If x  10 and y  12, then which of the following must be true ?

If x  10 and y  12, then which… | Answer

Subject

গাণিতিক যুক্তি

Topic

অসমতা

ক)

(x+y) $ \ge $ 22

খ)

(x+y) < 11

গ)

(x+y) > 14

ঘ)

(x+y) > 1

When you have two inequalities,

x \ge 10

and

y \ge 12

, you can always add them together to find the minimum possible value for the sum

(x+y)

. Adding the minimums gives

10 + 12 = 22

, so

(x+y)

must be greater than or equal to 22. Option B,

(x+y) < 11

, is impossible since

x

alone is already

\ge 10

. Option C,

(x+y) > 14

, is true but not the *must be true* statement; for example,

x=10, y=12

gives

x+y=22

, which is not

>14

. Option D,

(x+y) > 1

, is too weak compared to the proven

\ge 22

\frac{1}{a}

\frac{1}{{{a^{2\;}}}}