a and b are positive numbers. If a = b and c d, then (A) a + c

Question

a and b are positive numbers. If a = b and c > d, then (A) a + c < b + d (B) a + c > b + d (C) a – c > b – d (D) ac < bd (E) a + c < b – d

Abhishek009 · Answer

Add  a = b  and  c > d  you get ,  a + c > b + d , So Answer is (B)

Biswadeep20 · Answer

Since we have a and b as positive numbers. We can consider any such positive nunber(1, 1.5, 1.8, 3, etc). Both the numbers are equal.

Now, c is greater than d clearly states that the number c must be greater than d. Say, 4.8(c) > 3.4(d).

Since, a and b are equal, they don't play a role in the equation. Option B clearly is the answer as it states a+c > b+d. (a and b can be ignored).

Posted from my mobile device

callmeDP · Answer

IMO B

The best way to solve this question is given you know inequality rule that says:

You can eliminate two variables on two sides of the inequality if they are equal and positive.

so lets look at each option individually:

(A) a + c < b + d

a = b and both are positive hence using the above rule we have: a + c < a + d OR c < d .............. FALSE

(B) a + c > b + d

a = b and both are positive hence using the above rule we have: a + c > a + d OR c > d .............. TRUE

(C) a – c > b – d

a = b and both are positive hence using the above rule we have: a – c > a – d OR - c > -d .............. FALSE remember: c > d

(D) ac < bd

a = b and both are positive hence using the above rule we have: ac < ad OR c < d .............. FALSE

(E) a + c < b – d

a = b and both are positive hence using the above rule we have: a + c < a – d OR c < -d .............. FALSE

Hence, IMO answer is B

QuantMadeEasy · Answer

When a constant is added to both the sides of the inequality, the inequality sign does not change.
Hence, when 'a' is added to both the sides 
a + c > a + d 
as a = b; a + c > b + d

B is correct

a and b are positive numbers. If a = b and c > d, then (A) a + c < b +

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions