Numbers - Classification, Face-Place || QA || CAT 2021 || 5 April

For how many two-digit prime numbers the sum of the digits is also a prime number?

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Anita had to do a multiplication. Instead of taking 35 as one of the multipliers, she took 53. As a result, the product went up by 540. What is the new product?

An integer yields a perfect square if you add it to 100. The same integer also yields another perfect square if you add it to 168. The sum of the digits of this integer is

If the value of the repeating decimal 0.7434343434 … is expressed in the fractional form x/495, then the sum of the digits in x is

The sum of the cubes of the digits of the 3-digit positive number is 1136. The sum of the two in the unit’s and the ten’s place of the number is four times the digit in the hundred’s place. Further, when the digit of the number is written in the reverse order, the new number thus formed is 297 more than the original number. Find the number.

How many numbers between 1 to 1000 (both inclusive) are neither a perfect square nor a perfect cube?

Let D be a recurring decimal of the form, D = 0.a₁a₂a₁a₂a₁a₂ ..., where digits a₁ and a₂ lie between 0 and 9. Further, at most one of them is zero. Then which of the following numbers necessarily produces an integer, when multiplied by D?

If x is an irrational number and y is also an irrational number and both x and y are of the form ∓√I , where I is an integer. Also, I for x can only be a number from the set of A, where A ⋹ (–100, 150) and I for y belong to set of B, where B ⋹ (–90, 102), then in how many ways can the sum of x and y be rational.