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Math Expert V
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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Difficulty:   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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Manager  S
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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2
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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Manager  S
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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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
Intern  B
Joined: 28 May 2014
Posts: 25
Location: Singapore
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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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  S
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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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. If you are looking for similar approaches to tackle GMAT questions, you can visit us at http://www.gmatwhiz.com and take a look at our free trial.
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It is one of the most advanced test-prep platform, which offers high-quality content, personalized study plan, awesome analytics, and experienced mentors. 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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