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16 Aug 2019, 01:46
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
60% (02:28) correct
40%
(02:28)
wrong
based on 83
sessions
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Last year, a company sold six types of products, each a telephony product or a home appliance. The table above shows the annual revenue from each product as a fraction of the company's total annual revenue. If the company's telephony products generated revenue in excess of 1/2 of the total annual revenue, is Product 3 a telephony product?
(1) Product 1 and Product 6 are telephony products.
(2) Product 2, Product 4, and Product 5 are not telephony products.
Attachment:
image566.png [ 11.65 KiB | Viewed 1867 times ]
16 Aug 2019, 06:23
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Bunuel
Last year, a company sold six types of products, each a telephony product or a home appliance. The table above shows the annual revenue from each product as a fraction of the company's total annual revenue. If the company's telephony products generated revenue in excess of 1/2 of the total annual revenue, is Product 3 a telephony product?
(1) Product 1 and Product 6 are telephony products.
(2) Product 2, Product 4, and Product 5 are not telephony products.
Attachment:
image566.png
let total revenue be 60
so for each product we get a revenue ;
Product -1--2--3--4--5--6
Revenue-12-6-10--8--15--9
given that TP revenue >30
#1Product 1 and Product 6 are telephony products.
so product 3 may or may not be TP as sum of 1 & 6 ; 21 so either 3,5 can be TP
insufficient
#2
Product 2, Product 4, and Product 5 are not telephony products.
left with product 1,3,6 ; 12+10+9 ; 31 so product 3 is telephone product
IMO B
17 Sep 2019, 05:05
Kudos
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Bunuel
Last year, a company sold six types of products, each a telephony product or a home appliance. The table above shows the annual revenue from each product as a fraction of the company's total annual revenue. If the company's telephony products generated revenue in excess of 1/2 of the total annual revenue, is Product 3 a telephony product?
(1) Product 1 and Product 6 are telephony products.
(2) Product 2, Product 4, and Product 5 are not telephony products.
Attachment:
image566.png
Official Explanation
This question is basically an exercise in adding fractions. We're told that these unnamed products 1 through 6 are either telephony or home appliance products. The telephony products add up to or more. This question is inherently suited to analysis by cases, since there is a finite and not huge set of possible cases. On to the statements, separately first.
Statement (1) tells us that products 1 and 6 are telephony, and they sum to 1/5 + 3/20 = 7/20. They cannot be the complete set of telephony products, because their sum is less than half or 10/20. We're interested in product 3. Case I: product 3 is telephony. With product 3, the fraction rises above half, because product 3 is \(\frac{1}{6} \approx \frac{3.3}{20}\) and so the total is now approximately 10.3/20, which is greater than half. So this case is allowed by Statement (1), and hence the answer to the question posed could be "yes." Case II: product 3 is not telephony. This case is possible as long as we can get the telephony fraction above half. For example, if product 5 were telephony, that would bring the total to 7/20 + 1/4 = 12/20, which is more than half. We have two allowed cases that yield different answers to the question asked of us, so we don't have sufficient information to answer definitively. Statement (1) is insufficient.
Statement (2) tells us that two products are not telephony products. We will again analyze by cases. Case I from above is again allowed by this statement, because 2 and 5 are not telephony and the telephony total is above . Case II is not allowed, though. If 2, 4 and 5 are not telephony and 3 also is not telephony, the most telephony that we can get is 1 and 6. That would give us a telephony total of , which is less than . There is no possible case in which Statement (2) is true and 3 is not telephony. So we have sufficient information to answer the question posed (in the affirmative) and Statement (2) alone is sufficient.
The correct answer is (B).
