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| 1 - | 2 - | 3 - | 4 – π | | | |

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| 1 - | 2 - | 3 - | 4 – π | | | |

by Max@Math Revolution » Mon Nov 05, 2018 1:25 am

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[Math Revolution GMAT math practice question]

| 1 - | 2 - | 3 - | 4 - π | | | |

A. π
B. π - 1
C. π - 2
D. π - 3
E. 4 - π
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| 1 - | 2 - | 3 - | 4 - π | | | |

by fskilnik@GMATH » Mon Nov 05, 2018 3:15 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

| 1 - | 2 - | 3 - | 4 - π | | | |

A. π
B. π - 1
C. π - 2
D. π - 3
E. 4 - π
$$?\,\,\,:\,\,\,{\rm{expression}}$$
$$\left| {4 - \pi } \right| = 4 - \pi \,\,\,\,\,\,\left( {4 - \pi > 0} \right)$$
$$\left| {3 - \left( {4 - \pi } \right)} \right| = \left| {\pi - 1} \right| = \pi - 1\,\,\,\,\,\,\left( {\pi - 1 > 0} \right)$$
$$\left| {2 - \left( {\pi - 1} \right)} \right| = \left| {3 - \pi } \right| = \pi - 3\,\,\,\,\,\,\left( {3 - \pi < 0} \right)$$
$$? = \left| {1 - \left( {\pi - 3} \right)} \right| = \left| {4 - \pi } \right| = 4 - \pi \,\,\,\,\,\,\left( {4 - \pi > 0} \right)$$

The correct answer is therefore (E).


This solution follows the notations and rationale taught in the GMATH method.

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by GMATGuruNY » Mon Nov 05, 2018 3:17 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

| 1 - | 2 - | 3 - | 4 - π | | | |

A. π
B. π - 1
C. π - 2
D. π - 3
E. 4 - π

Let π=3 in the original expression and simplify the blue portion below:
| 1 - | 2 - | 3 - | 4 - 3 | | | |

Simplify the red portion below;
| 1 - | 2 - | 3 - 1 | | |

Simplify the green portion below:
| 1 - | 2 - 2 | |

= | 1 - 0 |

= 1

The correct answer choice must yield a value of 1 when π=3.
Only E works:
4 - π = 4 - 3 = 1

The correct answer is E.
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by Max@Math Revolution » Wed Nov 07, 2018 12:37 am
=>

| 1 - | 2 - | 3 - | 4 - π | | | |
= | 1 - | 2 - | 3 - ( 4 - π ) | | |
= | 1 - | 2 - | π - 1 | | |
= | 1 - | 2 - ( π - 1 ) | |
= | 1 - | 3 - π | |
= | 1 - ( π - 3 ) |
= | 4 - π |
= 4 - π

Therefore, the answer is E.
Answer: E
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by Scott@TargetTestPrep » Wed Nov 07, 2018 5:57 pm
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

| 1 - | 2 - | 3 - | 4 - π | | | |

A. π
B. π - 1
C. π - 2
D. π - 3
E. 4 - π
We have to work from the inside out. Keep in mind that if x ≥ 0, then |x| = x, and if x < 0, then |x| = -x.

Since 4 - π > 0, then | 4 - π | = 4 - π.

Since 3 - (4 - π) = π - 1 > 0, then | 3 - | 4 - π | | = π - 1.

Since 2 - (π - 1) = 3 - π < 0, then | 2 - | 3 - | 4 - π | | | = -(3 - π) = π - 3.

Since 1 - (π - 3) = 4 - π > 0, then | 1 - | 2 - | 3 - | 4 - π | | | | = 4 - π.

Answer: E

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