Is the line L1 steeper than line L2?

Question

GMATBusters’ Quant Quiz Question -8

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If the slope of line L1, L2 = m1, m2 respectively, is the line L1 steeper than line L2? 
1) m1 > m2 
2) \sqrt{m1m2-1}  >0

GMATBusters · Answer

The  slope  is calculated by finding the ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line. Slope can be negative, positive or zero
The  steepness , incline, or grade of a line is measured by the absolute value of the slope. A slope with a greater absolute value indicates a steeper line. Steepness is always non-negative.

The solution of the problem shall be as follows:
 https://www.youtube.com/watch?v=vEMGfstveJ0

Archit3110 · Answer

If the slope of line L1, L2 = m1, m2 respectively, is the line L1 steeper than line L2?
1) m1 > m2
2)√m1m2−1>0

we need to determine whether slope of line L1 > slope of line L2 ; m1>m2
slope can be upwards or downwards and bigger slopes , steeper they are

#1
m1>m2
m1-m2>0
we can have either both m1 & m2 to be -ve with condition m1>m2
 or we can have both m1 &m2 +ve with condition m1>m2
insufficient as slope of line L1 is > slope of Line L2 for both conditions of +/-ve
#2
√m1m2−1>0
m1 *m2 both +ve or both -ve ; insufficient
from 1 &2
nothing can be determined
IMO E

ashwini2k6jha · Answer

m1>m2?
State:1 sufficient
m1>m2
state2: not sufficient
m1*m2-1^1/2
m1*m2-1>=1
can not decide which one greater
Answer A

Raxit85 · Answer

If the slope of line L1, L2 = m1, m2 respectively, is the line L1 steeper than line L2?
1) m1 > m2 
 slope of L1 > L2, I'd guess that slope can give info about steepness of any line. So, L1 can be steeper than L2 Sufficient.

2)√ m1m2−1 - Not sufficient.

Ans. A

Kinshook · Answer

Asked: If the slope of line L1, L2 = m1, m2 respectively, is the line L1 steeper than line L2?

1) m1 > m2
Case 1: m2>=0; m1>m2>=0; L1 is steeper than L2
Case 2: m2<0; m1>0; L1 may be steeper than L2 (Case 2b) or L2 may be steeper than L1 (Case 2a) 
Case 3: 0>m1>m2; L2 is steeper than L1
NOT SUFFICIENT

2) \sqrt{m1m2−1}>0 
m1m2 - 1>0
m1m2>1>0
m1 & m2 have same signs.
Since m1 & m2 are interchangeable in the equation 
It can not be ascertained whether L1 is steeper than L2
NOT SUFFICIENT

(1) + (2)
1) m1 > m2
2) \sqrt{m1m2−1}>0 
m1m2 - 1>0
m1m2>1>0
m1 & m2 have same signs.
Case 1: m2>=0; m1>m2>=0; L1 is steeper than L2
Case 2: NOT valid since m1 & m2 have same signs
Case 3: 0>m1>m2; L2 is steeper than L1
It can not be ascertained whether L1 is steeper than L2
NOT SUFFICIENT

IMO E

mRTNXn6erkU

Tommy6e · Answer

Answer E is correct

If the slope of line L1, L2 = m1, m2 respectively, is the line L1 steeper than line L2?
To determine which slop is steeper we need to determine which of m1 and m2 has a higher ABSOLUTE value

Statement 1: insufficient
1) m1 > m2

Scenario 1: m1's absolute value is higher than m2's --> L1 is steeper
Example: m1 = 10, m2 = 2
Scenario 2: m1's absolute value is lower than m2's --> L2 is steeper 
Example: m1 = 10, m2 = -20

Statement 2: insufficient
2)sqrt(m1m2−1)
m1m2 has to be bigger than 1
This means m1 and m2 has the same sign (both negative or both positive)
We still can't determine which of the absolute values of m1 and m2 is higher.

Both statements:
We know m1>m2 and they both have the same sign.
We have two scenarios:
Scenario 1 - both are positives --> Ex: m1 = 10, m2 = 2 --> L1 is steeper
Scenario 2 - both are negative --> Ex: m1 = -2, m2 = -10 --> L2 is steeper

Thus, even with both statements, we do not have a clear definite answer.

uc26 · Answer

The slope of a line describes its steepness. So what the question is essentially asking is whether the slope of line L1 (m1) is higher than the slope of line L2 (m2). Is m1>m2?

(1) m1>m2. Directly gives us what we needed to answer the question. Sufficient.

(2) \sqrt{ m1m2-1 }>0
Squaring both sides,
m1*m2-1>0
m1*m2>1
We can have various possibilities here.
m1= 2 and m2= 1 in which case the answer is YES.
m1=1 and m2=2 in which case the answer is NO.
Not Sufficient.

Answer: A.

kapilagarwal · Answer

Ans : B alone sufficient

Posted from my mobile device

SR71Blackbird · Answer

The answer to this question is A. The symbol + or - tells use the direction whereas the magnitude (mod) gives us steepness.

Statement 1: m1 > m2 => M1 is steeper
Statement 2: on simplyfying we get m1> (1/m2) but the problem arises when m2 is proper or improper fraction. 
Ex: m2 = 5/6 => m1 > 6/5 m1 is steeper
Ex: m2 = 10/6 => m1 > 6/10 Cannot say which one is steeper.

zs2 · Answer

If the slope of line L1, L2 = m1, m2 respectively, is the line L1 steeper than line L2?
1) m1 > m2
2)m1m2−1−−−−−−−−√m1m2−1 >0

FRom -1 - we cannot conclude it will depend upon sign of m1 and m2. for example y=x and y=-x have different slopes but steepness is same. not sufficient

From -2 we get to know that signs of m1 and m2 are same but no magnitude , not sufficient

combining we can find what we needed. hence C is answer

1BlackDiamond1 · Answer

If the slope of line L1, L2 = m1, m2 respectively, is the line L1 steeper than line L2?
1) m1 > m2
Slope = rise/run
m1 > m2 therefore L1 is steeper than L2

Thus Statement 1 is sufficient.

Statement 2 
2)√m1m2−1 >0

we do not know the values of m1 and m2, therefore, statement 2 is insufficient.

Answer is A

jrk23 · Answer

i think "C" is the answer as from "B" we can say that both slopes are positive. 
So from first we can say which one is more steeper as both are lie in same quadrant now.

From steeper i am deducing whether its more incline or not.

Nth else.

Correct me if i am wrong.

jrk23 · Answer

i think "C" is the answer as from "B" we can say that both slopes are positive. 
So from first we can say which one is more steeper as both are lie in same quadrant now.

From steeper i am deducing whether its more incline or not.

Nth else.

Correct me if i am wrong.

Is the line L1 steeper than line L2?

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