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

1. Good post? |

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

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!

2. Good post? |
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.

3. Good post? |
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:
Not sufficient.

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

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.

4. Good post? |
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.

5. Good post? |
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

6. Good post? |
Originally Posted by 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.

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 ??

7. Good post? |
Originally Posted by ken_english
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.

8. Good post? |
Originally Posted by 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
The question stem states that the unit digit is non-zero, therefore it is an integer between 1 and 9 inclusive.

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