CAT 2025 Slot 1 · Quant · Question 17
CAT 2025 Slot 1 previous year question on Inequalities & Modulus, with the answer and a step-by-step solution.
The number of distinct pairs of integers \left( x,y \right) satisfying the inequalities x>y\ge 3 and x+y<14 is
Answer & solution
Answer: 16
Fix y and count the possible x each time.
The constraints are x>y and x<14-y.
y=3: x runs from 4 to 10, which is 7 values.
y=4: x runs from 5 to 9, which is 5 values.
y=5: x runs from 6 to 8, which is 3 values.
y=6: x can only be 7, which is 1 value.
y=7 would need x>7 and x<7 at once, so it stops here.
The total is 7+5+3+1=16.
More Inequalities & Modulus questions
- Q2f ( x )=(x²+2x-15)/(x²-7x-18) is negative if and only ifCAT 2021 Slot 1 · Quant · Inequalities & Modulus
- Q20The number of integers n that satisfy the inequalities | n-60 |< | n-100 |< | n-20 | isCAT 2021 Slot 1 · Quant · Inequalities & Modulus
- Q16For all real numbers x the condition | 3x-20 |+ | 3x-40 |=20 necessarily holds ifCAT 2021 Slot 2 · Quant · Inequalities & Modulus
- Q14The set of all real values of x for which (x²- | x+9 |+x )>0 , isCAT 2025 Slot 2 · Quant · Inequalities & Modulus
- Q13If 3x+2 | y |+y=7 and x+ | x |+3y=1 , then x+2y isCAT 2021 Slot 3 · Quant · Inequalities & Modulus
- Q18The number of distinct pairs of integers ( m,n ) satisfying | 1+mn |< | m+n |<5 isCAT 2021 Slot 3 · Quant · Inequalities & Modulus
All Inequalities & Modulus PYQs →
Take this paper as a timed test
Real exam timing, instant score, rank and topic-wise analysis.