I believe this is The Testing (2013) by Joelle Charbonneau.
It's the first book in a trilogy, and was followed up by Independent Study (2014) and Graduation Day (2014).
This review of the first book, from Kirkus Reviews, touches on a number of things mentioned in your description, such as a teenage, female protagonist, a male love interest, a dystopian future world where teens are selected for testing, and mutants.
There are no grades in this dystopian future—only survival.
It’s graduation day for 16-year-old Malencia “Cia” Vale, and she’s hoping to be selected for The Testing in Tosu City, a necessary prerequisite to attend the University. She is, along with three other Five Lakes colony teens. Embarking on the four-part series of challenges, Cia will learn whom to trust, even as she falls in love with Tomas, one of her fellow Five Lakes colonists. Cia must pass multiple-choice exams, hands-on survival tests and team challenges before facing the final test—a wilderness trek back to the University to prove her abilities as a leader. With a gun, compass and water in her bag, Cia will trek from the ruins of Chicago back to Tosu City, depending on her wits and her trust in Tomas. Charbonneau jumps into the packed dystopia field with a mashup of Veronica Roth’s Divergent (2011) and Suzanne Collins’ Hunger Games trilogy, but she successfully makes her story her own. Cia’s mechanical abilities are an unexpected boon to the overall character development, and it’s refreshing not to have a female protagonist caught up in a love triangle. There’s a nicely developed relationship between Cia and Tomas and genuine suspense surrounding another candidate’s motivations and intentions. Between the ruined world and the mutants, there’s plenty of threats to keep the pages turning.
This extract from the book itself mentions a pair of twin brothers, named Will and Gill.
The green-eyed twins look at each other. Without a word they rise, gather their plates, and move to the empty seats at our table. The longhaired one says, “You have no idea how good it is to hear someone finally admit they didn’t finish the damn tests.” He sticks his hand out. “I’m Will. My brother Gill and I are from Madison Colony.”
To Will's dismay, Gill fails to make it through the first round of tests.
Five minutes pass before the last two candidates arrive, followed by Dr. Barnes. One of them looks around the room, spots us, and breaks into a large smile. Zandri crosses to us and gives Malachi the first hug. Most of our group congratulates her, but I walk toward Will, who is still watching the door—waiting. Realizing his other half won’t be returning.
Dr. Barnes asks us to take our seats and congratulates the Testing candidates who remain. I have to lead Will to a chair. Force him into the seat. Tomas and I sit on either side of Will as he begins to tremble. From their stories, I know Will and Gill have never been apart for more than a couple of hours. I’ve watched them complete each other’s sentences. I wonder how one half will survive without the other.
Later in the story, Will becomes an antagonist. It's during this scene that he and Gill being championship crossbow marksmen is mentioned.
Will smiles. “Funny, but I was just going to say the same thing.”
It’s the smile that alerts me to the danger. Cold. Calculating. So unlike anything I’ve seen from him before. I shove Tomas to the side just as Will raises his gun and fires. But I’m not fast enough. I feel Tomas flinch as the bullet enters his abdomen. His eyes are wide with surprise and pain as he doubles over and sinks down to his knees.
My gun is up and targeted as Will shifts his attention to me.
“What the hell are you doing, Will?”
He smiles behind his gun. “Isn’t it obvious? I’m getting rid of my competition. I didn’t lose my brother and come all this way just to be told I’m not good enough to make it into the University. I made that choice early on. Only you wouldn’t die. Thankfully, a couple of the others were easier to kill before I ran out of quarrels. Both Gill and I are championship crossbow marksmen. He always takes first, but I give him a run for his money.”
The second round of testing involves the teens being asked to open a series of boxes, and then follow the instructions inside them.
We are called in groups of six. I am surprised when Malachi and Will are called with me, and we trail down the hall after a testing official. The Testing room holds six waist-high worktables in two rows—three in front, three in back—each with a small stool seated directly behind it. On the left-hand corner of each station is a small sign depicting a candidate symbol. In the center of every table is a large wooden box.
A silver-haired female official asks us to find the table marked with our symbol. My workstation is the back center one. Malachi’s is at the front to my right. Will is next to me on my left. He catches me looking at him and winks.
The official tells us to raise our hands when we complete the test in front of us. The box will be removed. When all candidates have finished the current box, a new test will be brought out. We are to complete as many tests as we can in the allotted time. This test will not break for lunch, she warns. Then she repeats Dr. Barnes’s instructions about raising our hands if we don’t know how to complete the test, stressing that we are not to guess at answers we are uncertain of. She tells us to solve the puzzle of opening the box and then follow the instructions for the test we find inside.
Within one of the boxes is a selection of plants, along with instructions asking the teens to distinguish the edible plants from the poisonous ones.
Test the plants inside the box for edibility. Separate those that are edible from those that are poisonous.
Again there is a warning: If you do not know an answer, do not guess. Set the unknown plant to the side.
Upon having completed this task, the teens are then instructed to ingest the plants they deemed to be edible.
Ten minutes later, everyone’s work has been checked. The Testing official has removed the plants the candidates separated as not edible and has recorded those in her notebook. Back up front, she asks us one last time if we want to change our answers. She calls each of our names and waits for us to answer yes or no. None of us takes her up on her offer.
“Well, then,” she says cheerfully, “you should have no problem ingesting a sample of each plant you have deemed edible.”
The room goes silent. Finally, I understand.
Yes—a wrong answer will be penalized. Dizziness. Vomiting. Hallucinations. Maybe even death.
I glance around at the tables in the room and see each Testing candidate has a different sampling of plants. There is no way to compare answers. Did I make a mistake? The boy in front of me seems confident he did not. He quickly samples each of his plants. Next to me, Will samples his four. I take a deep breath and eat the beech nut, a small piece of the sugary root I hope is chicory, and the other three plants. None of the plants I deemed poisonous would be fast-acting. We will have to wait to learn whether any of us has made a mistake.
After eating the plants, each of the teens is immediately presented with another box, containing a pulse radio which is to be restored to working order. However, a boy named Malachi is ill as a result of one of the plants he'd just eaten, which leads him to inadvertently trigger a lethal booby trap within his radio.
While working, I notice a few wires that clearly don’t belong in a pulse radio and some small metal hinged boxes that don’t look familiar. If I were at home, I would poke around to see what they contained. But this isn’t home. I will do only what I am certain of.
I screw the top back on the pulse radio and am about to raise my hand when I notice Malachi swaying on his feet. Fatigue or one of the plants he consumed? I think of the plants that I received and try to decide if one of them would cause this kind of reaction. Sweat pours down his face. His hands begin to shake as he starts work on an area of the radio that I ignored. One that contained an unfamiliar metal box. I know we are not supposed to help our fellow candidates, but Malachi’s shoulders are twitching and I am worried the plants he ingested no longer allow him to think rationally. I open my mouth to call out—to tell him not to touch the metal box.
But he already has. A moment later a nail imbeds itself in Malachi’s eye, and he drops to the floor like a stone.
The fourth round of testing involves the teens being instructed to make their way to Tosu City from a designated starting point. Their journey is to take place within a fenced-off testing area.
“All candidates will travel from your designated starting position through the area in between the blue and red boundaries to Tosu City. Both lines indicate fences that have been erected by Testing officials to help you understand and stay within the boundaries of the Testing area. Any candidate who leaves the Testing area at any time will be given a failing grade.
“Please do not make us enforce this rule.”
During this test, the protagonist, Cia, spots a grey-haired man on the other side of the fence, who throws her a bag of food.
I walk along the fence line on my way back to camp, on the lookout for other food. A handful of clover and a few wild carrots end up in my bag. I would like it to be more, but these will have to do. I turn my back on the fence and start to hike back to Tomas and Will when I hear a twig snap. Whipping around, I draw my gun and take aim, expecting to find an animal. Instead, on the other side of the fence, I see a gray-haired man. And he’s smiling at me.
Before I can say a word, the man throws a small bag over the fence and disappears into the brush. I stare at the bag, trying to decide if this is another test. Do I look in the bag and risk something exploding or leave it and walk away?
After several minutes, curiosity wins out. I pick up the bag, hoping to find some clue to the man’s identity inside. Instead, there is a loaf of bread, a small hunk of white cheese, a bag of raisins, and a bottle of water. I open the cap to the water and sniff it. The scent is clean and pure. A few drops of my chemicals confirm it.
A bit later, Cia is attacked by a clawed, hunchbacked creature, and shoots it in self-defence. She then concludes that the creature she just killed was in fact a deformed human being.
I am so pleased with my efforts that I don’t register the sound of something moving behind me. When I do, I barely have time to pull my gun free of my bag’s side pocket before my bicycle is hit from the side, sending me careening to the ground.
Scrambling out from under the bicycle, I see an animal leap and I roll to the right. Whatever the thing is, it hits the ground with a snarl. Before I can blink, it is up and launching another attack. This time I don’t move fast enough. I scream as the creature’s claws slash deep into my left arm. Whatever this thing is, I know I cannot outrun it. Even if I could get back on my bicycle, it’s doubtful I’d be able to outdistance something with such speed. The animal snarls as I roll out of its grasp, push to my feet, and race to put distance between us. I turn and extend the gun in front of me as it barrels toward me. As I aim, I finally get a look at it. Long legs matted in a tangle of brownish hair. Long arms that are extended toward me with three-inch claws I already know are razor sharp. A hunched back. Curled lips revealing blackish teeth. More brownish hair on the torso and back. And the eyes . . .
My finger pulls hard on the trigger, and I barely keep my footing as the gun jolts. The eyes of my attacker go wide. There is anger and fear as the wound in its chest blossoms with bright red blood. My enemy sinks to the ground and with its last breath lets out a cry that sounds like a call for help. Which it might be. Because now that I have looked into the dark blue eyes of my attacker I know this isn’t an animal. The eyes are too intelligent. Too much like the ones I see looking back at me in a reflector. The body was twisted and deformed, but there is no doubt. I just killed a human being.
Some time later, Cia and her love interest, Tomas, are surrounded by dozens of these mutated humans, when a tall, muscular boy named 'Brick' elects to save them by tearing into the mutants with a prolonged hail of machine gun fire.
Tomas scrambles to his feet first and holds out his hand. I take it as another rattle of bullets sparks the pavement and sends wounded watchers to their knees. The bullets chew apart limbs, torsos, heads—creating a gore unlike any I have ever imagined. The mutated humans shriek as bullets cut their comrades off at the knees. I catch a glimpse of blond hair, a tall, muscular build, and the dark metal machine gun atop a three-story building as Tomas pushes my bicycle toward me and yells to ride.
But I can’t. I know the boy wielding the gun. It’s Brick.
You can search through a preview of the entire trilogy here.