one component is 5 so b=1
Now 45 could be $$3^a$$ ==>a=log45/log3 = 3.465 ( $$3^{3.465}$$ almost=45). Hence a+b=4.465

Hence Ans is A.

GMAT will not give false information between the two facts so if

1.) A+B = 4, then

2.) A+B = 4 as well. and in your explanation A+B = 4.465.

Wouldn't the correct solution be D?

2.) A = 2, B = 2?

Hello soloyolodolo .... my sincere apologies. I really could not follow your point. It would be great if you can elaborate a little more.
_________________

Please let me know if I am going in wrong direction.
Thanks in appreciation.

Intern
Joined: 08 Sep 2018
Posts: 20
Location: United States
GMAT 1: 640 Q44 V33
Re: If a and b are positive, what is the value of a+b  [#permalink]

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02 Jan 2019, 01:23
u1983 wrote:
soloyolodolo wrote:
u1983 wrote:
(1) $$(3^a) (3^b)$$=81 - Sufficient- as $$(3^a) (3^b)$$=$$3^{a+b}$$=$$3^4$$ ==>a+b=4
(2) $$(3^a) (5^b)$$=225 - Not Sufficient - remember the cond is only positive not positive integer.
One way to think of the proof is :
225= 3.3.5.5 = 5.45
Case 1: $$3^2$$ * $$5^2$$ ==>a=2 & b=2.Hence a+b=4
Case 2:one component is 5 so b=1
Now 45 could be $$3^a$$ ==>a=log45/log3 = 3.465 ( $$3^{3.465}$$ almost=45). Hence a+b=4.465

Hence Ans is A.

GMAT will not give false information between the two facts so if

1.) A+B = 4, then

2.) A+B = 4 as well. and in your explanation A+B = 4.465.

Wouldn't the correct solution be D?

2.) A = 2, B = 2?

Hello soloyolodolo .... my sincere apologies. I really could not follow your point. It would be great if you can elaborate a little more.

1.) A+B = 4

2.) A+B = 4.465

Does that make sense?

I agree with your explanation of the answer, however based on GMAT rules. I think answer would be D?

Maybe someone else can help. I know there are numerous people in the forums who are much more intelligent and math wizards.

Posted from my mobile device
VP
Joined: 09 Mar 2018
Posts: 1007
Location: India
Re: If a and b are positive, what is the value of a+b  [#permalink]

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02 Jan 2019, 06:53
soloyolodolo wrote:

I agree with your explanation of the answer, however based on GMAT rules. I think answer would be D?

Maybe someone else can help. I know there are numerous people in the forums who are much more intelligent and math wizards.

Till the time someone else pitches in, inline is the Official Explanation

Statement (1) gives you that $$(3^a)(3^b)=81$$
Remember that to find the product of two exponential expressions with a common base, you simply add their exponents.
That means that $$(3^a)(3^b)=81$$ becomes 3^(a+b)=81

The right side of the equation can then be rewritten as $$3^4$$ giving you the equation 3^(a+b) = $$3^4$$
so a+b=4

You can therefore conclude that statement (1) is sufficient when taken on its own.

Statement (2) gives that $$(3^a)(5^b)=225$$
If you factor 225, it becomes $$(3^2)(5^2)=(3^a)(5^b)$$, At this point, it is tempting to say that a+b=4
But remember -- you haven’t been told even whether a and b are integers.
It is possible to say that a=4 and that b is equal to an irrational number (log5 $$\frac{225}{81}$$, if you do the math).

Because the equation could yield multiple values of a and b

You must conclude that statement (2) is insufficient and choose answer choice (A).
_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Re: If a and b are positive, what is the value of a+b   [#permalink] 02 Jan 2019, 06:53
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