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I got B, the official answer is E. I can see why the official answer is correct, but I'm not sure where my approach went wrong. Below is what I did:

I simplified the given equation to x=5a+2, where a is a constant, we're looking for y in x=7b+y, where y is the value of the remainder, if there's any.

1. I simply plugged in different values of x and see if there're more than 1 prime # that fits the bill. Starting w/a=1, I got x=7, 12, 17. Since both 7 and 17 are prime # and 7 is divisible by 7 but 17 isn't. 1 is insuff.

2. I got the equation: x+3=10c, so x=10c-3, where c is a constant. since we already know x=5a+2 from the question, we can set up the eqn as follows: 10c-3=5a+2 10c=5a+5 2c=a+1

Now I got stuck. It appears to me from the eqn. that x can not be divisible by 7. So what is going on here? or am I simply not interpreting the eqn. correctly?

When \(x\) is divided by 5, the remainder is 2. Is \(x\) divisible by 7?

1. \(x\) is a prime number 2. \(x + 3\) is a multiple of 10

I got B, the official answer is E. I can see why the official answer is correct, but I'm not sure where my approach went wrong. Below is what I did:

I simplified the given equation to x=5a+2, where a is a constant, we're looking for y in x=7b+y, where y is the value of the remainder, if there's any.

1. I simply plugged in different values of x and see if there're more than 1 prime # that fits the bill. Starting w/a=1, I got x=7, 12, 17. Since both 7 and 17 are prime # and 7 is divisible by 7 but 17 isn't. 1 is insuff.

2. I got the equation: x+3=10c, so x=10c-3, where c is a constant. since we already know x=5a+2 from the question, we can set up the eqn as follows: 10c-3=5a+2 10c=5a+5 2c=a+1

Now I got stuck. It appears to me from the eqn. that x can not be divisible by 7. So what is going on here? or am I simply not interpreting the eqn. correctly?

The highlighted statements are not correct as a and c are not constants. in fact they are variables.

1. \(x\) is a prime number: x could be 7 or 17 or 37 or 47 and so on.................. 2. \(x + 3\) is a multiple of 10: x could be again 7 or or 17 or 37 or 47 and so on..................

my bad in mislabeling "a" and "c" as constants instead of variables, but are there any mistakes in terms of my logic and approach in solving this type of problems? I understand there're multiple solutions for both 1) and 2). But I'm trying to understand how to reach that conclusion outside of brutally plugging in different #'s until I find the answer. This doesn't seem very efficient use of time on the GMAT.

my bad in mislabeling "a" and "c" as constants instead of variables, but are there any mistakes in terms of my logic and approach in solving this type of problems? I understand there're multiple solutions for both 1) and 2). But I'm trying to understand how to reach that conclusion outside of brutally plugging in different #'s until I find the answer. This doesn't seem very efficient use of time on the GMAT.

Thanks in advance.

Your approach for 1 is correct but 2 leads nowhere. Since you are looking for y, not a or c.
_________________

I got B, the official answer is E. I can see why the official answer is correct, but I'm not sure where my approach went wrong. Below is what I did:

I simplified the given equation to x=5a+2, where a is a constant, we're looking for y in x=7b+y, where y is the value of the remainder, if there's any.

1. I simply plugged in different values of x and see if there're more than 1 prime # that fits the bill. Starting w/a=1, I got x=7, 12, 17. Since both 7 and 17 are prime # and 7 is divisible by 7 but 17 isn't. 1 is insuff.

2. I got the equation: x+3=10c, so x=10c-3, where c is a constant. since we already know x=5a+2 from the question, we can set up the eqn as follows: 10c-3=5a+2 10c=5a+5 2c=a+1

Now I got stuck. It appears to me from the eqn. that x can not be divisible by 7. So what is going on here? or am I simply not interpreting the eqn. correctly?

From Statement 1: X is a prime number. from this we can say that x should be 7 or 17 or 47.... 7 is divisible by 7 but not 17 - not sufficient

From Statement 2: X+3 is multiple of 10 so again numbers should be 7, 17, 27... again 7 is divisible by 7 but not 17..

for these type of questions, its easier to solve by picking numbers instead of writing euqations..

I simplified the given equation to x=5a+2, where a is a constant, we're looking for y in x=7b+y, where y is the value of the remainder, if there's any. Now I got stuck. It appears to me from the eqn. that x can not be divisible by 7. So what is going on here? or am I simply not interpreting the eqn. correctly?

As statement 1 if x is prime number than it cannot be divided by 7 except 7 itself so we cannot say fully that x is divisible by 7 or not. As per statement 2 is x+3 is multiple of 10 then x can be 7,17,27,37,47,57,67,77 ... so from this 7,77 are divisible by 7 and others are not so insufficient.

I got B, the official answer is E. I can see why the official answer is correct, but I'm not sure where my approach went wrong. Below is what I did:

I simplified the given equation to x=5a+2, where a is a constant, we're looking for y in x=7b+y, where y is the value of the remainder, if there's any.

1. I simply plugged in different values of x and see if there're more than 1 prime # that fits the bill. Starting w/a=1, I got x=7, 12, 17. Since both 7 and 17 are prime # and 7 is divisible by 7 but 17 isn't. 1 is insuff.

2. I got the equation: x+3=10c, so x=10c-3, where c is a constant. since we already know x=5a+2 from the question, we can set up the eqn as follows: 10c-3=5a+2 10c=5a+5 2c=a+1

Now I got stuck. It appears to me from the eqn. that x can not be divisible by 7. So what is going on here? or am I simply not interpreting the eqn. correctly?

From Statement 1: X is a prime number. from this we can say that x should be 7 or 17 or 47.... 7 is divisible by 7 but not 17 - not sufficient

From Statement 2: X+3 is multiple of 10 so again numbers should be 7, 17, 27... again 7 is divisible by 7 but not 17..

for these type of questions, its easier to solve by picking numbers instead of writing euqations..

I agree, it is much faster to just plug in numbers then to derive an equation in this case

When is divided by 5, the remainder is 2. Is divisible by 7?

Stmt says X when divided by 5 gives Remainder (R) = 2... that means X=(5*a+2) X can be 2, 7, 12, 17, 22... (putting a =0,1,2...) and asks is X divisible by 7?

1. X is a prime number

this says X is prime both 7 and 17 are prime, not sufficient

2. (x+ 3) is a multiple of 10 again taking 7 and 17, both (7+3) and (17+3) are multiple of 10. not sufficient.

Since same numbers are used for both 1 and 2, answer E

one observation i have made is , when both the options are saying same ( like wht we have now)... 1. If Option A is suffcient, then Option B would be sufficient too making answer D 2. If Option A is insuffcient, then Option B would be insufficient too making answer E....

I go with E for the above question n i agree with the above explantions....
_________________

Regards, Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat

for option 1 > I picked couple of examples like 7,17,37 which are prime numbers and leaves remainder as 2. In all three of them, first one 7 is divisible by 7 but rest 17 and 37 are not. Clearly, we can not confirm the question under investigation "is number divisible by 7 or not?"

for option 2 > Again picked examples like 7, 17, 27, 37 and so on.. In all of them, first one is divisible by 7 not rest are not. So we can not again be pretty sure if the number is divisible by 7 or not.