What results if the number x is rounded to the nearest hundred?

Question

(1) The multiple of 20 that is closest to x is 140.
(2) x is within ten units of 140.

Bunuel - I understand statement 2 says 130 <= x <= 150 hence not sufficient.
I'm confused about statement 1. Can you please help.

Cheers

Vips0000 · Answer

Statement 1: 
multiple of 20 that is closest to x is 140.

Multiples of 20 are (...120, 140, 160......) and we know that closest one is 140. That would mean X has to be greater than 130 and less than 150 ( 130<x<150) for condition to be true. 
(Note, if x is less than 130, then it would be closer to 120 not 140. Also it can not be 130 as then it would be close to both 120 and 140.. same logic for 150)

But in such case, it is sufficient to answer the question. As rounding 149 would give 100 and 130 would also give 100.
Sufficient.

Statement 2: x is within ten units of 140.
130<=x<=150
But in such case, it is insufficient to answer the question. As rounding 150 would give 200 and 130 would also give 100.
insufficient.

Ans A it is.

stne · Answer

Hi

Can anyone more clarify this one

1) the multiple of 20 that is closest to x is 140. =  131 \leq x \leq 149 
(2) x is within ten units of 140. = doesn't this also mean the same as 1)
with win 10 units means  131 \leq x \leq 149

What does within mean, can we include 130 and 150 if it says within 10 units of 140, I thought within 10 units to mean less than 10 units

so shouldn't the answer be D?

Bunuel · Answer

What results if the number x is rounded to the nearest hundred? (1) The multiple of 20 that is closest to x is 140 --> 130 130\leq{x}\leq{150} . Notice that endpoints (130 and 150) are inclusive. If x=150 then the answer is 200 and if x is any other value then the answer is 100. Not sufficient. Answer: A. Similar questions to practice: the-numbers-x-and-y-are-not-integers-the-value-of-x-is-107346.html if-500-is-the-multiple-of-100-that-is-closest-to-x-and-99421.html Hope it helps.

stne · Answer

Thank you the confusion was with the word within, I thought " within" meant less than 10 and hence 130 and 150 could not be included. So if it says within 10 units, means 10 and less than 10 units (  x \leq 10  ) inclusive?

Bunuel · Answer

Yes, for example within 10 units from 15 is from 5 to 25, inclusive.

himanshujovi · Answer

The fact that within inclusive of boundary condition foxed me as well

devashish2407 · Answer

I have 2 questions.

1 : Does within always imply inclusiveness? 
2 : How does we decide that 150 is closer to 200 than it is closer to 100?

Bunuel ,  KarishmaB

Bunuel · Answer

1. Does "within" always imply inclusiveness?

I'd say "within" typically includes the boundary values. For instance, "within 10 units of 15" means from 5 to 25, including both 5 and 25. However, I'd expect a properly worded GMAT question to make it clearer.

2. How do we decide that 150 is closer to 200 than it is closer to 100?

Actually, 150 is equidistant from both 100 and 200. The difference from each is 50 units, so it is not closer to one over the other.

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What results if the number x is rounded to the nearest hundred?

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