Data Sufficiency Questions

[fayazq]

1. Is x^2 > x?
(1) If x is doubled, the result is less than 1.
(2) 0 is less than or equal to x; x<1


2. The symbol _ represents a digit in the 9-digit number 475,_23,202. What is the value of _?
(1) The missing digit is not a divisor of any other digit in the number.
(2) The sum of the 9 digits is equal to the square of an integer.

[myun]

1. Is x^2 > x?
(1) If x is doubled, the result is less than 1.
(2) 0 is less than or equal to x; x<1

In order to satisfy x^2 > x, x has to be x <0 or x>1.
(1) says 2x < 1, or x < 1/2. This is not enough to limit the range of x.
(2) says that 0 =< x < 1. This is still not enough, because if 0<x<1, x^2>x, but if x=0, x^2 = x.

Combining (1) and (2) does not help, either. The answer is (E)




2. The symbol _ represents a digit in the 9-digit number 475,_23,202. What is the value of _?
(1) The missing digit is not a divisor of any other digit in the number.
(2) The sum of the 9 digits is equal to the square of an integer.

(1) says that the missing digit can be 0, 6, 8, 9.
(2) says that the missing digit plus 25 is a square of an integer.
However, the only possibility is 25, because the sum cannot be 36.
So (2) is the enough condition to determine the missing number.

[Sara]

Myun,
I think the answer of the first question should be B.

1. Is x^2 > x?
(1) If x is doubled, the result is less than 1.
(2) 0 is less than or equal to x; x<1

Anybody please correct me if i'm wrong. I sometimes make silly mistakes.

Statement 1 > I agree with Myun solution for statement 1.
suppose x = 1/4 2x = 1/2 x^2 > x?
1/16 > 1/4 NO

x = -1 2x = -2 x^2 > x?
1 > -1 YES
Therefore, statement 1 is insufficient.

Statement 2

0<=x<1
mean you cannot find any proponents for x^2 > x
every example you can imagine always lead to either x^2 < x or x^2 = x.

With x^2 < x and X^2 =x, we have enough information to answer whether x^2 > x or not. So, statement 2 i sufficient.

For example,
3/4 --------------give x^2 = 9/16
2/3 4/9
1/2 1/4
1/3 1/9
1/4 1/16
1/8 1/64

Therefore, statement 2 is sufficient.
Ultimately, my final solution is B.

[tsdvj]

I agree with Sara

[asdada1]

E what if number is -5
B

[paam0101]

What is the OA for Q1? I think it is E because x=0 gives x^2=x and hence doesn't satisfy x^2>x

[check.stone]

We've dug deep for this one. Don't think we're likely to get an OA from the previous posters, but I think we're all in agreement on 1E and 2B.

[gmattrap]

1.B; 2.B

1. (i) X can be a fraction or -ve no =>> Insuff
(ii) 0 < x < 1 =>> x is a fraction. Hence, Suff

2. N.B: every integer is a divisor of itself, and every integer is a divisor of 0, except by convention 0. If a/b = c, => a = dividend, b = divisor & c = quotient.

(i) None of 0, 2, 3, 4, 5 and 7 is a multiple of the missing digit =>> 6, 8, 9 Hence, Insuff
(ii) 25 + x = N^2 => If N=5, x=0; If N=6, x=11 [wrong, b'cos X = single digit]
=> x can only be 0. Suff. Hence, B.

[gmattrap]

Oops! An oversight... Quite agree wt d explanation of q1 as given by Myun.
1E.

[chrisw123]

hi there, just found this site - looks awesome guys!
had to put my two cents in so I signed up

Isnt Question 1 : B ?

It is a yes/ no question, asking IF x^2> x or not...
with B - x is 0 or less than 1. Meaning that x^2 will never be greater than x. 0=0 and a fraction^2< original fraction...

Therefore we can use B to answer the question... ?

Am I wrong? Did I just waste my time writing all this? hehe.