These sums are from PETERSON's test series.

If S is a series of numbers of the form X, XX, XXX, XXXX, XXXXX, ..., where X is a non-zero digit, is every number in this series a multiple of the same prime number P?

(1) P is an odd number such that P < X

(2) X is a multiple of P

What is the solution
Y cant P be 1. And can anyone give explation ??

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Does 4x + 5y = 0?

(1) y = 0
(2) 8x = -10y

Please explain . Y is the option x = 0 and y = 0 not taken into account

Question 1)

1 is not a prime number.

Questions 2)

statement 2 is same as the original 4x + 5y = 0

Is the answer A

in the second one

a + b can be zero in 2 cases....

either a and b are zeros

or

one is the negative of the other.

Y is the 1st possibility not taken?

First Qn:

1) ANS C

With Statement 1, we can infer that, x could be any value between 1 and 9, whereas prime number could be, 3,5,7

It is insufficient to answer the qn

With Statement 2, X is a multiple of P, we can infer that, P can be 2,3,5,7,9 and X could be any value between 1 to 9

Combining both the statments we are left with P as 3 and X as 9 (because other prime numbers can not be a multiple of X, and less than the value of X)

Thus the entire series can be divisible by the same prime number, ie, 3

consider the different values of X, all but one which give sequences** that are multiples of a common factor.
X = 1: no common factor
X = 2: p could be 2
X = 3: p could be 3
X = 4: p could be 2 or 4
X = 5: p could be 5
X = 6: p could be 2 or 3
X = 7: p could be 7
X = 8: p could be 2
X = 9: p could be 3

(1)
if p is 3, then the answer is yes if x = 9, but no if x = 7. therefore, insufficient.

(2)
all such combinations of x and p appear in the above list, making the answer 'yes'. (in fact, it's trivial to see that, if p goes into x, it must also go into xx, xxx, ...) therefore, sufficient.

since (2) is sufficient and (1) is not, we don't need to consider the statements together.

remember that this is data sufficiency; all we have to be able to do is answer the yes/no question. we DO NOT have to be able to deduce unique values for x and p to be 'sufficient' (a mistake made by at least one poster on this thread).

remember that you're interested in the SUM 4x + 5y, so you should try to rearrange the data you're given to create this sum.

(1)
no information about x, so obviously insufficient. (the answer is 'yes' if x = 0 and 'no' if x is any other value.)

(2)
add 10y to both sides: 8x + 10y = 0
divide by 2: 4x + 5y = 0
yes
sufficient

since the problem asks about the combination 4x + 5y, you should IMMEDIATELY make the adjustments made to statement (2) here, in an effort to create that expression on one side of the equation.