Official GMAT Test Question - Arithmetic - The Beat The GMAT Forum

Official GMAT Test Question - Arithmetic

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sparkles3144: Master | Next Rank: 500 Posts; Posts: 145; Joined: Fri Jan 18, 2013 8:27 am; Thanked: 7 times

by sparkles3144 » Tue Apr 30, 2013 3:26 pm

Which of the following procedures is always equivalent to adding 5 given numbers and then dividing the sum by 5?

I. Multiplying the 5 numbers and then finding the 5 th root of the product.
II. Adding the 5 numbers, doubling the sum, and then moving the decimal point one place to the left.
III. Ordering the 5 numbers numerically and then selecting the middle number.

(A) None
(B) I only
(C) II only
(D) III only
(E) I and III

I am really lost.
Can someone please help me?

Thanks!

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Source: Beat The GMAT — Problem Solving | Tue Apr 30, 2013 3:26 pm

srcc25anu: Master | Next Rank: 500 Posts; Posts: 423; Joined: Fri Jun 11, 2010 7:59 amFollowed by: 2 members; Location: Seattle, WA; Thanked: 86 times

by srcc25anu » Tue Apr 30, 2013 4:56 pm

Adding 5 numbers and dividing the sum by 5:
Case 1: If numbers are {1,2,3,4,5} then sum = 15 and result = 15/5 = 3
Case 2: If numbers are {2,4,4,10,15} then sum = 35 and result = 35/5 = 7

ST1: Multiplying the 5 numbers and then finding the 5 th root of the product.
Case 1: Product of 5 nos = 120 and 5th root is NOT EQUAL to 3 (Not TRUE)
Caes 2: Product of 5 nos = 2^6 * 3 * 5^2 and 5th root is NOT EQUAL to 7 (Not TRUE)
NOT TRUE

St2: Adding the 5 numbers, doubling the sum, and then moving the decimal point one place to the left.
Case 1: Sum of 5 nos = 15, Mult by 2 = 30 and taking decimal 1 place to the left = 3 (True)
Case 2: Sum of 5 nos = 35, Mult by 2 = 70 and taking decimal 1 place to the left = 7 (True)
TRUE

ST3: Ordering the 5 numbers numerically and then selecting the middle number.
Case 1: Numerically ordering 5 nos = {1,2,3,4,5}, middle number = 3 (TRUE)
Case 2: Numerically ordering 5 nos = {2,4,4,10,15}, middle number = 4 (NOT TRUE)
Not True

Hence only statement 2 is always TRUE.
Ans C

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Ankur87: Master | Next Rank: 500 Posts; Posts: 110; Joined: Sun Aug 19, 2012 4:39 am; Thanked: 9 times; GMAT Score:640

by Ankur87 » Wed May 01, 2013 10:33 am

Ans:
take any 5 numbers :
1,3,4,5,6
Adding them : 1+3+4+5+6 = 19
19/5 = 3.8
A)incorrect.
B)
sum = 19
19*2 = 38 shifting decimal to left gives 3.8 which is equal to 19/5 i.e. 3.8
C)incorrect as it gives 4 as middle term.

sparkles3144 wrote:Which of the following procedures is always equivalent to adding 5 given numbers and then dividing the sum by 5?

I. Multiplying the 5 numbers and then finding the 5 th root of the product.
II. Adding the 5 numbers, doubling the sum, and then moving the decimal point one place to the left.
III. Ordering the 5 numbers numerically and then selecting the middle number.

(A) None
(B) I only
(C) II only
(D) III only
(E) I and III

I am really lost.
Can someone please help me?

Thanks!

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed May 01, 2013 11:39 am

sparkles3144 wrote:Which of the following procedures is always equivalent to adding 5 given numbers and then dividing the sum by 5?

I. Multiplying the 5 numbers and then finding the 5 th root of the product.
II. Adding the 5 numbers, doubling the sum, and then moving the decimal point one place to the left.
III. Ordering the 5 numbers numerically and then selecting the middle number.

(A) None
(B) I only
(C) II only
(D) III only
(E) I and III

I am really lost.
Can someone please help me?

Thanks!

Testing numbers is fine up to a point, in that it can help us rule out certain answer choices.
To be 100% certain, we need a more algebraic approach.

Let the five numbers be a, b, c, d and e.

We're looking for procedures equivalent to (a+b+c+d+e)/5

I. Multiplying the 5 numbers and then finding the 5th root of the product.
This is the same as 5throot(abcde) or (abcde)^(1/5)
(abcde)^(1/5) is NOT equivalent to (a+b+c+d+e)/5
Eliminate I

II. Adding the 5 numbers, doubling the sum, and then moving the decimal point one place to the left.
First, moving the decimal point one place to the left is the same as dividing by 10.
For example, 56.7/10 = 5.67
So, the procedure is the same as adding the 5 numbers, doubling the sum, and dividing by 10.
Using our numbers, we get 2(a+b+c+d+e)/10 = (a+b+c+d+e)/5
Perfect.
Keep II

VERY IMPORTANT: At this point, we need not check statement III, since there is no answer choice that says statements II and III both work.

Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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