GATE CSE 2017 Set 2 | Question: GA-7

Question

There are three boxes. One contains apples, another contains oranges and the last one contains both apples and oranges. All three are known to be incorrectly labeled. If you are permitted to open just one box and then pull out and inspect only one fruit, which box would you open to determine the contents of all three boxes?

• A. The box labeled ‘Apples’
• B. The box labeled ‘Apples and Oranges’
• C. The box labeled ‘Oranges’
• D. Cannot be determined

Answer 1

B. the box labelled 'Apples and Oranges'.

Reason.

We know that the box labeled "Apples and Oranges" can't contain both, so whatever we pick will be the correct label.

Without the loss of generality say picked item was an orange, what that means is that the box that is labeled "Apples" can't contain just oranges. It also can't contain just apples as it is known to be wrong. So it only can contain combination of oranges and apples. Now the third box labeld "Oranges" contains only apples.

Comments

@Arjun Sir

Suppose 

Box Contain	Box Level as
Orange	Apple
Apple-Orange	Orange
Apple	Apple-Orange

Now Suppose

• We first open Orange  box
• It contains Apple.
• We can conclude from here Apple-Orange box must contain Orange and Apple box must contain Apple-Orange.

---

Box Contain	Box Level as
Orange	Apple-Orange
Apple-Orange	Apple
Apple	Orange

Now Suppose

• We first open Orange  box
• It contains Apple-Orange.
• We can conclude from here , Apple-Orange box must contain Apple and Apple box must contain Orange.

---

So, we can conclude from here, opening orange box also we can determine , containts of other boxes.

Isnot it??

Similar for Apple box too.

So, any one box selection,  can lead us to right conclusion

Isn't it??

---

@srestha

I am probably missing your point. For a second table, if a box contains both apples and oranges, when you pick an object you will get to know what that object is. So if it was an apple (from orange labeled box) you still don't know if the box in reality is "apple" or "apple-orange".

For first table, (I am assuming there is typo in table header, i.e., order)

If last two rows in right column were swapped, it is still a valid assignment. Then how could you conclude that apple-orange box contains apple?

---

thanks , I missed the line " inspect only one fruit"

Answer 2

option B --both

lets assume:
box 1 is labelled Oranges (O)
box 2 is labelled Apples (A)
box 3 is labelled Apples and Oranges (A+O)
and that ALL THREE BOXES ARE LABELLED INCORRECTLY"

Pick a fruit from box 1,

1) if you pick an Orange:
- box 1's real label can only be O or A+O
- box 1's current label is O
- since ALL LABELS ARE INCORRECT then box 1's real label can not be O
- box 1's new label should then be A+O by elimination
- since ALL LABELS ARE INCORRECT
- box 2's label is changed to O
- box 3's label is changed to A
- SOLVED

2) if you pick an Apple:
- box 1's real label can only be A or A+O
- box 1's current label is O
- since ALL LABELS ARE INCORRECT then box 1's real label can not be O
- this still leaves us with the choice between label A and label A+O - which would both be correct
- FAILURE

Solution: The trick is to actually pick a fruit from the A+O labeled box

Pick a fruit from box 3:

1) if you pick an Orange:
- box 3's real label can only be O or A
- box 3's current label is A+O
- since ALL LABELS ARE INCORRECT then box 3's real label can not be A+O
- box 3's new label should then be O by elimination
- since ALL LABELS ARE INCORRECT
- box 1's label is changed to A
- box 2's label is changed to A+O
- SOLVED

2) if you pick an Apple:
- box 3's real label can only be O or A
- box 3's current label is A+O
- since ALL LABELS ARE INCORRECT then box 3's real label can not be A+O
- box 3's new label should then be A by elimination (not O)
- since ALL LABELS ARE INCORRECT
- box 1's label is changed to A+O
- box 2's label is changed to O
- SOLVED

link-https://www.glassdoor.co.in/Interview/There-are-three-boxes-one-contains-only-apples-one-contains-only-oranges-and-one-contains-both-apples-and-oranges-The-b-QTN_114922.html

Answer 3

Open the box that is labeled "Apples and Oranges".You know that since none of the labels are correct, the box must either contain only apples, or only orangesSuppose, that you remove an apple from that box. Therefore, that box is the "Apples Only" box.One of the two remaining boxes must be the "Oranges Only" box. However, one of them is labeled "Apples Only", and the other is labeled "Oranges Only". Therefore, the one labeled "Apples Only" is the box that contains only oranges, and the box labeled "Oranges Only" is the box that has both kinds of fruit.

So ans is b

Answer 4

Option should be B. The question has came aready in apple. Inc interview.

It's easier to draw it out.

There are only 2 possible combinations when all labels are tagged incorrectly.

All you need to do is pick one fruit from the one marked "Apples + Oranges".

If it's Apple, then change "Apple + Orange" to "Apple"
The "Apple" one change to "Orange"
The "Orange one change to "Apple + Orange"

If it's Orange, then change "Apple + Orange" to "Orange"
The "Apple" one change to "Apple + Orange"
The "Orange" one change to ""Apple"

source: https://www.glassdoor.co.in/Interview/There-are-three-boxes-one-contains-only-apples-one-contains-only-oranges-and-one-contains-both-apples-and-oranges-The-b-QTN_114922.htm

Comments

thx