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1/a+1/b+1/c or abc/ab+bc+ac
[#permalink]
Updated on: 30 Aug 2026, 11:11
Updated on: 30 Aug 2026, 11:11
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Question Stats:
55% (00:58) correct
44% (01:26) wrong based on 18 sessions
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Quantity A |
Quantity B |
\(\dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c}\) |
\(\dfrac{ abc}{ab+bc+ac}\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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Re: 1/a+1/b+1/c or abc/ab+bc+ac
[#permalink]
30 Aug 2026, 10:47
30 Aug 2026, 10:47
1
I think the Answer is D
===================================================================
SOLUTION BREAKDOWN
===================================================================
STEP 1: SIMPLIFY QUANTITY A
-------------------------------------------------------------------
Quantity A: 1/a + 1/b + 1/c
Finding the common denominator (abc):
Quantity A = (bc + ac + ab) / abc
= (ab + bc + ac) / abc
STEP 2: COMPARE QUANTITY A AND QUANTITY B
-------------------------------------------------------------------
Quantity A = (ab + bc + ac) / abc
Quantity B = abc / (ab + bc + ac)
Observation: Quantity B is the reciprocal (inverse) of Quantity A.
STEP 3: TEST VALUES
-------------------------------------------------------------------
Since no constraints are given for a, b, and c, we can plug in numbers:
Case 1: Let a = 2, b = 2, c = 2
- Quantity A = 1/2 + 1/2 + 1/2 = 1.5
- Quantity B = 1 / 1.5 = 0.67
- Outcome: Quantity A is greater (1.5 > 0.67)
Case 2: Let a = 6, b = 6, c = 6
- Quantity A = 1/6 + 1/6 + 1/6 = 3/6 = 0.5
- Quantity B = 1 / 0.5 = 2
- Outcome: Quantity B is greater (2 > 0.5)
CONCLUSION
-------------------------------------------------------------------
Because the outcome changes depending on the values selected,
the relationship cannot be determined.
CORRECT ANSWER:
D) The relationship cannot be determined from the information given.
===================================================================
===================================================================
SOLUTION BREAKDOWN
===================================================================
STEP 1: SIMPLIFY QUANTITY A
-------------------------------------------------------------------
Quantity A: 1/a + 1/b + 1/c
Finding the common denominator (abc):
Quantity A = (bc + ac + ab) / abc
= (ab + bc + ac) / abc
STEP 2: COMPARE QUANTITY A AND QUANTITY B
-------------------------------------------------------------------
Quantity A = (ab + bc + ac) / abc
Quantity B = abc / (ab + bc + ac)
Observation: Quantity B is the reciprocal (inverse) of Quantity A.
STEP 3: TEST VALUES
-------------------------------------------------------------------
Since no constraints are given for a, b, and c, we can plug in numbers:
Case 1: Let a = 2, b = 2, c = 2
- Quantity A = 1/2 + 1/2 + 1/2 = 1.5
- Quantity B = 1 / 1.5 = 0.67
- Outcome: Quantity A is greater (1.5 > 0.67)
Case 2: Let a = 6, b = 6, c = 6
- Quantity A = 1/6 + 1/6 + 1/6 = 3/6 = 0.5
- Quantity B = 1 / 0.5 = 2
- Outcome: Quantity B is greater (2 > 0.5)
CONCLUSION
-------------------------------------------------------------------
Because the outcome changes depending on the values selected,
the relationship cannot be determined.
CORRECT ANSWER:
D) The relationship cannot be determined from the information given.
===================================================================
