Which of the following sums is greater than 1?
Show Hint
- \( \text{1/2 + 1/3} \)
- \( \text{7/8 + 3/30} \)
- \( \text{15/16 + 2/40} \)
- \( \text{12/25 + 12/30} \)
- \( \text{35/102 + 2/3} \)
The Correct Option is
Solution and Explanation
(A) \( 1/2 + 1/3 = 3/6 + 2/6 = 5/6 \) (less than 1).
(B) \( 7/8 + 3/30 = 7/8 + 1/10 \); LCM(8,10)=40, \( 35/40 + 4/40 = 39/40 \) (less than 1).
(C) \( 15/16 + 2/40 = 15/16 + 1/20 \); LCM(16,20)=80, \( 75/80 + 4/80 = 79/80 \) (less than 1).
(D) \( 12/25 + 12/30 = 12/25 + 2/5 \); LCM(25,5)=25, \( 12/25 + 10/25 = 22/25 \) (less than 1).
(E) \( 35/102 + 2/3 \); LCM(102,3)=102, \( 35/102 + 68/102 = 103/102 \) (greater than 1).
Step 2: Compare to 1: only \( 103/102 \approx 1.0098 \) exceeds 1.
Step 3: (E) is the only sum greater than 1.
Step 4: Verify: others are fractions less than 1.
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