# Math Puzzle 11

This math puzzle 11 is on real numbers,arithmetic progression etc.**1) If 'a' and 'b' are real numbers such that b < a, then which of the following inequalities is true?**

I a < (a + b)/2 < b

II b < (b + a)/2 < a

III a < ab < b

I a < (a + b)/2 < b

II b < (b + a)/2 < a

III a < ab < b

A. I only B. II only C. III only D. I and II only E. II and III only

**2) If a/b is multiplied by a**

^{2}/b^{3}and the product is divided by -a^{2}/b^{2}the result is:A. -1 B. -a

^{2}/b

^{2}C. a

^{2}/ b

^{2}D. -a / b

^{2}E.-a / b

**3) The simplest form of (ab/ (a**

^{2}- b^{2})) - ((b/ (2a - 2b)) isA. 2ab /(a - b) B. 2ab / (a + b) C. 2 /(a

^{2}- b

^{2})

D. b / 2(a - b) E. b / 2(a + b)

**4) For what value of 'a' do the numbers 1, a and (14-a) taken in order, make an arithmetic progression?**

A. 3 B. 4 C. 5 D. 6 E. 15

**5) A sequence is given by a**

_{n}= n^{2}- 2n. Which of the following gives the (n-1) th term?A. (n - 1)

^{2}B. (n - 1)(n - 3) C. (n - 1)

^{2}- 2

D. (n - 1)(n - 2) E. 2(n - 1)

^{2}

**6) In a group of persons, each knows either French or German. If 100 know French, 50 know German and 20 know both, how many persons are there in the group?**

A. 100 B. 120 C. 130 D. 150 E. 180

**7) In a group of 70 persons, 32 drink coke but not coffee and 47 drink coke. How many drink coffee but not coke?**

A. 19 B. 23 C. 32 D. 42 E. 47

**8) If x*y = x**

^{3y}for all positive integers, what is (4*3)* 1/9?A. 4 B. 4

^{3}C. 4

^{6}D. 4

^{9}E. 4

^{18}

**9) The symbols @ and # are defined as A @ B = (A + B) 2 and**

A # B = (A - B) 2 , when A and B are real numbers. Each of the following is true except

A # B = (A - B) 2 , when A and B are real numbers. Each of the following is true except

A. (A @ B)+(A # B)=2(A

^{2}+B

^{2}) B. (A @ B)-(A # B)= 4AB

C. (A @ B)(A # B)=( A

^{2}- B

^{2}) D. A @ 0=A

^{2}E. (A # B)#0 = 0

**10) If f(x) = | |x| - 5|, what is the value of f(1)?**

A. 5 B. 4 C. -4 D. -5 E. -6

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