property of integer (just open to discuss, dun have OA)

[mathdumber]

Q1. The set S has following properties
(a) If x is in S, then 1/x is also in S
(b) If both x and y are in S, so is (x+y)

Is 3 in S?
(1) 1/3 is in S
(2) 1 is in S

Q2. If p is a prime number greater than 2, what is the value of p?
(1) there are a total of 100 prime numbers between 1 and p+1
(2) there are a total of p prime numbers between 1 and 3912

Q3. Is XY < 0
(1) 1/Y > 1/X
(2) X>0

Q4. If the units digit of the three-digit positive integer k is non-zero, what is the tens digit of k?
(1) the tens digit of k+9 is 3
(2) the tens digit of k+4 is 2

guys, i do not have the Official Answer to these questions, pls dun get mad at me...i just want to open the tread to discuss the approach and answers to these questions.

thanks!

[lsr]

Q1. The set S has following properties
(a) If x is in S, then 1/x is also in S
(b) If both x and y are in S, so is (x+y)

Is 3 in S?
(1) 1/3 is in S
(2) 1 is in S

First statement:
If 1/3 is in S then 1/(1/3) = 3 is also in S.
Sufficient.

Second statement:
If 1 is in S, then 1/1=1 is also in S, 1+1=2 is also in S, and 1+2=3 is also in S.
Sufficient.

Answer is D.

[lsr]

Q3. Is XY < 0
(1) 1/Y > 1/X
(2) X>0
Question stem:
Do X and Y have opposite signs?

First statement:
(X-Y)/(XY) > 0

Either XY>0 and X>Y
Y<X<0
0<Y<X

Or XY<0 and X<Y
X<0<Y
Not sufficient.

Second statement:
No information about Y.
Not sufficient.

Both statements:
Since X>0, then XY>0 (from first statement).
Sufficient.

Answer is C.


Another approach:

First statement:
We cannot infer about the respective signs of X and Y, both can be negative/positive, or Y is positive and X is negative.
Not sufficient.

Both statements:
X>0, then X/Y>1; since X/Y>0 then XY>0.
Sufficient.

[lsr]

Q4. If the units digit of the three-digit positive integer k is non-zero, what is the tens digit of k?
(1) the tens digit of k+9 is 3
(2) the tens digit of k+4 is 2

First statement:
Tens digit is 2. (since the units digit is >0, therefore units digit+9>=10)
Sufficient.

Second statement:
Tens digit is either 2 or 1. (if the units digit is =<3, then the tens digit is 2, and if the units digit is >3, then the tens digit is 1).
Not sufficient.

Answer is A.

[mathdumber]

lsr

for the statement 1, how did you know that the unit digit is >0??
for statement 2, how did you know that unit digit could be =< or => 3??

could you explain the approach of doing this type of question??

i really appreciate it...

thanks
Mathdumber

[ken_english]

Q1. The set S has following properties
(a) If x is in S, then 1/x is also in S
(b) If both x and y are in S, so is (x+y)

Is 3 in S?
(1) 1/3 is in S
(2) 1 is in S

First statement:
If 1/3 is in S then 1/(1/3) = 3 is also in S.
Sufficient.

Second statement:
If 1 is in S, then 1/1=1 is also in S, 1+1=2 is also in S, and 1+2=3 is also in S.
Sufficient.

Answer is D.

LSR, Don't you think x and y should be two distinct numbers ?? here you are taking the same member of the set (1) two times to make it 1+1 = 2

that way what it means is if x exist in the set 2x also exists ??

[lsr]

LSR, Don't you think x and y should be two distinct numbers ?? here you are taking the same member of the set (1) two times to make it 1+1 = 2

that way what it means is if x exist in the set 2x also exists ??

If you combine the two conditions in the question stem,
If x is in S, then 1/x is in S and x+1/x = (x^2+1)/x is also in S.

I agree with you, that if we take for example x=2, then we cannot say that 2+2 is in S.

But looking at the combined condition, for x=1; [(1^2+1)/1]=2 is also in S.

You can treat x and y=1/x for x=1 as two distinct members of S that have the same value.

[lsr]

lsr

for the statement 1, how did you know that the unit digit is >0??
for statement 2, how did you know that unit digit could be =< or => 3??

could you explain the approach of doing this type of question??

i really appreciate it...

thanks
Mathdumber

The question stem states that the unit digit is non-zero, therefore it is an integer between 1 and 9 inclusive.