Sam’s bowling scores for seven games were, in order played, 54, 35, 89

Question

Sam’s bowling scores for seven games were, in order played, 54, 35, 89, 76, 48, x, and y. Sam’s mode score for the seven games was 76, and his median score was 54. If x < y, which of the following could be the value of x?

A. 50

B. 55

C. 70

D. 76

E. 80

A. 50

B. 55

C. 70

D. 76

E. 80

GMATinsight · Answer

Mode = 76 i.e. At least one of the variables x, and y must be 76.

Arranging in increasing order - {35, 48,  54 , 76, x, 89}

Since 54 is median so other variable (which is not 76) must be less than or equal to 54 so that 54 becomes the median fo set

Also, it is given that x < y i.e. y must be 76 and x must be ≤54

Arranging in increasing order - {35, 48,  x   54 , 76, y, 89}

Only value among options which is less than or equal to 54 is 50

Answer: Option A

logro · Answer

Given that mode of the set is 76

Since each number is appearing just once if 76 is the mode then either x or y should be equal to 76 (this is y)

Now given that 54 is the median of the set

Since their are 7 elements in the set the median is the 4th element

If we re-arrange the known elements in the set in the ascending order we get 35,48,54, 76, 76, 89

Now we need to find the place for x such that 54 becomes the 4th element and the median of the set

That is only possible if x <54 in which case the elements in the set will be 35,48,x,54, 76, 76 and 89

Hence from the options only A satisfies this condition

MathRevolution · Answer

The median score was 54 and x < y.

=> 35, 48, 54, 76, 89

Mode: 76

=> 35, 48, 54, 76, y , 89

'x' has to be less than '54' so that median remains '54'.

Answer A

bumpbot · Answer

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Sam’s bowling scores for seven games were, in order played, 54, 35, 89

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Sam’s bowling scores for seven games were, in order played, 54, 35, 89

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