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Algebra Strategies problem

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Algebra Strategies problem

by gmattesttaker2 » Sat Jul 21, 2012 11:55 am
Hello,

This is taken from MGMAT Strategy Guide 2 (5th edition), P. 126:

A retailer sells only radios and clocks. If she currently has 44 total items in inventory, how many of them are radios?

1) The retailer has more than 28 radios in inventory

2) The retailer has less than twice as many radios as clocks in inventory


Ans: C


My approach was as follows:

r + c = 44

1) r > 28 - In-sufficient

However, I am not clear with what Statement 2 means. Can you please assist? Thanks a lot.


Best Regards,
Sri
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Source: — Data Sufficiency |
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by eagleeye » Sat Jul 21, 2012 12:14 pm
gmattesttaker2 wrote:Hello,

This is taken from MGMAT Strategy Guide 2 (5th edition), P. 126:

A retailer sells only radios and clocks. If she currently has 44 total items in inventory, how many of them are radios?

1) The retailer has more than 28 radios in inventory

2) The retailer has less than twice as many radios as clocks in inventory


Ans: C


My approach was as follows:

r + c = 44

1) r > 28 - In-sufficient

However, I am not clear with what Statement 2 means. Can you please assist? Thanks a lot.


Best Regards,
Sri
Here's how you interpret it.

"The retailer has less than twice as many radios as clocks in inventory"
Number of clocks = c
Number of radios = r
The retailer has twice as many radios as clocks => r/2 = c
The retailer has less than twice as many radios as clocks => r/2 < c.

Hence for second statement we just know that r<2c. Which means r can be either 1 or 2 or 3 etc. Insufficient.

From the first one we know that r>28. Also r+c=44. From the second one we have r/2 < c.
If r = 29, c = 44-29 = 15. Then 29/2 = 14.5 < 15. So both statements agree.
If r = 30, c = 44-30 = 14. Then 30/2 = 15 is not less than 14. So this statement does not meet r/2<c condition.
Therefore r = 29. Sufficient.

C is correct.

cheers!
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by gmattesttaker2 » Sat Jul 21, 2012 12:48 pm
eagleeye wrote:
gmattesttaker2 wrote:Hello,

This is taken from MGMAT Strategy Guide 2 (5th edition), P. 126:

A retailer sells only radios and clocks. If she currently has 44 total items in inventory, how many of them are radios?

1) The retailer has more than 28 radios in inventory

2) The retailer has less than twice as many radios as clocks in inventory


Ans: C


My approach was as follows:

r + c = 44

1) r > 28 - In-sufficient

However, I am not clear with what Statement 2 means. Can you please assist? Thanks a lot.


Best Regards,
Sri
Here's how you interpret it.

"The retailer has less than twice as many radios as clocks in inventory"
Number of clocks = c
Number of radios = r
The retailer has twice as many radios as clocks => r/2 = c
The retailer has less than twice as many radios as clocks => r/2 < c.

Hence for second statement we just know that r<2c. Which means r can be either 1 or 2 or 3 etc. Insufficient.

From the first one we know that r>28. Also r+c=44. From the second one we have r/2 < c.
If r = 29, c = 44-29 = 15. Then 29/2 = 14.5 < 15. So both statements agree.
If r = 30, c = 44-30 = 14. Then 30/2 = 15 is not less than 14. So this statement does not meet r/2<c condition.
Therefore r = 29. Sufficient.

C is correct.

cheers!

Hello Eagleeye,

Thank you very much for your explanation. It is clear now.

Best Regards,
Sri
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