In the following question, some statements are given followed by some conclusions. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follow the given statements, disregarding commonly known facts.

Statement:
Only gentlemen can become members of the club.
Many of the members of the club are officers.
Some of the officers have been invited for the dinner.
Conclusion:
I. All the members of the club have been invited for dinner
II. Some of the officers are not gentlemen
III. All gentlemen are members of the club
IV. Only gentlemen have been invited for dinner

Which two numbers should be interchanged to make the given equation correct?

78 $÷$ 48 $\times$ 8 $+$ (26 $\times$ 7) $-$ 39 $+$ (45 $+$ 15) = 210

Which two signs should be interchanged to make the given equation correct?

$39÷3\times 13+26-13=2$

Which two numbers should be interchanged to make the given equation correct?

$36\times 81÷9-(88÷4)+14+(22+7)=169$

Select the correct combination of mathematical signs that can sequentially replace the * signs and balance the given equation.

$221 * 17 * 12 * 130 * 24 * 50$

Select the correct combination of mathematical signs that can sequentially replace the * signs and make the equation correct.

$45*24*72*20*12*7$

By interchanging which two signs, the equation will be correct?

$13 - 9 \times 2 ÷ 3 + 16 = 3$

Select the correct sequence of mathematical signs that can sequentially replace the * signs and balance the given equation.

$6*10*55*162*9=23$

"Although the State government has been funding College XYZ for the past 10 yr, it has decided not to do so this year."—Local news report

Which ofthefollowing may not be a reasonfor the decision of the government to discontinue the funding of the said college this year?

Select the correct combination of mathematical signs that can sequentially replace the $*$ signs and make the equation correct.

$68 * 138 * 23 * 54 * 20$

By interchanging which two signs, the equation will be correct?

$11 + 16 \times 12 ÷ 4 - 2 = 21$