Problem Solving

The integer P is greater than 7. If the integer P leaves a reminder of 4 when divided by 9,all of the following must be true except

a.The number that is 4 less than P is a multiple of 9.

b.The multiple that is 5 more than P is a multiple of 9.

c.The number that is 2 more than P is a multiple of 3.

d.When divided by 3,P will leave a remainder of 1.

e.When divided by 2, P will leave a remainder of 1.

Answer is e. Can some one suggest the easiest and the best method to approach this..I dint really follow the explanation. I was wonderin if i can jus plug in numbers and try

Plugging in numbers is an exceptional way for these kinds of problems.

P > 7. When P is divided by 9, leaves a remainder 4. List out the numbers that satisfy these conditions.

13, 22, 31, 40, 49, 58, 67, ....

Now go to each option. Question is MUST be true EXCEPT.

A. (P - 4) is a multiple of 9. TRUE. The numbers would be 9, 18, 27, 36, .... . These are multiples of 9.
As an aside, you know that when P is divided by 9, it leaves a remainder of 4. This means that P is 4 more than a multiple of 9. If that 4 is deducted, then it becomes a multiple of 9.
ELIMINATE!

B. (P + 5) is a multiple of 9. TRUE. The numbers would be 18, 27, 36, 45 .... . These are multiples of 9.
ELIMINATE!

C. (P + 2) is a multiple of 3. TRUE. The numbers would be 15, 24, 33, 42, .... . These are multiples of 9.
ELIMINATE!

D. P % 3 --> 1. TRUE. 13 % 3 = 1, 22 % 3 = 1, .....
ELIMINATE!

E. P % 2 --> 1. FALSE. 13 % 2 = 1, BUT 22 % 2 = 0.
CORRECT!

The first value which comes to the mind is 13 , a trap and waste of 1 min.
Best is let P = 9n + 4 n is +ve as P > 7
a) 9n +4 - 4 = 9n can be divided by 9
b) 9n + 4 + 5 = 9n + 9 can be divided by 9
c) 9n + 4 + 2 = 9n +6 can be divided by 3
d) 9n+ 4 = 3n + 1 with a remainder 1 when divided by 3
e) 9n+4 = 9n/2 + 2 can be divided by 3 , if n is even then there will be no remainder.

In GMAT is there is a preponderance of the right ans to be in the latter half mostly D or E , sp. in these Qs ?