CellSure has two sales assistants, Lucas and Jose. Yesterday

Question

CellSure has two sales assistants, Lucas and Jose. Yesterday, \(\frac{2}{3}\) of the phones sold at CellSure had foldable screens, and Lucas sold \(\frac{9}{16}\) of those foldable-screen phones. If \(\frac{1}{2}\) of the phones sold by Jose had foldable screens, what fraction of the phones sold by Lucas had foldable screens?

A. \(\frac{2}{3}\)
B. \(\frac{3}{4}\)
C. \(\frac{4}{5}\)
D. \(\frac{9}{10}\)
E. \(\frac{15}{16}\)

Show Answer

Official Answer

D

A.  \frac{2}{3} 
B.  \frac{3}{4} 
C.  \frac{4}{5} 
D.  \frac{9}{10}  
E.  \frac{15}{16}

paragw · Answer

Here's my solution for this question

Edskore · Answer

This one's a classic case of a total splitting into two people, but the foldable subset splitting differently between them. The trap is trying to solve it with straight algebra and fractions stacked on fractions, when picking a smart number makes the whole thing collapse in about five lines.

1. We've got thirds, sixteenths, and halves floating around, so pick a total that plays nice with all three. 48 works (48/3 = 16, 48/16 = 3, 48/2 = 24).

2. Total foldable phones sold = 2/3 of 48 = 32.

3. Lucas sold 9/16 of those foldable phones, so his foldable count = 9/16 x 32 = 18.

4. That leaves Jose with 32 - 18 = 14 foldable phones.

5. We're told 1/2 of Jose's total phones were foldable, so Jose's total = 14 x 2 = 28.

6. Total phones sold = 48, so Lucas sold 48 - 28 = 20 phones overall.

7. Fraction of Lucas's phones that were foldable = 18/20 = 9/10.

Answer is D.

I fell into the trap the first time I saw this style of question, tried to track everything with one variable T and got lost in the fraction arithmetic halfway through. Picking a number that clears every denominator at once turns a messy weighted average problem into basic subtraction. Whenever a question throws thirds, sixteenths, and halves at you together, that's your cue to smart-number it instead of grinding through algebra.

onlyPlanA · Answer

This solution might take more time, but this is how I solved it.

Total cellphones = x
Phones with foldable screens =  \frac{2x}{3} 
Foldable phones sold by Lucas =  \frac{9}{16}(\frac{2x}{3})  =  \frac{3x}{8}

Now, given that half of the phones sold by Jose are foldable phones.
So, foldable phones sold by Jose (let J) = J/2

Now, foldable phones sold by Jose and foldable phones sold by Lucas (which is  \frac{3x}{8} ) = total foldable phones

So,  \frac{J}{2} + \frac{3x}{8} = \frac{2x}{3}

J = \frac{ 7x}{12}

Thus,  L = \frac{5x}{12}

this gives  x = \frac{12L}{5}

Hence, fraction of phones sold by Lucas that have foldable screens are:
 \frac{3}{8}(\frac{12L}{5}) = \frac{9L}{10}

kevincan · Answer

This would be wonderful in a 3 by 3 matrix !

onlyPlanA · Answer

kevincan , can you please explain the matrix method once? I always get confused solving any problem by that method. Thanks!

kevincan · Answer

Here you are, don’t be put off by the fact that the video start with a blank screen

onlyPlanA · Answer

Awesome.. Thank you so very much 🙏!

TheAdmissionHub · Answer

Total foldable phones sold:  f = \frac{2}{3}x

Total foldable phones sold by Lucas:  Lf = \frac{9}{16} f = \frac{9}{16}*\frac{2}{3}x = \frac{3}{8}x

Total foldable phones sold by Jose:   Jf = \frac{2}{3}x-\frac{3}{8}x = \frac{7}{24}x

We know that half of the phones sold by Jose were foldable, so the total number of phones sold by Jose is:  \frac{7}{24}x*2 = \frac{7}{12}x

Therefore, the total number of phones sold by Lucas is:  \frac{x- 7}{12x} = \frac{5}{12}

The fraction of foldable phones sold by Lucas is:  \frac{3}{8}x/\frac{5}{12}x = \frac{9}{10}x

Answer: D

CellSure has two sales assistants, Lucas and Jose. Yesterday

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

CellSure has two sales assistants, Lucas and Jose. Yesterday

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