If p is a two digit prime number, what is the value of p?

Question

(1) When p is divided by 4, the remainder is 3.

(2) p is 2 more than multiple of 7.

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gmatophobia · Answer

Given

p is a two digit prime number

Question

what is the value of p?

Statement 1

(1) When p is divided by 4, the remainder is 3.

p = 4 * x + 3

x = 2 ; p = 11
x = 4 ; p = 19

Hence this statement is not sufficient.

Statement 2

(2) p is 2 more than multiple of 7.

p = 7 * y + 2

y = 3 ; p = 23
y = 5 ; p = 37

Hence this statement is not sufficient.

Combined

4x + 3 = 7y + 2
4x = 7y - 1
4x = 4y + 3y -1
x = y +  \frac{(3y-1) }{ 4}

y = 3 ; x = 3 + 2 = 5

p = 23

y = 11 ; x = 11 + 8 = 19

p = 79

Hence combination also does not help.

Answer E

av1901 · Answer

Given information: p is a two digit prime number
To determine: Value of p

(1) When p is divided by 4, the remainder is 3.

As per the remainder equation:

p = 4x + 3  (where x is an integer quotient)
p = {11, 15, 19, 23}

The list will keep going on but since p is a prime number, we can discard 15 and even then we already have three different prime numbers in the list already

NOT SUFFICIENT

(2) p is 2 more than multiple of 7.

p = 7y + 2  (where y is an integer quotient)
p = {16, 23, 30, 37}

The list will keep going on but since p is a prime number, we can discard 16 and 30 and even then we already have two different prime numbers in the list already

NOT SUFFICIENT

Both statements combined

p = 4x + 3  and  p = 7y + 2  (where x and y are integer quotients)

Now, when we have two remainder equations, we can combine them by  taking the LCM of the two quotients and adding the first term common in both the lists 
For example: In the above 2 equations, we will take the LCM of 4 and 7, and add the first term common in both the individual lists

LCM of 4,7 = 28
First common terms in both lists (As can be seen in statements 1 and 2) = 23

So combined statement is as follows

p = 28z + 23

p = {23, 51, 79}

The list will keep going on but since p is a prime number, we can discard 51 and even then we already have two different prime numbers in the list already

NOT SUFFICIENT

Answer - E

tukaisg · Answer

Q : If p is a two digit prime number, what is the value of p?

The question stem asks to find out a definite value for P.

Statement number 1 says :

(1) When p is divided by 4, the remainder is 3.

We can form an equation out of this .

p = 4x + 3

Statement 1 is inconclusive to find out a single value of p.  Option A,D is gone.We are left with B,C,E ,

(2) p is 2 more than multiple of 7.

This is a fancy way of saying that p has reminder of 2 when divided by 7 .

p = 7y + 2

Statement 2 is also inconclusive to find out a single value of p.

Option B is also gone .We are left with C and E .

We try combining statement 1 and 2 .

4x + 3 = 7y + 2

now we have two choices either get the value of x or y .

Since we have already invested finding the range of x , I am going to find out the value of y using x as variable

so , 4x + 3 = 7y + 2 becomes

=> y = (4x+1)/7

using the range of x derived earlier 1 < x < 24

We have to find out a integer value of y

so using x = 5 we get y = 3
x = 12 y = 7

At this point we don't need to find the value of p to mark the option E as we have ready have two values of x within range that satisfies the y.

However , lets find out the value of p for understanding purpose , substituting x in the 1st equation {23,51 .... }

Hence there is not a definite value of p .  option C is eliminated . 
 
We have the correct option E .

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If p is a two digit prime number, what is the value of p?

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