9:{"metadata":[["$","title","0",{"children":"iimkbmsat0025 - If n ≤ 4 and 2 ≤ m ≤ n ≤ 5, then what is the greatest possible value of (n - m)(n + m)? | PYQs + Solutions | AfterBoards"}],["$","meta","1",{"name":"description","content":"undefined Let me understand the constraints first. We have: - n \\<=q 4 - 2 \\<=q m \\<=q n \\<=q 5 Combining these constraints: 2 \\<=q m \\<=q n \\<=q 4

Now I'll simplify the expression using the difference of squares formula: (n - m)(n + m) = n^2 - m^2 This is because (a-b)(a+b) = a^2 - b^2

To maximize n^2 - m^2, I need: - Maximum value of n^2 → choose lar>=st possib<= n - Minimum value of m^2 → choose smal<=st possib<= m From our constraints: - Lar>=st possib<= n = 4 - Smal<=st possib<= m = 2 Checking: 2 \\<=q 4 \\<=q 4 ✓

Calculating the maximum value: (n - m)(n + m) = n^2 - m^2 = 4^2 - 2^2 = 16 - 4 = 12 Verification: (4-2)(4+2) = 2 6 = 12 ✓ The greatest possib<= value is 12."}],["$","link","2",{"rel":"manifest","href":"https://www.afterboards.in/manifest.json","crossOrigin":"$undefined"}],["$","meta","3",{"name":"keywords","content":"IIM-K (BMSAT),QA,Algebra,Inequalities"}],["$","meta","4",{"name":"robots","content":"index, follow"}],["$","meta","5",{"name":"category","content":"education"}],["$","meta","6",{"name":"google-site-verification","content":"google"}],["$","meta","7",{"property":"og:title","content":"iimkbmsat0025 - If n ≤ 4 and 2 ≤ m ≤ n ≤ 5, then what is the greatest possible value of (n - m)(n + m)? | PYQs + Solutions"}],["$","meta","8",{"property":"og:description","content":"undefined Let me understand the constraints first. We have: - n \\<=q 4 - 2 \\<=q m \\<=q n \\<=q 5 Combining these constraints: 2 \\<=q m \\<=q n \\<=q 4

Now I'll simplify the expression using the difference of squares formula: (n - m)(n + m) = n^2 - m^2 This is because (a-b)(a+b) = a^2 - b^2

Calculating the maximum value: (n - m)(n + m) = n^2 - m^2 = 4^2 - 2^2 = 16 - 4 = 12 Verification: (4-2)(4+2) = 2 6 = 12 ✓ The greatest possib<= value is 12."}],["$","meta","9",{"property":"og:url","content":"/iimk-bmsat-past-year-questions/2025/QA/47"}],["$","meta","10",{"property":"og:site_name","content":"AfterBoards | JIPMAT Preparation"}],["$","meta","11",{"property":"og:image","content":"https://www.afterboards.in/pyp/AfterBoards%20CUET%20Past%20Year%20Papers%20with%20Solutions.webp"}],["$","meta","12",{"property":"og:type","content":"website"}],["$","meta","13",{"name":"twitter:card","content":"summary_large_image"}],["$","meta","14",{"name":"twitter:site","content":"afterboards.in"}],["$","meta","15",{"name":"twitter:title","content":"iimkbmsat0025 - If n ≤ 4 and 2 ≤ m ≤ n ≤ 5, then what is the greatest possible value of (n - m)(n + m)? | PYQs + Solutions"}],["$","meta","16",{"name":"twitter:description","content":"undefined Let me understand the constraints first. We have: - n \\<=q 4 - 2 \\<=q m \\<=q n \\<=q 5 Combining these constraints: 2 \\<=q m \\<=q n \\<=q 4

Now I'll simplify the expression using the difference of squares formula: (n - m)(n + m) = n^2 - m^2 This is because (a-b)(a+b) = a^2 - b^2

Calculating the maximum value: (n - m)(n + m) = n^2 - m^2 = 4^2 - 2^2 = 16 - 4 = 12 Verification: (4-2)(4+2) = 2 6 = 12 ✓ The greatest possib<= value is 12."}],"$L18","$L19","$L1a","$L1b","$L1c","$L1d","$L1e","$L1f","$L20","$L21"],"error":null,"digest":"$undefined"}

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