Question

information about the students at jackson high school is shown in the table.

	girls	boys	total
eleventh grade		179
twelfth grade	156		306
total	523	511	1,034

which statement must be true?

• out of the 352 eleventh graders at the school, 173 of them are girls.
• out of the 511 boys at the school, 150 of them are tenth graders.
• out of the 523 tenth graders at the school, 173 of them are boys.
• out of the 376 girls at the school, 182 of them are eleventh graders.

Explanation:

Step1: Analyze Tenth Grade Boys

For Tenth Grade, Total = Girls + Boys. So Boys in Tenth Grade = \( 376 - 194 = 182 \). Wait, no, let's check each option:

Option 1: Eleventh Grade Girls

Total Girls = 523. Tenth Girls:194, Twelfth Girls:156. So Eleventh Girls = \( 523 - 194 - 156 = 173 \). Total Eleventh Graders: Let's find total eleventh. Total students:1034. Tenth:376, Twelfth:306. So Eleventh Total = \( 1034 - 376 - 306 = 352 \). So Eleventh Girls:173, which matches "Out of 352 eleventh graders, 173 are girls". Wait, but let's check other options.

Option 2: Tenth Grade Boys out of total boys

Total boys:511. Tenth boys: \( 376 - 194 = 182 \), not 150. So wrong.

Option 3: Tenth graders (total tenth? Wait, total tenth is 376, not 523. The option says "523 tenth graders" which is wrong (523 is total girls). So this is wrong.

Option 4: 376 girls? No, total girls is 523. 376 is tenth grade total. So wrong.

Wait, recheck Option 1: Eleventh Grade total students: 1034 - 376 (tenth) - 306 (twelfth) = 352. Eleventh Grade girls: 523 (total girls) - 194 (tenth girls) - 156 (twelfth girls) = 173. So yes, out of 352 eleventh graders, 173 are girls. Wait, but let's check the first option again. Wait, the first option says "Out of the 352 eleventh graders at the school, 173 of them are girls." That's correct. Wait, but let's check the third option: "Out of the 523 tenth graders" – no, tenth graders total is 376, 523 is total girls. So that's a mistake in the option. So the correct option is the first one? Wait, no, wait:

Wait, let's recalculate:

Total students:1034.

Tenth:376, Twelfth:306, so Eleventh: \( 1034 - 376 - 306 = 352 \) (correct).

Total girls:523. Tenth girls:194, Twelfth girls:156, so Eleventh girls: \( 523 - 194 - 156 = 173 \) (correct). So Eleventh graders:352, girls:173. So Option 1: "Out of the 352 eleventh graders at the school, 173 of them are girls." This is correct.

Wait, but let's check Option 3: "Out of the 523 tenth graders" – no, tenth graders are 376, 523 is total girls. So that's wrong. Option 4: "376 girls" – total girls is 523, 376 is tenth grade total (boys + girls). So wrong. Option 2: Tenth boys: 376 - 194 = 182, not 150. So wrong. So the correct option is the first one: "Out of the 352 eleventh graders at the school, 173 of them are girls."

Wait, but the first option is: "Out of the 352 eleventh graders at the school, 173 of them are girls." Let's confirm:

Eleventh Grade Total: 352 (from 1034 - 376 - 306). Eleventh Grade Girls: 523 (total girls) - 194 (tenth girls) - 156 (twelfth girls) = 173. So yes, 173 out of 352 eleventh graders are girls. So this statement is true.

Answer:

A. Out of the 352 eleventh graders at the school, 173 of them are girls.