TS Police Constable Prelims 2022 · Question 50

Question 50 of the TSLPRB Police Constable Preliminary Written Test 2022 (28 August 2022). Try it first, then open the answer and explanation.

1. PC Prelims 2022 · Q50 · Arithmetic · Numbers & Simplification

   If the 5 digit number 57xy4 is divisible by 11, then number of such possible numbers is

   1. 8
   2. 9
   3. 12
   4. Infinitely many

   57xy4 అనే 5 అంకెల సంఖ్య 11 చే భాగింపబడితే, అలా సాధ్యమయ్యే సంఖ్యల సంఖ్య

   1. 8
   2. 9
   3. 12
   4. అనంతమైనన్నీ
   Show answer

   Answer: (2) 9

   సమాధానం: (2) 9

   By the test for 11, (5 + x + 4) − (7 + y) = x − y + 2 must be 0 or 11. y = x + 2 gives 8 numbers (x = 0 to 7: 57024, 57134, ..., 57794) and x − y = 9 gives one more, 57904 = 11 × 5264, so there are 9 such numbers; 8 is the trap answer that misses 57904.

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