Last week, Raina and Bob made a combined total of $190$ sales at a computer store. Raina made how many more sales than

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Wed Oct 28, 2020 8:30 am

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Last week, Raina and Bob made a combined total of $190$ sales at a computer store. Raina made how many more sales than Bob?

(1) The difference between the number of sales Raina made and the number of sales Bob made was ten percent of the number of sales Raina made.

(2) Bob made $\dfrac9{19}$ of the total number of sales made by himself and Raina.

Answer: D

Source: Veritas Prep

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Source: Beat The GMAT — Data Sufficiency | Wed Oct 28, 2020 8:30 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

Re: Last week, Raina and Bob made a combined total of $190$ sales at a computer store. Raina made how many more sales

by deloitte247 » Fri Oct 30, 2020 12:14 pm

Let the no. of sales by Rama = x
Let the no. of sales by Bob = y
x + y = 190 and y = 190 - x
Target question => Raina made how many more sales than Bob?
x - y = ??
Statement 1: The difference between the number of sales Raina made and the number of sales Bob made was 10% of the number of sales Raina made.
x - y = 10% of x = 0.1x
From the question stem; y = 190 - x.
Hence, x - (190 - x) = 0.1x
2x - 190 = 0.1x
1.9x = 190
x = 190/1.9 = 100
From y = 190 - x = 190 - 100 = 90
So x - y = 100 - 90 = 10. Statement 1 is SUFFICIENT.

Statement 2: Bob made 9/19 of the total number of sales made by himself and Raina.
$$y=\frac{9}{19}of\ \left(x+y\right)\ from\ the\ question\ stem\ x+y=190$$
$$y=\frac{9}{19}\cdot190=9\left(10\right)=90$$
$$x+y=190;\ \ So\ x+90=190,\ then\ x=100$$
$$Therefore\ x-y=100-90=10$$
Hence, statement 2 is SUFFICIENT.

Since each statement alone is sufficient, the correct answer is option D.

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