If x^2 - 100

Question

If  x^2-100 \lt 300 ,  x  can take how many integer values?

A. 42
B. 39
C. 38
D. 37
E. 19

M07-31

chetan2u · Answer

x^2-100<300.....x^2<400....x<|20|.........-20<x<20 
So x can take any value from -19 to 19..
Total 19 positive integers + 19 negative integers +0=19+19+1=39

B

BrentGMATPrepNow · Answer

Take: x² - 100 < 300
Add 100 to both sides to get: x² < 400

We know that 20² EQUALS 400, so  x must be less than 20 
For example,  19 ² < 400, so one possible solution is x =  19 
Likewise,  18 ² < 400, so another possible solution is x =  18 
Keep going to see that...
Another possible solution is x =  17 
Another possible solution is x =  16 
.
.
.
Another possible solution is x =  1 
Another possible solution is x =  0

ARE WE DONE? 
NO!

Negative values also work. 
For example, ( -1 )² = 1, and 1 < 400. So another possible solution is x =  -1 
And ( -2 )² = 4, and 4 < 400. So another possible solution is x =  -2 
And ( -3 )² = 9, and 9 < 400. So another possible solution is x =  -3 
.
.
.
And ( -19 )² = 361, and 361 < 400. So another possible solution is x =  -19 
HOWEVER, ( -20 )² = 400, and 400 is NOT less than 400.

So, the integer solutions are:  -19, -18, -17, . . . . 17, 18, 19 
There are 39 such solutions.

Answer: B

Cheers,
Brent

dave13 · Answer

x^2 - 100 < 300 (add 100 to both sides) x^2 - 100+100 < 300+100 x^2 < 400 square both sides x<20 So x can be -19 or +19 , because \sqrt{x^2}=|x| -19

) IMPORTANT PROPERTIES 1. |x|≥0 2. \sqrt{x^2}=|x| 3. |0|=0 4. |−x|=|x| 5. |x−y|=|y−x| . |x - y| represents the distance between x and y , so naturally it equals to |y - x| , which is the distance between y and x . 6. |x|+|y|≥|x+y| Note that "=" sign holds for xy≥0 (or simply when x and y have the same sign). So, the strict inequality (>) holds when xy<0 7. |x|−|y|≤|x−y| Note that "=" sign holds for xy>0 (so when x and y have the same sign) and |x|≥|y| (simultaneously).

KSBGC · Answer

x^2<300 +100

x^2 < 400.

Notes: 20^2 = 400. It means Highest value of x must be 19 and lowest value must be -19.

-19<x<19.

As we are dealing with  x^2  , negative value doesn't affect our calculation.

No. of x. : 19 - (-19) +1 = 39.

The best answer is B.

ScottTargetTestPrep · Answer

Simplifying, we have:

x^2 < 400

√(x^2) < √400

|x| < 20

Since all the integers from -19 to 19, inclusive, have an absolute value less than 20, there are 39 integers.

Answer: B

Bunuel · Answer

If  x^2-100 \lt 300 ,  x  can take how many integer values?

A. 42
B. 39
C. 38
D. 37
E. 19

Given:  x^2-100 \lt 300 ;
 
 x^2 \lt 400 ;
 
 |x| \lt 20 ;
 
 -20 \lt x \lt 20 , so  x  can take 39 integer values from -19 to 19, inclusive (19 negative integers, 0, and 19 positive integers).

Answer: B

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If x^2 - 100 < 300, x can take how many integer values?

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If x^2 - 100 < 300, x can take how many integer values?

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