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Suppose 1 <= x, y, z <= 9 are integers such that x > z. Let alpha and beta be the three-digit numbers given by alpha = xyz and beta = zyx so that x, y, z are the digits as they are shown. Set gamma = alpha – beta. How many of the following statements are always true? I. 2 does not divide gamma. II. 3 divides gamma. III. 5 does not divide gamma. IV. 7 does not divide gamma. V. 11 divides gamma. VI. 13 does not divide gamma. **[CAPF (ACs) 2026]**

1. Suppose 1 <= x, y, z <= 9 are integers such that x > z. Let alpha and beta be the three-digit numbers given by alpha = xyz and beta = zyx so that x, y, z are the digits as they are shown. Set gamma = alpha – beta. How many of the following statements are always true? I. 2 does not divide gamma. II. 3 divides gamma. III. 5 does not divide gamma. IV. 7 does not divide gamma. V. 11 divides gamma. VI. 13 does not divide gamma. **[CAPF (ACs) 2026]**

 

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