Is 5^ ( x +2 ) /25

Question

Is   5^ ( x  +2 ) /25 < 1?

5^x < 1
x < 0

I know the approach I should've taken now. At first I tried subbing 0 and -ve numbers for   5^x  . Can anyone explain why this approach is wrong?

 Edited by HongHu to avoid the confusion.

ericttz · Answer

s 5^x+2/25 < 1?

5^x < 1
x < 0 

I think your approach is sound. And the easiest approach. Starting with second, x < 0. 5^-1 is 1/25 so 3/25 total is less than one. Sufficient as that is the largest value. With clue 1 you cannot have 5^0 =1 or 1 2/25 as it is less than one. Hence it must be with clue 2, 1/25 or smaller and add in 2/25 for maximum 3/25. 

I would answer D.

Anyone else?

Eric

rishi_jhaver · Answer

You can definitely get the answer by B.
As far as A:
5^x needs to be less than 1.
If we can show that 5^x is = (24/25), the answer of the question will always be > 1. But we cant show this.
Hence A will always result in the answer being less than 1.

Hence A & B on their own are sufficient. => ANS IS D...

Fig · Answer

I get (E)

..... Because nothing is said about x such that it's an integer or a real number

In both statments, if we take x = -0,000000001, we have 5^-0,000000001 almost equal to 1. Then, 5^-0,000000001 + 2/25 > 1. Also, if x=-1, then 1/5 + 2/25 = 3/25 < 1 This sort of problem will never happen in a real GMAT question. The DS/PS will be clear

Notice (out of scope): 5^x < 1 <=> ln(5^x) < ln(1) as the ln() fonction increases when x increases and 5^x cannot be negative <=> x*ln(5) < 0 <=> x < 0 as ln(5) > ln(1) = 0 In other words, the 2 statments are perfectly equivalent

ggarr · Answer

5^x  +2/25 < 1

  0^+2  /25 < 1 =   0  
  -1^+2  /25 < 1 =   1/25  
  -2^+2  /25 < 1 =   4/25  
  -3^+2  /25 < 1 =   9/25  
  -4^+2  /25 < 1 =   16/25  
  -5^+2  /25 < 1 = 25/25 =   1  

We have three different answer types above: one 0, 3 fractions and one whole number. This would make statement 1 INSUFFICIENT. What is wrong with the above approach?

The OE is:

Is 5^x+2/25 < 1 = 5^x(5^2)/25 < 1 = 5^x(25)/25 < 1 = 5^x < 1 SUFFICIENT

Fig · Answer

5^0 = 1

.... and so, 5^0 is not inferior to 1 as stated in 1

ggarr · Answer

yes. but the statement says:

5^x < 1 
why can't I replace   5^x   with a -ve or 0? I can see a problem if we were focusing on the exponential x itself. We're not. Does this make sense to anyone?

subhen · Answer

I am getting D. My approach is as follows.

First reduce the question to its simplest form.

5^x+2/25 < 1?

--> (5^x*5^2)/25 < 1

--> Basically the question is asking if 5^x < 1

St 1: if St1 is true then 5^x < 1 and which answers the given question. Immediately eliminate choices B, C and E
Now we need to find out if it is choice A or choice D.
St2 is also true because if x < 1 irrespective of whether it's a fraction or an integer 5^x will always be less than 1

eg. 5^(-1/2) = 1/sqrt(5) < 1

Hence D should be the answer
5^x < 1
x < 0

prude_sb · Answer

5^x + 2/25 < 1

5^x < 23/25

for stat 1: x < 0 
for all values of x where 5^x is between 23/25 and 1 the inequality is violated

for stat 2: 5^x < 1
same as above leaves us hanging 5^x can be 0.99995 or 0.00005 ...

neither statements are suff so E

trivikram · Answer

I think its B.....


5^(2+x) + 2 <5^2

25*5^x +2 < 25

25*5^x can be 24.xyz or 10.abc

So A ruled out

braindancer · Answer

You can't, because for  no  x will 5^x be <= 0.

Andr359 · Answer

(1) That 5^x < 1 is not sufficient to state 5^x + 2/25 < 1. Insuff => B, C or E. (2) That x < 0 is not sufficient either. From the stem: thereÂ´s a single value of x for which 5^x = 23/25: x = log(23/25)/log5 = -0.05181). For x < -0.05181 the inequality holds, for 0> x >= -0.05181, it doesnÂ´t, therefore (2) is insufficient => C or E. (1&2) Both state the same: x < 0, therefore: E.

Sumithra · Answer

I understand the Q to be 
Is 5^(x+2)/25 < 1? 
If I'm right, simplifying we get,
 /25<1
5^x<1
So the Q: is 5^x<1?

S1: says the same so suff.
S2: x<0 
ggarr, I can't understand your Q. Did you want to substitute -ve or 0 for x then 5^0 =1 and 5^-1 =1/5 which is <1 so suff

My ans D

trivikram · Answer

Oh...is it 5^(x+2)/25 < 1? and not 5^x+2/25 < 1?

Then it should be D

Andr359 · Answer

As the question was originally written, without (), it means

5^x + 2/25 < 1.

Exponents precede +, -, not the other way around.

Cheers

HongHu · Answer

I see the disagreement arises from the unclearness of the question stem and I have thus edited it to clearify the question.

Mishari · Answer

Is 5^(x+2)/25 < 1? 

(1) 5^x < 1 
(2) x < 0 

5^(x+2)/25 = 5^(x+2) / 5^2
5^(x+2) * 5^-2 = 5^x
5^x is < 1 only if x is negative.

 either statement by itself is sufficient 
 Answer is D

Fig · Answer

Ok.... Thanks HongHu

Now with the original inequation rewritten, I agree with (D)

Andr359 · Answer

Yep. Clear D. Thanx HongHu

prude_sb · Answer

thanks hong clear D

Is 5^ ( x +2 ) /25 < 1? 5^x < 1 x < 0 I know the

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