Problem Solving

For each of the following statements, state whether it is true or false. If a statement is true, give one example that demonstrates that it is true. If a statement is false, give one example that shows it is false.

a, All composite numbers less than 10 are even numbers

b, If a counting number is a multiple of both two and six, then the number is a multiple of 12

c, If the sum of the digits of a counting number greater than 20 is a multiple of three, then the number itself is a multiple of three

d, If the sum of digits of a 2-digit counting number is a multiple of four, then the number is a multiple of four

e, If a and b are real number and a > b, then a^2 > b^2

Woa your third such post. Is this some kind of a homework?
I would like to see your answers to these before answering it.

hannah_lewis11 wrote:For each of the following statements, state whether it is true or false. If a statement is true, give one example that demonstrates that it is true. If a statement is false, give one example that shows it is false.

a, All composite numbers less than 10 are even numbers

b, If a counting number is a multiple of both two and six, then the number is a multiple of 12

c, If the sum of the digits of a counting number greater than 20 is a multiple of three, then the number itself is a multiple of three

d, If the sum of digits of a 2-digit counting number is a multiple of four, then the number is a multiple of four

e, If a and b are real number and a > b, then a^2 > b^2

a, All composite numbers less than 10 are even numbers

Composite nos. are the nos. which have facors other than 1 & itself.

Composite nos. less than 10 are = (4, 6, 8 & 9); Clearly 9 is odd. So False.

b, If a counting number is a multiple of both two and six, then the number is a multiple of 12

Set of counting number; a multiple of both two and six = {6, 12, 18, 24, 30....} &

Set of counting number; a multiple of 12 is = {12, 24, 36....}. false.

c, If the sum of the digits of a counting number greater than 20 is a multiple of three, then the number itself is a multiple of three

Rule of divisibility of 3...If sum of the digits is divisible by 3, then no. is divisible by 3.True.
Check--{21, 24, 27, 30...}

d, If the sum of digits of a 2-digit counting number is a multiple of four, then the number is a multiple of four

See set of sum of digits of a 2-digit counting number is a multiple of four = {40,44,48,80,84,88}; True.

e, If a and b are real number and a > b, then a^2 > b^2

False. If a & b are +ive then True else false. FALSE.

d, If the sum of digits of a 2-digit counting number is a multiple of four, then the number is a multiple of four

See set of sum of digits of a 2-digit counting number is a multiple of four = {40,44,48,80,84,88}; True.

BUT FOR 31 ,17,31... MANY MORE ITS FALSE

d)
For a number to be divisible by 4, the number formed by the last two digits (10's place and 1's place taken in that order) shall be divisible by 4. For example 220 is divisible by 4 as the number formed by last two digits ie., 20 is divisible 4. Similarly, 458 is not divisible by 4, as 58 is not divisible by 4.
'The sum of digits' rule which is applicable for "divisibility by 3" won't suite for "divisibility by 4".
Hence, the answer is False

aneesh.kg wrote:Woa your third such post. Is this some kind of a homework?
I would like to see your answers to these before answering it.

Good call! How do these questions relate to the GMAT?