Part of 27 pebbles is removed from on the desk by 2 persons in turn. A

Question

Part of 27 pebbles is removed from on the desk by 2 persons in turn. After removing by 2 persons, is the number of the remained pebbles an odd number?

1) One person removed 4 pebbles more than the other person removed.
2) The sum of the number of pebbles removed is 8

* A solution will be posted in two days.

Kurtosis · Answer

St1: Let 'x' be the number of pebbles removed by the 1st person.
Number of pebbles removed by second person = x + 4
Total number of pebbles removed by the two persons = x + x + 4 = 2x + 4 = 2(x + 2) --> even value
Number of pebbles remaining = 27 - even = odd - even = odd
St1 is sufficient

St2: Number of pebbles remaining = 27 - 8 = 19 - odd --> Sufficient

Answer: D

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Part of 27 pebbles is removed from on the desk by 2 persons in turn. After removing by 2 persons, is the number of the remained pebbles an odd number?

1) One person removed 4 pebbles more than the other person removed.
2) The sum of the number of pebbles removed is 8

When you modify the question in the original condition, it becomes 27-(a+b)=odd?. Then there are 2 variables(a,b), which should match with the number of equations. So you need 2 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer. 
When 1) & 2), a=2, b=6 are derived, which makes 27-8=19=odd. It is yes and C is the answer. However, since this is an integer(hidden) question, which is one of the key questions, apply the mistake type 4. For 2), since a+b=8, 27-8=19=odd, which is yes and sufficient.
For 1), in a=b+4, a+b=b+4+b=2(b+2)=even is derived, which is yes and sufficient. Therefore, the answer is D. This is the mistake type 4(B) question.

mvictor · Answer

is it a 700 level question though??? solved in under 30 sec....
2. this is definitely sufficient, as we are told how many pebbles were removed. 27-8=19 odd.

let's look at 1st statement:
suppose first person removed x pebbles.
second one removed x+4.
total removed x+x+4 or 2x+4. since the coefficient for x is 2 - 2x is an even number. 2x+4 is again an even number. we have odd number of pebbles (27). odd - even = odd.
1 - sufficient.

answer is D.

Akuthiala · Answer

Statement 2 sufficient we know how many were removed and how may left
Statement 1 sufficient = the sum of removed pebbles will always be even 0,4 1,5 2,6 etc Number of original pebbles = odd, So odd-even = odd

Purnank · Answer

This question is based on following properties,

odd + odd = even
even + even = even
these two conditions works with first statement and you will see no matter what the count of both alway going to be even and 27-even = odd. hence sufficient.
and
odd - even = odd this condition works with second statement. hence sufficient.

both statement alone sufficient. Hence D.

Part of 27 pebbles is removed from on the desk by 2 persons in turn. A

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GMAT Data Sufficiency (DS) Questions

Part of 27 pebbles is removed from on the desk by 2 persons in turn. A

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