Is the Sum of 5 different positive integers greater then 35?

Question

(1) the median number is 10
(2) the largest number is 12

OA is ___, but I can't understand why:

if we have 8-9-10-11-12 >35
If we have 0-1-10-11-12<35?

Why GMAT doesn't count 0 as a positive integer???

dvd920 · Answer

I think 0 is neither positive nor negative, but it is even

1) smallest 1 2 10 11 12 = 36

2) could be 8 9 10 11 12 or 1 2 10 11 12

agentzap · Answer

ok, thanks - but when GMAT says "non-negative" we mean 0, 1, 2 etc?

boomtangboy · Answer

Hi, 0 is a neutral number hence it can be positive as well as negative. Non-negative on the GMAT excludes any negative real number & zero Hope this helps :-D

Bunuel · Answer

Is the Sum of 5 different positive integers greater then 35?

(1) the median number is 10. The median of a set with odd # of terms is just a middle term (when ordered in ascending/descending order). Now, the minimum sum will have the set with following 5 different positive integers {1, 2, 10, 11, 12} --> sum=1+2+10+11+12>35. Sufficient.

(2) the largest number is 12 --> if the set is {1, 2, 3, 4, 12} then the answer will be NO, but if the set is {8, 9, 10, 11, 12} then the answer will be YES. Not sufficient.

Answer: A.

agentzap

OA is ___, but I can't understand why:

if we have 8-9-10-11-12 >35
If we have 0-1-10-11-12<35?
Why GMAT doesn't count 0 as a positive integer???

Zero is neither positive, nor negative, it's neutral (not only for the GMAT but generally).
A positive number is a real number that is greater than zero.
A negative number is a real number that is smaller than zero.

agentzap

ok, thanks - but when GMAT says "non-negative" we mean 0, 1, 2 etc?

Non-negative numbers include all numbers more than or equal to zero.

For more on this topic check Number Theory chapter of Math Book: math-number-theory-88376.html

Hope it helps.

Bunuel · Answer

Bumping for review and further discussion.

vishnu440 · Answer

1,2,10,10,10.. has median 10 but sum is <35.. please correct me

Bunuel · Answer

Check the stem:
Is the Sum of 5  different  positive integers greater then 35?

Divyadisha · Answer

Trick is- DIFFERENT/ DISTINCT Statement 1:- if median is 10 (i.e the third number ), minimum value of two numbers on the right will be 11 and 12. And since the numbers are positive. minimum value of left two numbers will be 1 and 2 1+2+10+11+12 > 35 Sufficient. Statement B:- Largest number is 12. If other small numbers are 1, 2, 3, 4 then the sum is <35. And if the numbers are same as we derived in option A, the sum is >35. Not sufficient. A is the answer I can't thank enough to Bunuel to help me improvise in inequalities

bumpbot · Answer

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Is the Sum of 5 different positive integers greater then 35?

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