Vedic Patterns G Strategy | Inequality | EASY | CAT 2025 Slot 1
The number of distinct pairs of integers (x, y) satisfying the inequalities x > y ≥ 3 and x + y < 14 is ____.
Answer
We fix y and find all possible x values that satisfy both conditions:
x > y
x + y < 14
| y | Allowed x values | Count |
| 3 | 4, 5, 6, 7, 8, 9, 10 | 7 |
| 4 | 5, 6, 7, 8, 9 | 5 |
| 5 | 6, 7, 8 | 3 |
| 6 | 7 | 1 |
| Total | 16 |
Vedic Pattern + Concepts of Logs DPAC G Strategy
The number of distinct integers n for which log(1/4) of (n² − 7n + 11) > 0 is _____.
Answer
log(1/4) of (n² − 7n + 11) > 0 is _____.
Using DPAC Strategy: Cycle
n² − 7n + 11 < (1/4)0 → n² − 7n + 11 < 1
Now we need values of n which satisfy 0 < n² − 7n + 11 < 1
Compute E(n) = n² − 7n + 11 for nearby integers:
n = 1 → E = 5 (not in (0,1))
n = 2 → E = 1 (equals 1, excluded)
n = 3 → E = −1 (negative, excluded)
n = 4 → E = −1 (negative, excluded)
n = 5 → E = 1 (equals 1, excluded)
For n ≤ 0 or n ≥ 6, E ≥ 5 (too large).
Therefore no integer n satisfies 0 < E < 1. Final answer: 0.
Note: Official OG says answer is 2. Which is challenged by Cetking
PnC G Strategy | Concepts of PnC
A cafeteria offers 5 types of sandwiches. Moreover, for each type of sandwich, a customer can choose one of 4 breads and opt for either small or large sized sandwich. Optionally, the customer may also add up to 2 out of 6 available sauces. The number of different ways in which an order can be placed for a sandwich, is
- 880
- 600
- 800
- 840
Answer
Given 5 sandwiches
4 breads
2 sizes
Sauces: choose 0, 1, or 2 from 6
Number of sauce choices:
0 sauces → 1 way
1 sauce → 6 ways
2 sauces → 15 ways
Total = 22 ways.
Total combinations =
5 × 4 × 2 × 22 = 880.
Answer: 880
