Combinatorics: Addition Without Carry
XAT 2011 · Quantitative Ability & Data Interpretation · Medium · Arithmetic
Little Pika who is five and half years old has just learnt addition. However, he does not know how to carry. For example, he can add 14 and 5, but he does not know how to add 14 and 7. How many pairs of consecutive integers between 1000 and 2000 (both 1000 and 2000 included) can Little Pika add?
- A.
150
- B.
155
- C.
156
- D.
258
- E.
None of the above
Answer
C
Explanation
To add and without carrying, no digit addition can produce a carry. Analyzing ranges gives 150 standard pairs plus 6 special cases (like 1099+1100), totaling 156 pairs.
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