Tami purchased several identically priced metal frames and several ide

Question

Tami purchased several identically priced metal frames and several identically priced wooden frames for a total pretax price of $144. What was the total pretax price of the metal frames that Tami purchased?

(1) The price of each metal frame was 60% greater than the price of each wooden frame.
(2) Tami purchased twice as many wooden frames as metal frames.

DS50571.01

Jsound996 · Accepted Answer

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

BrentGMATPrepNow · Answer

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

RK007 · Answer

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

chrtpmdr · Answer

why is 0.8 + 1 = 1.2 ?

Archit3110 · Answer

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

AdiBir · Answer

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 .

Gustavoncf · Answer

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

AdiBir · Answer

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

Chidinho · Answer

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

KarishmaB · Answer

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.

pgwodehouse · Answer

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

KarishmaB · Answer

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.

pgwodehouse · Answer

Thanks  VeritasKarishma

wishmasterdj · Answer

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..'

ueh55406 · Answer

It's not, it's 1.8WB

T-bezz · Answer

X = price metal frame
M = quantity metal frame

Y= price wood frame
W = quantity wood frame

value of X?

XM+YW=$144

If we rewrite the Q

(144-YW)/M=X

(1) X= 60% greater than Y --->  X=16/10Y  "No Suff."

Even with substitution we have variables for which we don't know the value

(2) W=2M ---> "No Suff"

Same as above

(3)

Substitute the value from statement (1) & (2)

16/10YM + 2YM=144 
 16YM+20YM=1440 
 36YM=1440 
 YM = 40

Finally substitute 40 into the equation

16/10 (40) = 64

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