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Arville owns three times as many screwdrivers as he does

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by BTGmoderatorLU » Fri Dec 27, 2019 4:53 pm
Source: Veritas Prep

Arville owns three times as many screwdrivers as he does hammers and pliers put together. The number of hammers he owns is how many times the number of pliers he owns?

1) The ratio of screwdrivers to hammers owned by Arville is 21:4.
2) The ratio of screwdrivers to pliers owned by Arville is 7:1.

The OA is D
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Source: — Data Sufficiency |
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by deloitte247 » Sun Dec 29, 2019 12:36 am
Let screwdriver = s
Let hammer = h
Let pliers = p
Therefore, s = 3 (h+p)
Statement 1=> The ratio of screwdrivers to hammer owned by Arville is 21 : 4.
s : h = 21 : 4
From question stem
s = 3 (h + p)
21 = 3 (4 + p)
21 = 12 + 3p
3p = 9
p = 9/3 = 3
Therefore, h : p = 4 : 3 $$\frac{h}{p}=\frac{4}{3}$$
Hence, h = 4p/3, and total number of Arville's hammers is 4/3 of the plier he owns. Hence, statement 1 is SUFFICIENT.

Statement 2=> The ratio of screwdrivers to pliers owned by Arville is 7:1
s:p = 7:1
From question stem => s = 3 (h+p)
7 = 3 (h+1)
7 = 3h + 3
3h = 4
h = 4/3
Therefore, h:p = 4/3 : 1
$$h=\frac{4p}{3}$$
Total number of Arville's hammers is 4/3 of the pliers he owns. Hence, statement 2 is SUFFICIENT.
Since each statement alone is SUFFICIENT.

Answer = option D
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