In a recent survey, twenty families reported their incomes for 1995.

Question

In a recent survey, twenty families reported their incomes for 1995. Was the range of reported 1995 incomes for these families greater than $60,000?

(1) Thirteen of the reported incomes were between $20,000 and $35,000.

(2) Seven of the reported incomes were between $80,000 and $95,000.

ID 07879

NoHalfMeasures · Accepted Answer

Statement 1: We only know about the 13 values and know nothing about the remaining values
Statement 2: We only know about the 7 values and know nothing about the remaining values

1+2 --> lowest possible range is = 80k-35k = 45k and the highest possible= 95k-20k = 75k. Since the range is between 45k to 75k impossible to tell if it is greater than 60k. Insuff!

Ans: E

Bunuel · Answer

Thirteen of the reported incomes were between $20,000 and $35,000 does not necessarily mean that any of the incomes must be $20,000 or $35,000. It means that $20,000 < (all 13 incomes) < $35,000.

The same logic applies to the second statement.

farful · Answer

Statement 1 is insufficient as it only provides the lower bound.
Statement 2 is insufficient as it only provides the upper bound.

Now let's combine both statements, and try the extremes.
Case 1: 13 incomes of 34,000 and 7 incomes of 81,000
Range = 81,000 - 34,000 = 47,000.

Case 2: 13 incomes of 21,000 and 7 incomes of 94,000
Range = 94,000 - 21,000 = 73,000.

In case 1, range is less than 60,000 and in case 2 the range is greater than 60,000.

Thus, the answer is E.

septwibowo · Answer

This question and statements, quite ambiguous for me.

"Thirteen of the reported incomes were between $20,000 and $35,000." --> I thought that $20.000 and $35.000  MUST  be among thirteen.
But, as we can see in the answer, $20.000 and $35.000  MAY or MAYBE  among thirteen.

Could you please explain  Bunuel  ? What can we learn from this case?

alainca · Answer

This is one where the English and Math don't match. In English, when one says "Thirteen of the reported incomes were between $20,000 and $35,000" one implies that at least one salary is 20,000 (or just above it) and one salary is 35K or just below it. In English, this is how one specifies a range, by saying "all x were between y and z."

It's surprising that this was an official GMAT question. Perhaps this ambiguity is why it was retired.

mihir0710 · Answer

I beg to differ on that statement.
Even in general english usage when we say that something is between X & Y, it does not necessarily mean that "something" is X or Y.
For eg. All Top Indian B-schools are ranked between 25 to 35 in global FT Rankings.
Does this mean, one of the Indian B-Schools is ranked 25 or 35 ?? 
I hope you would agree, Not necessarily.

alainca · Answer

I disagree. If you said to me that all Top Indian B Schools are ranked between 25 to 35, I would assume that one is ranked 25 and one 35. Otherwise why would you give that range? If I said to you all basketball players in the NBA are between 5'11 and 7'3, you would assume that there is an example on each extreme.

LoneSurvivor · Answer

This is a nice question. I absolutely love it. This shows how GMAT plays with our minds.

gmexamtaker1 · Answer

chetan2u   GMATBusters   nick1816

Hello I was wondering whether someone could clarify whether between 20.000 and 35.000 means (20.000-35.000) or   ( so are those numbers inclusive or not)?

GMATBusters · Answer

open interval : (a,b) means all number between a and b but NOT equal to a or b
Closed interval :   means all number between a and b or equal to a or b

But this is NOT tested in GMAT.

"between a and b " means a and b are NOT included.

nisen20 · Answer

Too vague to tell the EXACT range.
Is this a real GMAT material?

bumpbot · Answer

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In a recent survey, twenty families reported their incomes for 1995.

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In a recent survey, twenty families reported their incomes for 1995.

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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