A collection of 36 cards consists of 4 sets of 9 cards in

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Sat Nov 30, 2019 7:30 am

A collection of 36 cards consists of 4 sets of 9 cards in each set are numbered 1 through 9. If one card has been removed from the collection, what is the number on that card?

(1) The units digit of the sum of the numbers on the remaining 35 cards is 6.
(2) The sum of the numbers on the remaining 35 cards is 176.

[spoiler]OA=D[/spoiler]

Source: Official Guide

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Source: Beat The GMAT — Data Sufficiency | Sat Nov 30, 2019 7:30 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

by deloitte247 » Sun Dec 01, 2019 6:25 am

Given that;
1 collection = 36 cards
36 cards = 4 sets at 9 card per set
Each set contains cards that are numbered 1-9

Question => what is the number on the card that was removed?

Statement 1 => The units digit of the sum of the numbers on the remaining 35 cards is 6
Sum of digits on all 9 cards = 1 +2 +3 +4 +5 +6 +7 +8 +9 = 45
Sum for all the 4 set = 4 * 45 = 180
When one card is removed, sum of the remaining 35 cards has the last digit to be = 6
180 - 1 = 179, 180 - 2 = 178, 180 - 3 = 177, 180 - 4 = 176, 180 - 5 = 175, 180 - 6 = 174
180 - 7 = 173, 180 - 8 = 172, 180 - 9 = 171
180 - 4 = 176 is the only card that will have the sum of the remaining 35 cards to be = 176 (with the last digit as 6)
Hence, number on the card removed = 4 ; statement 1 is SUFFICIENT

Statement 2 => The sum of the numbers on the remaining 35 cards is 176
Sum of digits on all 9 cards = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 +9 = 45
Sum of all the 4 sets = 4 * 45 = 180
From this statement 2 => 180 - (value of chosen card) = 176
180 - 176 = value of chosen card
chosen card = 4
Statement 2 is SUFFICIENT

Since each statement alone is SUFFICIENT
Answer = option D

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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 » Sun Dec 01, 2019 6:42 am

Vincen wrote:A collection of 36 cards consists of 4 sets of 9 cards in each set are numbered 1 through 9. If one card has been removed from the collection, what is the number on that card?

(1) The units digit of the sum of the numbers on the remaining 35 cards is 6.
(2) The sum of the numbers on the remaining 35 cards is 176.

[spoiler]OA=D[/spoiler]

Source: Official Guide

Target question: What is the number on the card?

Given: A collection of 36 cards consists of 4 sets of 9 cards in each set are numbered 1 through 9.

Statement 1: The units digit of the sum of the numbers on the remaining 35 cards is 6.
1+2+3+4+5+6+7+8+9=45
Since there are 4 sets of cards numbered 1 to 9, the SUM of all 36 cards = 4(45) = 180

When we remove one card, the sum of the REMAINING 35 cards = --6 (units digit 6)
In other words, 180 - (value of chosen card) = --6
So, the value of the chosen card must be 4
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The sum of the numbers on the remaining 35 cards is 176.
In other words, 180 - (value of chosen card) = 176
So, the value of the chosen card must be 4
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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