If Jack’s and Kate’s annual salaries in 1985 were each 10 percent high

Question

If Jack’s and Kate’s annual salaries in 1985 were each 10 percent higher than their respective annual salaries in 1984, what was Jack’s annual salary in 1984 ?

(1) The sum of Jack’s and Kate’s annual salaries in 1984 was $50,000.

(2) The sum of Jack’s and Kate’s annual salaries in 1985 was $55,000.

EMPOWERgmatRichC · Accepted Answer

Hi alisbadr,

The rule that you're referring to applies to 'systems' of equations. For example, if you have 2 variables and 2 UNIQUE equations (with nothing complex such as exponents or absolute values), then you can solve for each of the variables. The key word there is "unique" though - the equations must be DIFFERENT from one another.

With the equations J + K = 50,000 and 1.1J + 1.1K = 55,000, you do NOT have 2 unique equations (the 2nd equation is just the first equation multiplied by 1.1).

J + K = 50,000
1.1J + 1.1K = 1.1(50,000)

Thus, you do not have a system here and there's no way to solve for the values of J and K (if you try to, then you will probably end up with a solution that shows 0 = 0).
 
GMAT assassins aren't born, they're made,
Rich

RSOHAL · Answer

Given:
Person/Year 1984 1985
Jack's Sj 1.10Sj
Kate,s Sk 1.10Sk

Statement I:
Sj + Sk = $50,000, Non sufficient

Statement II:

1.10Sj + 1.10Sk = $55,000 Non sufficient

Both Statements I and II:

SI and SII are same. If you multiply SI with 1.10, you will get SII.
Hence both statements together are also not sufficient.

E is Correct answer.

Nadiuska · Answer

Can someone else solve this using any other approach.
I came down to C, without going into any further calculations. I thought that from statement one we have one equation and from the second statement we have another, combining both should give us the salary of the variables. But then when I performed the calculations, after seeing answer is E, a variable cancels out and we are left with nothing. But I don't know, logically speaking, shouldn't the 2 statments suffice?

Here is what I did:
55= J+K
50= 0.9J+0.9K

50= 0.9(55-K)+0.9K; 50=-0.9K+49.5+0.9K

EMPOWERgmatRichC · Answer

Hi Nadiuska,

On DS questions, it's really important that you make sure you're answering the question that is ASKED. This prompt asks us for Jack's salary in 1984, but we're never given enough information to differentiate Jack's salary from Kate's salary.

Here are two quick examples to work through:

1) What if Jack and Kate BOTH had a salary of $25,000?
2) Now, what if Jack had a salary of $30,000 and Kate had a salary of $20,000?

You should see (either with a little bit of 'math work' or 'conceptually') that the correct answer is E.

GMAT assassins aren't born, they're made,
Rich

SidJainGMAT · Answer

Both statements give you the same equation (individually and together), which is in 2 variables. Hence its not sufficient.

Hence its straightforward E.

Salsanousi · Answer

Basically we are given that Jack’s and Kate’s salaries are each 10% more than the year before

Statement 1) J + K = 50,000 in 1984

No information on Jack’s salary per se.

Insufficient

Statement 2) J + K = 55,000 in 1985

No information on how we have this 55,000 could be 20,35 could be 25,30 etc..

Now combine 1 and 2

We have 10% increase in 1985 yet we cannot say if Jack’s salary in 1984 is 20,25,30 or any other number.

C is insufficient.

Answer choice E

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CEdward · Answer

If Jack’s and Kate’s annual salaries in 1985 were each 10 percent higher than their respective annual salaries in 1984, what was Jack’s annual salary in 1984 ?

(1) The sum of Jack’s and Kate’s annual salaries in 1984 was $50,000. Clearly insufficient.

J + K = 50000

J can be anything.

(2) The sum of Jack’s and Kate’s annual salaries in 1985 was $55,000. Clearly insufficient. This is talking about 1985.

C: The only new thing we can deduce is 5000 = 0.10J + 0.10K

1 equation, 2 unknowns.

Insufficient.

E.

alisbadr · Answer

RSOHAL  &  EMPOWERgmatRichC  something is missing for me.

Since each of their salaries was 10% higher in 1985, shouldn't "EACH" mean that

1.1J + 1.1K = 55,000 in 1985
J + K = 50,000 in 1984

In this case, we have two unknowns and two equations so we can get the answer.

alisbadr · Answer

Ok it is clear now, thank you.

MasteringGMAT · Answer

Let Jack's annual salary in 1984 be J and Kate's annual salary in 1984 be K.

From the problem statement, we know that:

Jack's annual salary in 1985 was 1.1J (10% higher than J).
Kate's annual salary in 1985 was 1.1K (10% higher than K).
We are asked to find J, Jack's annual salary in 1984.

Statement 1 tells us that J + K = $50,000, but it doesn't give us any information about J or K individually. So, we cannot determine Jack's annual salary in 1984 from statement 1 alone.

Statement 2 tells us that J + K = $55,000 in 1985, but we still cannot determine J or K individually. This statement doesn't provide any direct information about Jack's salary in 1984, so we cannot determine Jack's annual salary in 1984 from statement 2 alone either.

Using both statements together, we know that:

J + K = $50,000 (from statement 1)
J × 1.1 + K × 1.1 = $55,000 (from statement 2)

Simplifying the second equation, we get:

1.1J + 1.1K = $55,000
J + K = $50,000 (which we know from statement 1)

Subtracting the second equation from the first, we get:

0.1J + 0.1K = $5,000

Substituting J + K = $50,000, we get:

0.1J + 0.1($50,000 - J) = $5,000

Simplifying this equation, we get:

0.2J = $10,000

J = $50,000/2 = $25,000

Therefore, Jack's annual salary in 1984 was $25,000. The answer is (C), using both statements together we could solve for J.

I am not sure why option (C) is wrong

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If Jack’s and Kate’s annual salaries in 1985 were each 10 percent high

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