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Math Expert
Joined: 02 Sep 2009
Posts: 60727

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03 Dec 2019, 01:18
00:00

Difficulty:

55% (hard)

Question Stats:

71% (02:49) correct 29% (02:57) wrong based on 50 sessions

David decides to start a business making gift baskets. He estimates that if he charges x dollars per gift basket, he will sell $$65-5x$$ baskets per day. If his estimate is accurate, which of the following sets describes all values of x for which will he collect revenue in excess of $150 per day? A. $$2<x<15$$ B. $$x<3$$ or $$x>10$$ C. $$x<2$$ or $$x>15$$ D. $$3<x<10$$ E. $$5<x<6$$ Are You Up For the Challenge: 700 Level Questions _________________ Manager Joined: 10 Dec 2017 Posts: 177 Location: India Re: David decides to start a business making gift baskets. He estimates th [#permalink] ### Show Tags 03 Dec 2019, 02:28 1 Bunuel wrote: David decides to start a business making gift baskets. He estimates that if he charges x dollars per gift basket, he will sell $$65-5x$$ baskets per day. If his estimate is accurate, which of the following sets describes all values of x for which will he collect revenue in excess of$150 per day?

A. $$2<x<15$$

B. $$x<3$$ or $$x>10$$

C. $$x<2$$ or $$x>15$$

D. $$3<x<10$$

E. $$5<x<6$$

Are You Up For the Challenge: 700 Level Questions

$$X*(65-5X)>150$$
$$65X-5X^2>150$$
$$5X^2-65X+150<0$$
$$X^2-13X+30<0$$
$$(X-3)(X-10)<0$$
3<X<10
D:)
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5748
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

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03 Dec 2019, 03:12
we can solve linearly or plugin values of x= 4,5,6..9 we get revenue sales>180
IMO D

Bunuel wrote:
David decides to start a business making gift baskets. He estimates that if he charges x dollars per gift basket, he will sell $$65-5x$$ baskets per day. If his estimate is accurate, which of the following sets describes all values of x for which will he collect revenue in excess of $150 per day? A. $$2<x<15$$ B. $$x<3$$ or $$x>10$$ C. $$x<2$$ or $$x>15$$ D. $$3<x<10$$ E. $$5<x<6$$ Are You Up For the Challenge: 700 Level Questions VP Joined: 24 Nov 2016 Posts: 1139 Location: United States Re: David decides to start a business making gift baskets. He estimates th [#permalink] ### Show Tags 04 Dec 2019, 08:02 Bunuel wrote: David decides to start a business making gift baskets. He estimates that if he charges x dollars per gift basket, he will sell $$65-5x$$ baskets per day. If his estimate is accurate, which of the following sets describes all values of x for which will he collect revenue in excess of$150 per day?

A. $$2<x<15$$

B. $$x<3$$ or $$x>10$$

C. $$x<2$$ or $$x>15$$

D. $$3<x<10$$

E. $$5<x<6$$

$$PQ=R:x(65-5x)>150$$
$$5x^2-65x+150<0…x^2-13x+30<0$$
$$(x-10)(x-3)<0…(less.than=inside.rng)…3<x<10$$

Ans (D)
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9167
Location: United States (CA)

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05 Dec 2019, 20:28
Bunuel wrote:
David decides to start a business making gift baskets. He estimates that if he charges x dollars per gift basket, he will sell $$65-5x$$ baskets per day. If his estimate is accurate, which of the following sets describes all values of x for which will he collect revenue in excess of \$150 per day?

A. $$2<x<15$$

B. $$x<3$$ or $$x>10$$

C. $$x<2$$ or $$x>15$$

D. $$3<x<10$$

E. $$5<x<6$$

Are You Up For the Challenge: 700 Level Questions

Using the formula revenue = price x number sold, we see that the revenue is x(65 - 5x), and we create the inequality:

x(65 - 5x) > 150

65x - 5x^2 - 150 > 0

Multiplying the inequality by -1, we have:

5x^2 - 65x + 150 < 0

x^2 - 13x + 30 < 0

(x - 3)(x - 10) < 0

We see that if 3 < x < 10, then (x - 3)(x - 10) would be negative, i.e., less than 0.

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