Is d e?

Question

GMATBusters’ Quant Quiz Question -2

Is d > e?

1)  \sqrt{d} > \sqrt{e} 
2)  d^3 > e^3

urshi · Answer

For statement 1 , We cant check negative values since they will be undefined.

OPTION : D

minustark · Answer

Since, both square root and odd power of a number retains the original sign of the numbers, so we can say that each of the statement is sufficient for proving that d > e. For example, when, d = 1/4, e = 1/16,\(\sqrt{ d}\) = 1/2, which is greater than the \(\sqrt{e}\) = 1/4. Again, when \(\sqrt{d}\) == -2, \(\sqrt{e}\) = -3, then d = -4, e = -9, so, d > e.

d^3 = -8, e^3 = -27, then d = -2, e =-3, so d > e. Again when d = 1/8, e = 1/ 27, d = 1/2, e = 1/3. d > e.

D is the answer.

d^3 = -8, e^3 = -27, then d = -2, e =-3, so d > e. Again when d = 1/8, e = 1/ 27, d = 1/2, e = 1/3. d > e.

D is the answer.

Varunsawhney8 · Answer

Always Check inequalities by substituting integer, fraction, negative and zero values

Statement 1,

For different values d > e Values of \sqrt{d^3} > \sqrt{e^3 } Result

Positive Integer Values 3 2 1.73 1.41 Satisfy
Positive Fraction Values 0.25 0.16 0.5 0.4 Satisfy

Sufficient

Statement 2,

d^3>e^3

For different values d > e Values of d^3 > e^3 Result

Positive Integer Values 3 2 27 8 Satisfy
Positive Fraction Values 1/2 1/3 1/8 1/27 Satisfy
Negative Integer Values -2 -3 -8 -27 Satisfy
Negative Fraction Values -1/3 -1/2 -1/27 -1/8 Satisfy

Sufficient

RajatJ79 · Answer

Is d > e?

We will have to check if the above equation stands for three cases

Case 1: >1 i.e. positive integers ----------- Let d=7 and e=5
Case 2: >0 but <1 i.e. +ve decimals ------ Let d=0.7 and e=0.5
Case 3: <0 i.e. -ve integers ---------------- Let d=-5 and e=-7

Considering statement 1 alone
1) √d>√e

For 7 and 5, using statement 2 you get the answer as a Yes
√7 = 2.64
√5 = 2.23

For 0.7 and 0.5, using statement 2 you get the answer as a Yes
√0.7 = 0.836
√0.5 = 0.707

Square roots of -ve integers are complex numbers which need be considered here.

Looking at the above cases, you get a definite answer i.e. as a Yes
Statement 1 alone is Sufficient to answer Is d > e?

Considering statement 2 alone
2) d^3>e^3

For 7 and 5, using statement 2 you get the answer as a Yes
7^3 = 343
5^3 = 125

For 0.7 and 0.5, using statement 2 you get the answer as a Yes
0.7^3 = 0.343
0.5^3 = 0.125

For -5 and -7, using statement 2 you get the answer as a Yes
-5^3 = -125
-7^3 = -373

Looking at the above cases, you get a definite answer i.e. as a Yes
Statement 2 alone is Sufficient to answer Is d > e?

As both statements are sufficient by themselves, the Answer is Options D

njindal · Answer

Answer is " D " . Statement 1 : \sqrt{d} > \sqrt{e} According to this option, both d and e greater than zero (because of square root). For all positive numbers, \sqrt{d} > \sqrt{e} implies that d > e We can verify this statement with few examples: - Let \sqrt{d} = 0.2, \sqrt{e} = 0.1 => d = 0.04, e = 0.01 Therefore, d > e - Let \sqrt{d} = 4, \sqrt{e} = 2 => d = 16, e = 4 Therefore, d > e We can say for sure, Statement 1 is alone sufficient to solve the problem . The answer to the asked question "Is d > e " is " always True " with condition in Statement 1. Statement 2 : d^3>e^3 All real numbers are possible as values for d and e. Case 1: d < 0 , e < 0 For all negative numbers, d^3>e^3 implies that d > e . We can verify this conclusion with few examples: - Let d^3 = -0.1, e^3 = -0.2 => d = -0.46, e = -0.58 Therefore d > e - Let d^3 = -8, e^3 = -27 => d = -2, e = -3 Therefore d > e This case returns the answer for "Is d > e " as always True . Case 2: d > 0 , e > 0 For all positive numbers, d^3>e^3 implies that d > e . We can verify this conclusion with few examples: - Let d^3 = 0.2, e^3 = 0.1 => d = 0.558, e = 0.46 Therefore d < e - Let d^3 = 27, e^3 = 8 => d = 3, e = 2 Therefore d > e This case returns the answer for "Is d > e " as always True . Case 3: d > 0 , e\leq{0} For all numbers for above case, d^3>e^3 implies that d > e . We can verify this conclusion with few examples: - Let d^3 = 0.2, e^3 = 0 => d = 0.558, e = 0 Therefore d < e - Let d^3 = 27, e^3 = -8 => d = 3, e = -2 Therefore d > e This case returns the answer for "Is d > e " as always True . Therefore, Statement 2 is alone sufficient to solve the problem . we can say that Statement 2 alone also will return " Always True " for "Is d > e ". Since both of the statements independently returns the value for given question. The answer is D (EACH statement ALONE is sufficient to answer the question)

Archit3110 · Answer

Is d > e?

1) √d>√e
2) d^3>e^3

target is d>e

#1
√d>√e
for square roots value cannot be -ve so for any value of √d>√e ; d>e eg ( 9,4) ; (1/4;1/9) sufficient
#2
d^3>e^3
here we can check with both +,-ve integer and fractions 
eg ; (3,2) ; ( -2,-3) ; (-1/3,-1) ( 1/2,1/3) d>e always sufficient
OPTION D

ashh · Answer

yes d > e.

Option D

Both statements alone are sufficient.

nothing345 · Answer

Is d > e?

1. sqrt. d is greater than sqrt. e
Try out a few test cases: 
d=4, e=1 
sqrt d = 2, sqrt e = 1 
d>e

d=0.5, e=0.25 
d>e again.

Don't need to test negatives because they don't have real roots. 
 1 is SUFFICIENT.

2. d=1 e=-1 
d=1 e=-1 d>e

d=-0.25 e=-0.5 d>e 
 2 is also SUFFICIENT.

The answer is D.

dishra · Answer

Is d > e?

1) √d>√e
2) d3>e3

Statement 1) √d>√e =>√d-√e>0 => (√d-√e)* (√d+√e) >0 * (√d+√e) ( √d+√e is always positive, hence, sign will not change)
 (√d-√e)* (√d+√e) >0 => d-e >0 => d> e ,  YES, Sufficient

Statement 2) d3>e3 => d3 - e3 > 0 => (d - e)(d2+ de + e2) >0 , since (d2+ de + e2) is always positive
(d - e) >0 => d-e >0 => d> e ,  YES, Sufficient

Answer D, both statements individually are sufficient

Is d > e?

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GMAT Data Sufficiency (DS) Questions

Is d > e?

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