Tami purchased several identically priced metal frames and several ide

Let's say:
# of Metal Frames = M
# of Wooden Frames = W
Price of Metal Frame = A
Price of Wooden Frame = B

When we set the equation up:
MA + WB = $144

What we are trying to solve for: The value of MA

1.) A = 1.6B Not sufficient
2.) W = 2M Not sufficent

1+2
Substitute MA for from statement 1 and 2. You should get this:
((W/2)*1.6B) + WB = 144
0.8WB + WB = 144
1.2WB = 144
WB = 144/1.2

We know the value of WB, we can plug in 144/4.2 into WB.
MA + (144/1.2) = 144

You can directly solve for MA, the answer is C

Given: Tami purchased several identically priced metal frames and several identically priced wooden frames for a total pretax price of $144.

Let W = the NUMBER of wooden frames purchased
Let w = the PRICE (in dollars) of ONE wooden frame
So, Ww = the COST of buying W wooden frames

Let M = the NUMBER of metal frames purchased
Let m = the PRICE (in dollars) of ONE metal frame
So, Mm = the COST of buying M metal frames

We can now write: Ww + Mm = 144

Target question: What is the value of Mm?
ASIDE: You can see that I rephrased the target question to match the variables I'm using.

Aside: Here’s a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100

Statement 1: The price of each metal frame was 60% greater than the price of each wooden frame.
In other words: m = w + (60% of w)
So: m = w + 0.6w
Simplify: m = 1.6w
We also have this equation: Ww + Mm = 144
Do we have enough information to find the value of Mm?
No.
If we replace 1.6w with 1.6w, we get: Ww + M(1.6w) = 144
At this point we can see that we don't have enough information to find the value of Mm
Statement 1 is NOT SUFFICIENT

Statement 2: Tami purchased twice as many wooden frames as metal frames.
We can write: W = 2M or we can write: M = 0.5W
We also have this equation: Ww + Mm = 144
Is this enough information to find the value of Mm?
No.
If we replace M with 0.5W, we get: Ww + (0.5W)m = 144
At this point we can see that we don't have enough information to find the value of Mm
Statement 2 is NOT SUFFICIENT


Statements 1 and 2 combined
From the given information we know that Ww + Mm = 144
Statement 1 tells us that m = 1.6w
Statement 2 tells us that M = 0.5W

Replace m and M to get: Ww + (0.5W)(1.6w) = 144
Simplify: Ww + 0.8Ww = 144
Simplify: 1.8Ww = 144
Divide both sides by 1.8 to get: Ww = 80

In other words we now have: 80 + Mm = 144
Subtract 80 from both sides to get: Mm = 64
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

Just a lil correction - It's w=2m and not m=2w.

why is 0.8 + 1 = 1.2 ?
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let qty of MF be a and WF = b
price of MF = x and WF = y
givenn
ax+by=144
target find ax value
#1
The price of each metal frame was 60% greater than the price of each wooden frame.
x=1.6y
insufficient
#2
Tami purchased twice as many wooden frames as metal frames.
b=2a
insufficient
from 1 &2
b/2*1.6y +by=144
solve for by = 80
and ax = 144-80 ; 64
sufficient
OPTION C

Let number of metal frames be x and number of wooden frames be y.
Let price of metal frames be p and prices of wooden frames be q.
According to the question: p*x + q*y = 144 (i)
We need to find the value of p*x.
Now lets move on to the statements.

1) Tells us that p = 1.6*q(60% greater than q) . Still no information about the number of metal and wooden frames.
Not sufficient
2) Tells us that y = 2*x. No information about prices.
Not sufficient

1) and 2) combined:
put p = 1.6*q and y = 2*x in (i)
1.6*q*x + 2*q*x = 144.
Solving this we get value of q*x. Multiply it by 1.6 and we get p*x.
Hence 1) and 2) together are Sufficient.

Wait, this seems confuse to me, aren't we suppose to find the PRICE of the metal frames?

with 1 and 2 we can only find the total value paid for the metal frames

We need to find the total pretax price of metal frames, not price per piece of the metal frames.

VeritasKarishma chetan2u Bunuel Can this problem be solved using weighted averages? If yes, how? If no, why?

You can use weighted averages.

If price of wooden frame is 10x, price of metal frame is 16x.
Since w:m = 2:1 (say she purchased 2y wooden frames and y metal frames), average price will be 12x (the distance between 10x and 16x will be divided in the ratio 1:2 to get the average or use weighted avg formula)

Average price = 144/3y = 12x
xy = 4

We need the value of 16x * y which is 64.
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I have a query with regards to the wording of the question here -

The question mentions 'pre-tax price' specifically. However the statements mention only price. since pre-tax is written so specifically, should price in the statements refer to post-tax price?

chetan2u VeritasKarishma Bunuel
Kindly help understand please - I tried reading the question again however, I am unable to understand why pre-tax is written specifically when in the statements price means the same as pre-tax price.

Thanks

Yes, there is certainly some discrepancy here. The question stem says "pre-tax price" while the statements say "price". One would wonder whether tax has any role to play in it. An actual GMAT question should not have any such ambiguity.
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Thanks VeritasKarishma

I always get stumped by the wording. Even though the word total qualifies it, whenever I see price, I think of the per unit cost/amount, and thus I thought we had to calculate the price (per unit) of the metal frame. But a good thing to keep in mind is to either be on the look out for 'total' or it would be phrased as 'amount paid for metal frames..'

It's not, it's 1.8WB

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