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At a supermarket, the ratio of the number of shampoos to the number of

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Joined: 02 Sep 2009
Posts: 61232
At a supermarket, the ratio of the number of shampoos to the number of  [#permalink]

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07 Feb 2020, 03:36
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55% (hard)

Question Stats:

57% (02:35) correct 43% (03:21) wrong based on 28 sessions

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At a supermarket, the ratio of the number of shampoos to the number of soaps is 8 to 5, and the ratio of the number of drinks to the number of shampoos is 3 to 4. If the ratio of the soaps to the number of cereals is 9 to 2, what is the ratio of the number of drinks to the number of cereals?

A. 4:3
B. 15:6
C. 45:16
D. 15:4
E. 27:5

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Joined: 07 May 2019
Posts: 194
At a supermarket, the ratio of the number of shampoos to the number of  [#permalink]

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07 Feb 2020, 05:12
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At a supermarket, the ratio of the number of shampoos to the number of soaps is 8 to 5, and the ratio of the number of drinks to the number of shampoos is 3 to 4. If the ratio of the soaps to the number of cereals is 9 to 2, what is the ratio of the number of drinks to the number of cereals?

A. 4:3
B. 15:6
C. 45:16
D. 15:4
E. 27:5

Solution:

• $$\frac{Shampoos }{ Soaps }= \frac{8}{5} …………. (i)$$
• $$\frac{Drinks }{ Shampoos} = \frac{3}{4 }…………...(ii)$$
• $$\frac{Soaps }{Cereals }= \frac{9}{2} ……………. (iii)$$
• Multiplying all (i), (ii) and (ii) together, we get,
o $$\frac{Drinks }{ Cereals }$$= $$\frac{Drinks}{Shampoos} *\frac{Shampoos}{Soap}*\frac{Soaps}{Cereals}$$ $$= \frac{3}{4}*\frac{8}{5}*\frac{9}{2 }= \frac{27 }{5}$$
Thus, the correct answer is Option E.
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Joined: 14 Dec 2019
Posts: 247
Location: Poland
GMAT 1: 570 Q41 V27
WE: Engineering (Consumer Electronics)
Re: At a supermarket, the ratio of the number of shampoos to the number of  [#permalink]

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07 Feb 2020, 15:07
1
At a supermarket, the ratio of the number of shampoos to the number of soaps is 8 to 5, and the ratio of the number of drinks to the number of shampoos is 3 to 4. If the ratio of the soaps to the number of cereals is 9 to 2, what is the ratio of the number of drinks to the number of cereals?

A. 4:3
B. 15:6
C. 45:16
D. 15:4
E. 27:5

$$\frac{Sh}{So} = \frac{8}{5}$$; $$\frac{D}{Sh} = \frac{3}{4}$$; $$\frac{So}{C} = \frac{9}{2}$$; $$\frac{D}{C} = ?$$

$$\frac{D}{C} = \frac{D*9}{2*So} = \frac{D*9*8}{2*5*Sh} = \frac{3*9*8}{2*5*4} = 27:5$$ -> Answer - E
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Joined: 28 May 2014
Posts: 25
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Concentration: Strategy
GMAT 1: 590 Q44 V27
Re: At a supermarket, the ratio of the number of shampoos to the number of  [#permalink]

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07 Feb 2020, 20:51
GMATWhizard wrote:
At a supermarket, the ratio of the number of shampoos to the number of soaps is 8 to 5, and the ratio of the number of drinks to the number of shampoos is 3 to 4. If the ratio of the soaps to the number of cereals is 9 to 2, what is the ratio of the number of drinks to the number of cereals?

A. 4:3
B. 15:6
C. 45:16
D. 15:4
E. 27:5

Solution:

• $$\frac{Shampoos }{ Soaps }= \frac{8}{5} …………. (i)$$
• $$\frac{Drinks }{ Shampoos} = \frac{3}{4 }…………...(ii)$$
• $$\frac{Soaps }{Cereals }= \frac{9}{2} ……………. (iii)$$
• Multiplying all (i), (ii) and (ii) together, we get,
o $$\frac{Drinks }{ Cereals }$$= $$\frac{Drinks}{Shampoos} *\frac{Shampoos}{Soap}*\frac{Soaps}{Cereals}$$ $$= \frac{3}{4}*\frac{8}{5}*\frac{9}{2 }= \frac{27 }{5}$$
Thus, the correct answer is Option E.

Great visualization and by far the best approach to not make any silly mistakes. I tend to take ratios for such problems, often resulting in careless errors. What I have learnt is that fractions are better to deal with in such cases.
Manager
Joined: 07 May 2019
Posts: 194
Re: At a supermarket, the ratio of the number of shampoos to the number of  [#permalink]

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10 Feb 2020, 03:47
cathygeorge123 wrote:
GMATWhizard wrote:
At a supermarket, the ratio of the number of shampoos to the number of soaps is 8 to 5, and the ratio of the number of drinks to the number of shampoos is 3 to 4. If the ratio of the soaps to the number of cereals is 9 to 2, what is the ratio of the number of drinks to the number of cereals?

A. 4:3
B. 15:6
C. 45:16
D. 15:4
E. 27:5

Solution:

• $$\frac{Shampoos }{ Soaps }= \frac{8}{5} …………. (i)$$
• $$\frac{Drinks }{ Shampoos} = \frac{3}{4 }…………...(ii)$$
• $$\frac{Soaps }{Cereals }= \frac{9}{2} ……………. (iii)$$
• Multiplying all (i), (ii) and (ii) together, we get,
o $$\frac{Drinks }{ Cereals }$$= $$\frac{Drinks}{Shampoos} *\frac{Shampoos}{Soap}*\frac{Soaps}{Cereals}$$ $$= \frac{3}{4}*\frac{8}{5}*\frac{9}{2 }= \frac{27 }{5}$$
Thus, the correct answer is Option E.

Great visualization and by far the best approach to not make any silly mistakes. I tend to take ratios for such problems, often resulting in careless errors. What I have learnt is that fractions are better to deal with in such cases.

Hey …,

Glad to see that you found the approach useful.
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Re: At a supermarket, the ratio of the number of shampoos to the number of   [#permalink] 10 Feb 2020, 03:47
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