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20 Sep 2020, 12:00
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A
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Difficulty:
75%
(hard)
Question Stats:
58% (02:37) correct
42%
(02:32)
wrong
based on 369
sessions
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Among the computers at a store, 55 have a hard drive with at least 1 terabyte capacity, and 40 have at least a 3.2-gigahertz CPU. If the total number of computers exceeds 100, and 20 of the computers have neither a hard drive with 1-terabyte or greater capacity nor a CPU of 3.2 gigahertz or greater, which of the following could be the number of computers that have both a 1-terabyte or greater hard drive and a 3.2-gigahertz or greater CPU?
I. 10
II. 15
III. 20
A. I only
B. II only
C. III only
D. I and II
E. II and III
I. 10
II. 15
III. 20
A. I only
B. II only
C. III only
D. I and II
E. II and III
20 Sep 2020, 13:28
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In such questions, I personally always find it easier to map the data in a tabular form.
(I don't know if there is a name for this method)
Anywho, first and foremost, using the data given in the question, make a table as given below:
untitled.png [ 19.66 KiB | Viewed 7130 times ]
I have marked the unknown ie. computers >1TB and >3.2 G Hz as x
I have marked the other unknown ie. Total no. of computers in the store as T
Now using the table, we can form the following equations:
untitled (2).png [ 25.52 KiB | Viewed 7070 times ]
Now lets take the bottommost horizontal row, (Even the rightmost vertical column can be considered
)
We know 55 + 60 - x = T
115-x = T <------------- (1)
We know that T has to be greater than 100.
Plugging in the values into (1), we get
I) x = 10, T = 105 ----> Hence, possible.
II) x= 15, T = 100 ----> Not possible as T>100.
III) x = 20, T = 95 -----> Again, not possible.
Hence only (I) is possible.
Option A is our answer.
(I don't know if there is a name for this method)
Anywho, first and foremost, using the data given in the question, make a table as given below:
Attachment:
untitled.png [ 19.66 KiB | Viewed 7130 times ]
I have marked the unknown ie. computers >1TB and >3.2 G Hz as x
I have marked the other unknown ie. Total no. of computers in the store as T
Now using the table, we can form the following equations:
Attachment:
untitled (2).png [ 25.52 KiB | Viewed 7070 times ]
Now lets take the bottommost horizontal row, (Even the rightmost vertical column can be considered
)We know 55 + 60 - x = T
115-x = T <------------- (1)
We know that T has to be greater than 100.
Plugging in the values into (1), we get
I) x = 10, T = 105 ----> Hence, possible.
II) x= 15, T = 100 ----> Not possible as T>100.
III) x = 20, T = 95 -----> Again, not possible.
Hence only (I) is possible.
Option A is our answer.
General Discussion
20 Sep 2020, 12:43
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Total no of computers with 1tb HD=55
with 3.2 Tb CPU=40
computers with don't have anything =20
Now depending upon total no of computers , number of computers having both will change
Total comp are more than 100 .
So assuming comp will be around 101 will give us computers have HD and CPU or both will be 81
and total of COmp with HD and CPU= 55+40=95
so comp with both will be 95-81=14.
So answer will be less than or equal to 14
So Option A is 5
Answer will be A.
with 3.2 Tb CPU=40
computers with don't have anything =20
Now depending upon total no of computers , number of computers having both will change
Total comp are more than 100 .
So assuming comp will be around 101 will give us computers have HD and CPU or both will be 81
and total of COmp with HD and CPU= 55+40=95
so comp with both will be 95-81=14.
So answer will be less than or equal to 14
So Option A is 5
Answer will be A.
