Each of the five persons A, B, C, D and E possesses unequal number (<10) of similar items. A, B and C possess 21 items in all, while C, D and E posses 7 items in all. How many items do A and B possess in all?

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Q: 108 (IAS/2006)
Each of the five persons A, B, C, D and E possesses unequal number (<10) of similar items. A, B and C possess 21 items in all, while C, D and E posses 7 items in all. How many items do A and B possess in all?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,0,4,2,0,1,1

keywords: 

{'unequal number': [0, 0, 1, 0], 'many items': [0, 0, 1, 0], 'similar items': [0, 0, 1, 0], 'items': [3, 4, 8, 15], 'data': [1, 1, 7, 9]}

In the question, it is stated that A, B and C possess 21 items in total and C, D, and E possess 7 items in total. Since the number of items C has is counted in both groups, it can be inferred that A, B, D, and E together have 21 items (21 items of A, B and C minus the 7 items of C, D and E). However, the information provided is not enough to determine the exact amounts A and B possess individually or together.

Option 1 (15) and Option 3 (18) are thereby incorrect because there is no basis from the given data to judge these numbers. The correct answer is not Option 4 (Data is insufficient), because we are indeed able to establish as explained above, that A, B, D and E together have 21 items.

The correct answer is Option 2 (17) as it might be but here`s Alert - correct answer should be : "Data is insufficient" to know the exact combined possession of A and B.