The "spin" of any two-digit number is defined as double the amount of

Question

The "spin" of any two-digit number is defined as double the amount of the tens digit of the number. For instance, the "spin" of 54 is 10. Is the "spin" of x divisible by 4?

(1) The sum of the digits of x is 9. 
(2) x > 50

Nikhil · Answer

The "spin" of any two-digit number is defined as double the amount of the tens digit of the number.

To find whether the spin of x is divisible by 4

Statement 1

The sum of the digits of x is 9

=> x can be 18 satisfying the sum of digits 1 + 8 to be 9 and spin of x = 2(1) = 2 which is not divisible by 4

=> x can be 27 satisfying the sum of digits 2 + 7 to be 9 and spin of x = 2(2) = 4 which is divisible by 4

Statement 1 is not sufficient

Statement 2

x > 50

=> x can be 51 satisfying the condition x > 50 and spin of x = 2(5) = 10 which is not divisible by 4

=> x can be 62 satisfying the condition x > 50 and spin of x = 2(6) = 12 which is divisible by 4

Statement 2 is not sufficient

Combining statements 1 and 2

The sum of the digits of x is 9. and x > 50

=> x can be 54 satisfying the sum of digits 5 + 4 to be 9 and 54 > 50 and spin of x = 2(5) = 10 which is not divisible by 4

=> x can be 63 satisfying the sum of digits 6 + 3 to be 9 and 63 > 50 and spin of x = 2(6) = 12 which is divisible by 4

Statements 1 and 2 together are not sufficient

Hence option E

ccooley · Answer

This one is going to be all about translating the question into plain English. When is the spin of a number divisible by 4? When twice the tens digit is divisible by 4.

When will that happen? Well, if you double an even number, it's divisible by 4. If you double an odd number, it isn't. So, the question is really asking: 'is the tens digit of X even?'

Statement 1: We don't know whether the tens digit of x is even or odd. Insufficient.

Statement 2: We don't know whether the tens digit of x is even or odd. Insufficient.

Both statements together: I'm pretty sure this will still be insufficient, but at this point I'd want to check with specific cases, just to be totally sure. For a number to fit both statements, its tens digit should be 5 or higher (to make it bigger than 50), and the ones digit should be 9 minus the tens digit.

Two numbers that work are 54 and 63. 54 has an odd tens digit, and 63 has an even tens digit. Since we can get both results, the statements are still insufficient together.

The correct answer is E.

SaquibHGMATWhiz · Answer

Solution:      
  Pre Analysis:  
  Let the 2 digit intere  x=10a+b  where a and b are tens and units digit 
 We are asked  if  2a=4k  or not  where k is a positive integer

Statement 1:   The sum of the digits of x is 9
  Accordign to this statement,  a+b=9  
 Let is take 2 cases: 
   a=7, b=2 : then  2a=2	imes 7=14  is  not divisible by 4   
  a=6, b=3 : then  2a=2	imes 6=12  is  divisible by 4    
 Thus,  statement 1 alone is not sufficient and we can eliminate options A and D

Statement 2:   x > 50
  We can take the same 2 cases that we took in statement 1 
 Thus,  statement 2 alone is also not sufficient

Combining:   
  After combining too, we can take the same 2 cases that we took in statement 1

Hence the right answer is    Option E

The "spin" of any two-digit number is defined as double the amount of

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