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20 Aug 2024, 01:30
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E
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Difficulty:
95%
(hard)
Question Stats:
36% (02:29) correct
64%
(02:20)
wrong
based on 101
sessions
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Yesterday, Tom had only racing cars and robots in toys. Out of the total number of toys that he had yesterday, 11/20 were racing cars. Today, his dad bought some new racing cars and robots for him. If he didn’t lose or break any toy from yesterday, is the fraction of the robots that he has today is less than yesterday?
(1) Less than 1/2 of the new toys are robots.
(2) Today, the number of total toys he has is 1/4 more than the total number of toys that he had yesterday.
(1) Less than 1/2 of the new toys are robots.
(2) Today, the number of total toys he has is 1/4 more than the total number of toys that he had yesterday.
20 Aug 2024, 03:54
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If \(\frac{11}{20}\) were racing cars, then \(\frac{9}{20}\) were robots, or 45% were robots.
(1) Less than 1/2 of the new toys are robots.
Assume that in total there were 20 toys in total prior to the dad buying new toys.
The smallest possible whole number for the amount of new toys that the dad bought is 3. In this instance 2 were new cars and one was a robot. This makes the new ratio then: \(\frac{9}{23}\) - in which case the fraction of the robots did go down.
However, if the father bought 80 new toys, and say 39 were robots then the new fraction will be: \(\frac{48}{100}\) which is larger.
INSUFFICIENT
(2) Today, the number of total toys he has is 1/4 more than the total number of toys that he had yesterday.
Once again, going with the notion that there were 20 toys in total, then now there will be 25 toys in total.
If his dad bought him only a single robot then the new fraction is \(\frac{10}{25}\) which is lower than 45%.
However if 4 of the 5 toys were robots, then the new fraction for the robots is \(\frac{13}{25}\) which is 52%.
Without further information, one cannot deduce if the fraction increased or decreased.
INSUFFICIENT
(1+2)
Putting the two together, and once again using 20 as the original number of toys, one knows that 5 toys were bought. However, in this instance one needs to not view the robots as only being represented by whole numbers: The minimum possible whole number for the amount of new robots bought is 1 and the greatest is 2:
If one robot was bought the fraction is \(\frac{10}{25}\), or 40%.
If two robots were bought the fraction is \(\frac{11}{25}\), or 44%. Both of which are lower.
HOWEVER, say the father had bought 2.4 robots (which still fits the threshhold of 'less than 1/2 of the new toys are robots'), then the new fraction is \(\frac{11.4}{25}\), or 45.6%, which is greater than the original fraction of robots.
INSUFFICIENT
ANSWER E
(1) Less than 1/2 of the new toys are robots.
Assume that in total there were 20 toys in total prior to the dad buying new toys.
The smallest possible whole number for the amount of new toys that the dad bought is 3. In this instance 2 were new cars and one was a robot. This makes the new ratio then: \(\frac{9}{23}\) - in which case the fraction of the robots did go down.
However, if the father bought 80 new toys, and say 39 were robots then the new fraction will be: \(\frac{48}{100}\) which is larger.
INSUFFICIENT
(2) Today, the number of total toys he has is 1/4 more than the total number of toys that he had yesterday.
Once again, going with the notion that there were 20 toys in total, then now there will be 25 toys in total.
If his dad bought him only a single robot then the new fraction is \(\frac{10}{25}\) which is lower than 45%.
However if 4 of the 5 toys were robots, then the new fraction for the robots is \(\frac{13}{25}\) which is 52%.
Without further information, one cannot deduce if the fraction increased or decreased.
INSUFFICIENT
(1+2)
Putting the two together, and once again using 20 as the original number of toys, one knows that 5 toys were bought. However, in this instance one needs to not view the robots as only being represented by whole numbers: The minimum possible whole number for the amount of new robots bought is 1 and the greatest is 2:
If one robot was bought the fraction is \(\frac{10}{25}\), or 40%.
If two robots were bought the fraction is \(\frac{11}{25}\), or 44%. Both of which are lower.
HOWEVER, say the father had bought 2.4 robots (which still fits the threshhold of 'less than 1/2 of the new toys are robots'), then the new fraction is \(\frac{11.4}{25}\), or 45.6%, which is greater than the original fraction of robots.
INSUFFICIENT
ANSWER E
