Given that 0.0001402 x 10^q

Question

Given that  0.0001402 * 10^q < 5^{(-2)} , and q is an integer, which of the following is the largest possible value of q?

A. 1
B. 2
C. 3
D. 4
E. 5

GMATinsight · Answer

0.0001402 * 10^q < 5^{(-2)}

i.e.  0.0001402 * 10^q * 5^{(2)} < 1

i.e.  14.02 *10^{-5} * 10^q * 25 < 1

i.e.  350 * 10^{q-5} < 1

Now, we need to convert  350 * 10^{q-5}  into 0.350 for it to be smaller than 1 
i.e. decimal point to be shifted 3 units to the left

i.e. q-5 must be -3 or smaller

i.e.  (q-5)_{max} = -3 
i.e.  q_{max} = -3+5 = 2

Answer: Option B

VermaPulkit · Answer

For every increase in positive integer value of q the decimal point will shift 1 place to right.

5^-2 is 0.04 therefore for the inequality to remain true 10 can have maximum power of 2.

As soon as q = 3 the decimal will shift 3 places to right and expression will become 0.14... which is greater than 0.04.

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Kinshook · Answer

Asked: Given that  0.0001402 * 10^q < 5^{(-2)} , and q is an integer, which of the following is the largest possible value of q?

0.0001402 * 10^q < 5^{(-2)} = 1/25 = .04 
 .01402 = 0.0001402 * 10^2< .04 
q_max = 2

IMO B

sujoykrdatta · Answer

0.0001402 * 10^q < 5^{-2} Multiply 10^2 to both sides: (why? The idea is to get rid of 5^{-2} . But we could have just multiplied 25. However, multiplying 25 with 0.0001402 is a bit complicated. Comparatively, dividing by 4 is easier. 0.0001402 * 10^2 * 10^q < (\frac{1}{25}) * 10^2 => 0.01402 * 10^q < 4 => 0.01402 * 10^q < 4 Dividing by 4: => \frac{0.01402}{4} * 10^q < 1 => \frac{0.00701}{2} * 10^q < 1 => 0.003505 * 10^q < 1 We can multiply 0.003505 with 100 and still it will be less than 1. However, if we multiply by 1000, it exceeds 1. Thus, the largest value of q can be 2 => q (max) = 2 Answer B

sujoykrdatta · Answer

Let's calculate 1/25 = 0.04
Thus: 
0.0001402 * 10^q < 0.04

Multiplying 100 with 0.0001402 = 0.01402 < 0.04
Multiplying 1000 with 0.0001402 = 0.1402 > 0.04

Thus: q = 2
 Answer B

bumpbot · Answer

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Given that 0.0001402 x 10^q < 5^(-2), and q is an integer, which of th

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