A group of three friends ordered five identically priced des

Question

A group of three friends ordered five identically priced desserts. The restaurant applied a 20% discount, and the group then added a 10% tip on the discounted amount.

The youngest friend paid y dollars, half as much as each of the other two friends. What was the original price of each dessert, in terms of y?

A. 10y/9
B. 25y/22
C. 13y/11
D. 6y/5
E. 11y/9

harjas2222 · Answer

y= half of two friends

so we can say

y + 2y + 2y = 5y Total sum paid

5y= 1.1 * (discounted sum)
 5y/11 = discounted price

discounted price also= 0.8 * original 
 thus 5y/11 = 0.8*x
 5y/11 * 0.8 = x
 50y/88 = 25y/44 ans B

Dereno · Answer

Let the dessert prize be p.

5 identical desserts means, the total prize is 5p.

Discounted at 20% = 5p * (4/5)

Additional tip of 10% on the discounted price = 5p * (4/5) + (1/10)*5p * (4/5)

= (11/10)*5p * (4/5)

= 22p/5

Total bill amount = 22p/5

Amount split up among three friends = 2y, 2y, y respectively.

5y = 22p/ 5

Then p = (25/22)*y

p =  (25*y/22)

Option B

sunshineeee · Answer

The youngest friend paid y dollars, half as much as each of the other two friends.

--> Half of two friends doesn't mean y + 2y where y = 1/2 (x+z), where the other 2 friends are the accumulated ones, not every single one?

egmat · Answer

Hi sunshineeee,

Good instinct to slow down on that sentence, because the whole setup hinges on it. Let me point to the one word that settles it.

The sentence says the youngest paid  "half as much as  each  of the other two friends."  That word  each  is the key. It tells you to compare the youngest's payment against  one  of the other friends at a time - not against the two of them added together.

So the correct reading is:
- Youngest =  y 
- Friend 2 =  2y  (because y is half of  that  friend's amount)
- Friend 3 =  2y  (same comparison)
- Total = y + 2y + 2y =  5y

Your version - y =  1⁄2 (x + z) - is exactly what the sentence would mean if it said  "half as much as the other two friends  combined ."  But it says "each," so the comparison is one-to-one, not against the pooled pair.

Here's a nice confirmation. The group's bill works out to  4.4p  (five desserts -  5p , then × 0.8  for the discount, then × 1.1  for the tip). Setting  4.4p  =  5y  gives p =  25y/22 , which is answer  B . If instead you used your combined reading, the total becomes only  3y , and  4.4p  =  3y  gives  15y/22  - which isn't even an option. So the wording  and  the answer choices both point to the "each" reading.

Quick way to lock the phrase in - read these two and feel the difference: 
- "Tom is half as tall as  each  twin." - each twin is  2×  Tom.
- "Tom is half as tall as the twins  combined ." - the twins together are  2×  Tom.

Same word swap, completely different equation - so always let "each" vs. "combined" decide.

Answer: B

A group of three friends ordered five identically priced des

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A group of three friends ordered five identically priced des

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards