I got this question on an IQ test?

Question

Ralph likes 25 but not 24; he likes 400 but not 300; he likes 144 but not 145. Which does he like:

10 50 124 200 1600

Can you explain which is the correct answer and why?

Answer 1

The answer is 1600. This is because it's square root is a whole number.

The square root of 25 is 5

The square root of 400 is 20

The square root of 144 is 12

Answer 2

All the numbers he likes are squares, so he would like 1600 ;-)....Little known fact.....Ralph also made a guest appearance on Rainman

Answer 3

Ralph likes to eat crayons..

Answer 4

1600 as he likes only  square numbers. he like 25 which is the square of 5, 400 of 20 and 144 of 12 so 1600 is of 40

Answer 5

1600 because he likes square numbers

Answer 6

Simple,

Ralph likes 1600 but how did he arrive to the fact he like this.

Is that your question, or are you Ralph.

Answer 7

The answer is 1600.

Ralph like numbers which, when factorised into primes, are composed of a product of primes which have even exponents in canonical form. Or putting it another way the numbers Ralph likes have even numbers of each prime factor that appears in the product of prime factors that go to make up that number.

Factorising the numbers we see:

25 = 5^2

400 = 2^4 x 5^2

144 = 2^4 x 3^2

All these numbers have even exponents. Ralph like 'em.

24 = 2^3 x 3

300 = 2^2 x 5^2 x 3

145 = 5 x 29

These have one number in their product with an odd exponent and the same is true for 10, 50, 124 and 200.

Since,

1600 = 2^6 x 5^2

Ralph likes it!

Answer 8

That, unfortunately, is not a valid IQ test question.

Try WISC, Stanford-Binet or Woodcock-Johnson if you really need to know your IQ.

Answer 9

40*40=1600

Answer 10

Taim is correct. 1600 is another square number - 40x40=1600.

Answer 11

1600!

25, 400 and 144 are all square numbers meaning it is a product of 2 whole numbers

5x5  = 25, 20x20 = 400, 12x12 = 144

among the selections, only 1600 is the square number:

40x40 = 1600

Answer 12

124

because Ralph is Ralph

Answer 13

He likes square numbers so the answer is 1600. =]