Let's denote the tallest male, tallest female, shortest male and shortest female as

Tm,

Tf,

Sm &

Sf.

From the question stem it can be seen that :-

Tm -

Sm = 40

Tf -

Sf = 30

Statement 1:

The average height of the male students in the class is 10 centimeters greater than the average height of the female students in the class.

Case I:

Now think about a scenario where you have just two males having height 190 and 150cms so as to satisfy the condition of range being 40; Avg height = 170cms

And you have just two females in class with height 175 and 145 so as to satisfy the condition of range being 30; Avg height = 160cms.

Now we can see that the average height of the male students in the class is 10 centimeters greater than the average height of the female students in the class.

The range of the class in this case will be 190 - 145 = 45

Case II:

But the condition of average height of male being 10 more than average height of female can be achieved in many ways.

For example there are two males 190 and 150 cms.Range is 40 Avg height is 170.

there are 4 females of heights 180,155,155,150 cms. Range is 30. Avg height is 160.

But now the range of the entire class will be 190 -150 = 40

So the range is now different from previous example.

Since we do not know the number of male and female students we cannot determine range of the entire class! So statement 1 is not sufficient.

Statement 2:The shortest female student in the class is 15 centimeters shorter than the shortest male student in the class.

Sm -

Sf = 15

This means the tallest female is 15cms taller than shortest male. And we know the longest male is 40 cms taller than shortest male.

This makes it clear that the tallest student in class is

Tm and shortest student in class is

Sf

So the range of the class will be

Tm -

Sf

Now from question stem we know that

Tm -

Sm = 40

Tm - (15+

Sf) = 40

Tm -

Sf = 55

Range of the class is 55.

Statement 2 is sufficient.

Answer

BAmbarish

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Thank you

Ambarish