CAT 2021 Slot 1 · Quant · Question 11
CAT 2021 Slot 1 previous year question on Numbers Basics, with the answer and a step-by-step solution.
How many three-digit numbers are greater than 100 and increase by 198 when the three digits are arranged in the reverse order?
Answer & solution
Answer: 70
Let the number be 100x+10y+z.
Reversing gives 100z+10y+x,
so 99\left( z-x \right)=198 and z-x=2.
The pairs \left( x,z \right) are \left( 1,3 \right),\left( 2,4 \right),\ldots ,\left( 7,9 \right), which is 7 pairs, and y takes 10 values.
The total is 7\times 10=70.
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